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The Paern is in the Details: An Evaluation of Interaction
Techniques for Locating, Searching, and Contextualizing Details
in Multivariate Matrix Visualizations
Yalong Yang
Virginia Tech
Blacksburg, VA, USA
yalongyang@vt.edu
Wenyu Xia
Carnegie Mellon University
Pittsburgh, PA, USA
wenyux@andrew.cmu.edu
Fritz Lekschas
Harvard University
Boston, MA, USA
lekschas@seas.harvard.edu
Carolina Nobre
Harvard University
Boston, MA, USA
cnobre@seas.harvard.edu
Robert Krueger
Harvard University
Boston, MA, USA
krueger@seas.harvard.edu
Hanspeter Pster
Harvard University
Boston, MA, USA
pster@seas.harvard.edu
Multivariate Matrix Interaction Techniques
Data Point
MULTIVARIATE DETAILS:
- Time series:
- Attributes:
- Aggregates:
Overview+Details
Pan&Zoom
Fisheye Cartesian TableLens
Focus+Context
Region of Interest
TASKS:
1. Locate region by details
2. Search for details within region
3. Contextualize patterns by details
Figure 1: In a multivariate matrix visualization (MMV) each cell represents a data point that is associated to multiple time
points, attributes, or other data points (through aggregation). To study a region of interest, an analyst typically needs to locate
the region, search for details within the region, and identify contextual patterns using details. Multiple interaction approaches
can be used to conduct this exploration but which one is most eective for dierent tasks: focus+context, pan&zoom, or
overview+details?
ABSTRACT
Matrix visualizations are widely used to display large-scale net-
work, tabular, set, or sequential data. They typically only encode a
single value per cell, e.g., through color. However, this can greatly
limit the visualizations’ utility when exploring multivariate data,
where each cell represents a data point with multiple values (re-
ferred to as details). Three well-established interaction approaches
can be applicable in multivariate matrix visualizations (or MMV):
focus+context,pan&zoom, and overview+detail. However, there is
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CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA
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ACM ISBN 978-1-4503-9157-3/22/04.
https://doi.org/10.1145/3491102.3517673
little empirical knowledge of how these approaches compare in
exploring MMV. We report on two studies comparing them for
locating, searching, and contextualizing details in MMV. We rst
compared four focus+context techniques and found that the sh-
eye lens overall outperformed the others. We then compared the
sheye lens, to pan&zoom and overview+detail. We found that
pan&zoom was faster in locating and searching details, and as good
as overview+detail in contextualizing details.
CCS CONCEPTS
•Human-centered computing →Empirical studies in visu-
alization;Empirical studies in HCI.
KEYWORDS
Multi-level navigation, multivariate, matrix, focus+context,
overview+detail, pan&zoom
arXiv:2203.05109v1 [cs.HC] 10 Mar 2022
CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA Yang and Xia, et al.
ACM Reference Format:
Yalong Yang, Wenyu Xia, Fritz Lekschas, Carolina Nobre, Robert Krueger,
and Hanspeter Pster. 2022. The Pattern is in the Details: An Evaluation of
Interaction Techniques for Locating, Searching, and Contextualizing Details
in Multivariate Matrix Visualizations. In CHI Conference on Human Factors
in Computing Systems (CHI ’22), April 29-May 5, 2022, New Orleans, LA, USA.
ACM, New York, NY, USA, 15 pages. https://doi.org/10.1145/3491102.3517673
1 INTRODUCTION
Plotting a series of data points in a regular two-dimensional grid—a
matrix visualization—is a space-ecient approach for visualizing
large-scale and dense network [
32
,
86
], tabular [
59
,
60
], set [
72
], or
sequential data [
1
,
15
,
44
]. In a matrix visualization, a cell typically
only encodes a single value of a data point, e.g., through color.
However, for multivariate data, multiple attributes or values (called
details hereafter) are associated with each data point. We refer to
the matrix visualization of multivariate data as multivariate matrix
visualization (MMV). MMV are widely used in various applications.
For example, analysts frequently use them to explore temporal
data [
6
,
7
,
10
,
12
,
30
,
83
,
89
], such as ecologists studied multi-year
international food trade through MMV [
43
], and biologists studied
dynamic Bayesian networks with MMVs to model probabilistic
dependencies in gene regulation and brain connectivity across
time [
81
]. Additionally, MMVs can also be used to show multiple
attributes of a data point [
38
,
63
,
72
,
88
] or aggregated values from
details [
24
,
26
,
49
,
51
]. For instance, MMV can help pathologists
interpret multiclass classications by visualizing multiple class
probabilities at once [
63
] in histopathology [
85
], and MMV can be
used to help analyze complex multi-variate geographic data [33].
Exploring MMV requires people to investigate the details in each
single cell, which is usually challenging because each matrix cell’s
display space is limited and often cannot show all data points in full
detail. To enable analysts to eectively explore MMV, a common
strategy is to selectively visualize the details of a subset of data
points. To this end, three general interaction approaches can be used
for MMV: focus+context (or lens), pan&zoom, and overview+details.
In this work, we consider MMV where matrix cells change their
representation from a single to a multi-value visualization (i.e., from
a single color to a line chart) with these interaction techniques.
However, adapting these interactions to MMV is not trivial as the
MMV’s special characteristics need to be taking into consideration.
Focus+context magnies a selected region (referred to as the focus)
within the context to show it in greater detail. To make space for
the magnied region, the surrounding area (referred to as context)
is compressed in size. Not all focus+context techniques are suitable
for MMV. The distortion from many focus+context techniques, like
a pixel-based sheye lens, produce irregular shapes of cells that
may prohibit eective exploration in MMV. On the other hand,
Responsive matrix cells [
38
], Mélange [
27
,
28
], LiveRAC [
55
], and
TableLens [
68
] are representative focus+context techniques that
are applicable to MMV. Overview+detail technique provides two
spatially-separate views with dierent levels of detail. One view
shows the details, and the other oers the context. For example,
Burch et al. [
17
] used overview+detail to facilitate the exploration
of MMV. Pan&zoom presents the visualization at a certain detail
level while enabling the user to zoom into the visualization and pan
to other regions. For instance, TimeMatrix [
89
] provides pan&zoom
for the users to navigate a MMV in dierent levels of details.
Focus+context, pan&zoom, and overview+details have been ex-
tensively compared in various applications [
9
,
18
,
21
,
71
,
77
,
87
]
(more details in Sec. 2). However, mixed results were found about
their eectiveness, indicating the applied scenarios might largely
inuence their performance. Thus, it is not applicable and reli-
able to compile guidelines for MMV only from prior results. Yet,
to the best of our knowledge, there is no user study comparing
them in the context of MMV. To close this gap, we conducted two
extensive user studies to compare the eectiveness of dierent in-
teraction techniques for MMV. Our goal is to better understand
how people interactively explore multivariate details associated
with data points in MMV. Thus, in our evaluation, we did not vary
the visual encoding and used a simple visualization within each
matrix cell to reduce the complexity and potential confounding
factors. To this end, we chose a line chart to visualize a time series
in each matrix cell, as exploring temporal data is one of the most
frequently reported applications for MMV [
6
,
7
,
10
,
12
,
30
,
83
,
89
],
and line charts are a widely-used technique for visualizing tem-
poral data. We are especially interested in the eectiveness of dif-
ferent interaction techniques for navigating MMV and retrieving
details from matrix cells, as it is the unique aspect that distinguishes
MMV from univariate matrix visualizations. After analyzing the
literature [
2
,
5
,
10
,
33
,
62
], taxonomies [
47
,
48
,
57
,
61
,
82
,
87
] and
real-world applications [
43
,
63
], we derived and tested three fun-
damental interaction tasks that cover a wide range of MMV use
cases: locating a single cell and then inspecting the details inside;
searching a region of interest (ROI) of multiple cells to nd the cells
that match the target pattern; and contextualizing patterns using
details, which requires inspecting both the details and the context.
These three tested tasks can act as “primitive” interactions to serve
more sophisticated visual analytic scenarios.
Given the diversity of focus+context techniques [
27
,
28
,
38
,
55
,
68
], the many ways their distortions could impact the perception
and task performance, and their overall good performance in some
applications [
9
,
35
,
74
], we compared dierent lenses in
our rst
study
. To identify representative lenses, we followed Carpendale’s
taxonomy for distortion [
19
] and identied four lenses: Cartesian
lens [
73
] applies non-linear orthogonal distortion; TableLens [
68
]
with orthogonal distortion (step and stretch); and a sheye lens
technique that is adapted to matrix visualizations [
19
,
70
]. Overall,
the results indicate that sheye lens performed as well as or better
than other techniques in the tested tasks. Participants also rated
the sheye lens as the easiest technique for locating matrix cells.
Our second study
compared the sheye lens — the overall best
performing focus+context technique from the rst study — against a
pan&zoom and an overview+detail technique. We found pan&zoom
was faster than focus+context and overview+detail techniques in
locating and searching for details and as good as overview+detail in
contextualizing details. Pan&zoom was also rated with the highest
usability and lowest mental demand in almost all tasks. Our results
contribute empirical knowledge on the eectiveness of dierent
interaction techniques for exploring MMV. We also discuss promis-
ing improvements over existing techniques and potential novel
techniques inspired by our results.
The Paern is in the Details CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA
2 RELATED WORK
A foundation of exploring MMV is enabling interactive inspection
of multiple levels of detail. Several interaction approaches have
emerged for this purpose, such as focus+context, overview+detail,
and pan&zoom. Cockburn et al. distill the issues with each ap-
proach [
21
]: focus+context distorts the information space; overview+
detail requires extra eort for users to relate information between
the overview and the detail view; pan&zoom leads to higher work-
ing memory as the users can only see one view at a time. Yet, it is
still unclear to what extent these ndings apply to MMV.
Focus+context (or lens) techniques.
A common group of fo-
cus+context techniques is lenses, introduced by Bier et al. [
13
,
79
]
as generic see-through interfaces between the application and the
cursor. Lenses apply magnication to increase the detail in local
areas. Lenses can further reveal hidden information, enhance data
of interest [
45
], or suppress distracting information [
25
,
40
]. While
emphasizing details, matrix analysis tasks can necessitate all cells
of the matrix to be concurrently visible. To achieve this, Carpendale
et al. [
19
] discuss various distortion possibilities with smooth transi-
tions from focus to context in rectangular uniform grids (matrices).
Depending on the data, dierent spatial mapping techniques can
be advantageous. Bifocal Display [
3
] introduces a continuous one-
dimensional distortion for 2D data by stretching a column in focus
and pushing all other columns aside. The TableLens technique [
68
]
distorts a 2D grid in two dimensions: stretching the columns and
rows of the cell in focus only (non-continuous) and shifting the
remaining non-magnied cells outward. LiveRAC [
55
] adapts the
idea of TableLens in showing time-series data. Document Lens [
70
]
oers 3D distortion of 2D elds. Mélange [
28
] is a 3D distortion
technique to ease comparison tasks. It folds the intervening space
to guarantee the visibility of multiple focus regions. Responsive
matrix cells [
38
] combine focus+context with semantic zooming to
allow analysts to go from the overview of the matrix to details in
cells. Given the diversity of focus+context techniques, we tested the
eectiveness of four representative lenses derived from Carpendale
et al.’s taxonomy [
19
]: Cartesian lens [
73
], two TableLens varia-
tions [68], and an adapted sheye lens [70].
Evaluating Focus+context techniques.
Most previous stud-
ies on focus+context concentrate on parameter testing and dierent
types of focus+context techniques have not be compared empiri-
cally. McGun and Balakrshnan [
54
] investigated the acquisition
of targets that dynamically grow in response to users’ focus of
attention. In their study with 12 participants, they found that per-
formance is governed by the target’s size and can be predicted with
Fitts’ law [
31
]. Gutwin et al. [
34
] found that speed-coupled atten-
ing improved focus-targeting when using sheye distortion with 10
participants. However, sheye techniques can also introduce read-
ing diculties. To alleviate this issue, Zanella et al. [
91
] showed that
grids aid readability in a larger study with 30 participants. Finally,
Pietriga’s study [
64
] with 10 participants compared dierent tran-
sitions between focus+context and found that gradually increasing
translucence was the best choice. Most previous studies were also
with a small number of participants. With 48 participants, our study
is less outlier-prone and potentially has a smaller margin of error.
Overview+detail techniques.
Prominent examples for 2D nav-
igation are horizontal and vertical scrollbars with thumbnails [
20
]
and mini-maps [
90
], as well as more distinct linked views [
69
]
with dierent perspectives for overview and details. MatLink [
36
]
encodes links as curved edges to give detail at the border of the
matrix for improving path-nding. Lekschas et al. [
49
] propose
an overview+detail method to compare regions of interest at dif-
ferent scales through interactive small multiples. In their system,
each small multiple provides a detailed view of a small local matrix
pattern. They later show that this approach can be extended to
support pattern-driven guidance in navigating in MMVs [
50
]. Co-
CoNutTrix [
41
] visualized network data using NodeTrix [
37
] on a
high-resolution large display. We used a standard overview+detail
design in our second user study, where we placed the overview and
detail view side-by-side, and the user can interactively select the
ROI in the overview to update the detail view.
Pan&Zoom techniques.
The literature distinguishes between
geometric and semantic zooming. The former species the spatial
scale of magnication. Van Wijk and Nuij summarize smooth and
ecient geometric zooming and panning techniques and present
a model to calculate a solution for optimal view animations [
80
].
Semantic zooming, by contrast, changes the level of detail by vary-
ing the visual encoding, not only its physical size [
16
]. Lekschas
et al. [
49
] categorize interaction in matrices into content-agnostic
and content-aware approaches. Content-agnostic approaches, such
as geometric panning&zooming, operate entirely on the view level,
while the latter "incorporate the data to drive visualization." ZAME [
26
]
and TimeMatrix [
89
] are content-aware technique that relies on
semantic zoom. It rst reorders [
75
] rows and columns to group
related elements and then aggregates neighboring cells dependent
on the current zoom level. Horak et al. [
38
] provide both geometric
and semantic zooming in matrices. However, their technique has
not been empirically evaluated. In our second user study, following
a widely used design (e.g., Google Maps), we tested the pan&zoom
condition, which allows the user to scroll the mouse wheel to con-
tinuously zoom in and out a certain region of the matrix.
Evaluating focus+context, overview+detail, and pan&zoom.
These three interaction techniques have been extensively evaluated
in various applications, but not in the context of MMV. Baudisch et
al. [
9
] found that focus+context had reduced error rates and time
(up to 36% faster) over pan&zoom and overview+detail for nding
connections on a circuit board and the closest hotels on a map.
Similarly, Gutwin et al. [
35
] concluded sheye views to be advanta-
geous over overview+details and zooming for large steering tasks.
Shoemaker and Gutwin [
74
] also found sheye lens superior over
standalone panning and over zooming for multi-point target acqui-
sition on images. On the other hand, Rønne and Hornbæk [
71
] had
opposite ndings for locating, comparing, and tracking objects on
geographic maps. They found sheye had the worst performance,
while overview+detail performed best. These previous studies had
mixed results for dierent applications, and none of them were
conducted in the context of MMV. Most similar to our second study
is the study with 12 participants by Pietriga et al. [
65
] for multiscale
search tasks. They found overview+details superior over the sheye
lens, while both techniques outperformed pan&zoom. They tested
the conditions in a matrix-like application but with no multivariate
details in the cells. They also only tested one searching task, and
the tested sheye lens was the classical one with non-linear radial
distortion, which breaks the regularity of the grid.
CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA Yang and Xia, et al.
(a) Cartesian lens (Cartesian) (b) Fisheye lens (Fisheye) (c) TableLens Stretch (Stretch) (d) TableLens Step (Step)
Figure 2: Study 1 visualization conditions with 50×50 matrices: four interactive lenses tested in the user study. An interactive
demo is available at https://mmvdemo.github.io/, and has been tested with Chrome and Edge browsers.
3 STUDY 1 — DIFFERENT LENSES IN MMV
This rst study is intended to address the gaps in the literature
described above in terms of how dierent distortions can impact
perception and task performance in using focus+context (or lens)
techniques for exploring MMV. As this study was the rst to com-
pare dierent lenses in MMV, there was little empirical knowledge
about the user performance with dierent lenses. Thus, our rst
study is exploratory rather than conrmatory. We pre-registered
the study at https://osf.io/dxsr5. Meanwhile, test conditions are
demonstrated in the supplementary video, and detailed results of
statistical tests are provided in supplementary materials.
3.1 Experimental Conditions
Using lenses to explore MMV selectively enlarges an ROI of the
matrix, so that the enlarged cells have enough space to show the
detail. These enlarged cells are also referred as focus cells. To make
space for the focus cells, lenses introduce two types of distortions:
focal and contextual distortion. Focal distortion applies to cells at
the inner border of the lens. Contextual distortion, on the other
hand, applies to cells outside the lens.
Unlike lenses in a map or images, lenses in MMV have more
constraints. While, there are more exibility with their elementary
units in a map or images, the cells in MMV are all the same size
and laid in a regular grid (i.e., rows and columns are orthogonal
to each other). Additionally, according to Carpendale et al. [
19
],
gaps are also considered an important distortion characteristic. In
summary, we identied three characteristics for the distortions of
lenses in MMV:
regularity
—whether the cells are rendered in a reg-
ular or orthogonal grid,
uniformity
—whether the cells are sized
uniformly, and
continuity
—whether the cells are laid out continu-
ously. Those characteristics can be used to model both the focal and
contextual distortions in the lenses. We chose four lenses for our
study, according to Carpendale et al.’s distortion taxonomy [19]:
Cartesian
distorts the entire matrix continuously such that
the cells are proportional sized based on their distances to the cursor
(Fig. 2(a)). In Cartesian, cells in focal and contextual regions are
all in a regular grid but sized dierently.
Fisheye
magnies the center part of the focus and shrinks
the surrounding area around the lens’s inner boundary. The focal
cells need to be rendered in a regular grid and sized uniformly. To
Factor Cartesian Fisheye TableLens (Stretch) TableLens (Step)
Focal distortion
Regularity ✔Partial ✔ ✔
Uniformity ✘Partial ✔✔
Continuity ✔✔ ✔ ✔
Contextual distortion
Regularity ✔ ✔ ✔ ✔
Uniformity ✘✔Partial ✔
Continuity ✔ ✔ ✔ Partial
Table 1: Characteristic Comparison: of the four tested
lenses.
continuously embed the focal region inside the contextual region,
distortion must be applied to the focal area’s transition area. As a
result, cells inside the transition area are rendered irregularly and
are sized dierently (see Fig. 2(b)).
Stretch and Step
are two variations of TableLens that en-
large a xed number of rows and columns around the focal point
and uniformly compress the remaining matrix. Stretch stretches
the enlarged rows and columns on either of the two axes (Fig. 2(c));
Step preserves the cells’ aspect ratio by adding white space around
enlarged rows and columns on either of the two axes, which in-
troduces discontinuities (see the blank space in Fig. 2(d)). Stretch
and Step both have regular and uniform cells in the focal region.
We summarize the characteristics of the four tested lenses in Ta-
ble 1. The four tested lenses cover a variety of characteristics, and
the study is to investigate how those characteristics aect percep-
tion and interaction performance.
3.2 Data
We used time series as the multivariate data in our study, as it
is widely used [
6
,
10
,
12
,
30
,
83
,
89
] and has not been empirically
tested in the context of MMV before. We generated task datasets
consisting of three dimensions (
𝑥
,
𝑦
, and
𝑡
): with
𝑥
and
𝑦
as the rows
and columns in the matrix and
𝑡
as the number of time instances in
the time series. For a particular value of
𝑡
, the
𝑥
and
𝑦
dimensions
are shown as a traditional univariate matrix, which we refer to as
the context. The
𝑡
dimension is revealed interactively upon placing
the lens over a focus region. Enlarging the cells under a lens’s focal
area provides space for displaying this
𝑡
dimension as a line chart,
which we refer to as the focus. Each data set contains
𝑥×𝑦×𝑡
values, and each cell contains 𝑡values as multivariate details.
The Paern is in the Details CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA
1. Pattern
Type Map
Background Non-target
Non-target 2
Target
2. Place
Pattern Types
3. Sample
Cluster
4. Generate
Instances
Figure 3: Data Generation. To generate a unique dataset for
each trial, we following this 3-step pipeline. First, we sam-
pled the location of target patterns. Second, for each target
pattern location we sampled cluster of target pattern types.
Finally, for each cell we generate a 5-point temporal pattern
instance based on the cell’s assigned pattern type.
Pattern type Data distribution
Upward Beta with 𝛼=2and with 𝛽=1
Downward Beta with 𝛼=1and with 𝛽=2
Tent Beta with 𝛼=4and with 𝛽=4
Trough Beta with 𝛼=1
3and with 𝛽=1
3
Background Fréchet with 𝛼=5, s=1, m=0
Table 2: Pattern Distribution Functions: Pattern instances
are generated from the histogram of 100 sampled values
from the associated data distribution. The probability den-
sity function of each pattern type is shown in Fig. 4.
We included two data sizes: Small with 50
×
50
×
5and Large
with 100
×
100
×
5. We decided to test large matrices because small
matrices have enough space for each cell to show the multivariate
details constantly, and interaction is less necessary for them. We
also chose to study the scalability in terms of the matrices’ size and
keep the detail’s size (i.e., the number of time instances) unchanged.
The goal of the tasks is to evaluate and compare the temporal
patterns that arise along the third dimension (i.e., the details). As
shown in Fig. 3, our data generation consisted of three steps: rst
we sampled a matrix of dierent pattern types, then we expanded
the target pattern types into clusters, and nally sampled the actual
pattern instances for each cell. To avoid memory eects and ensure
that participants would have to inspect the patterns under the focal
area, we sampled pattern instances from ve distinct distributions
(Fig. 4) inspired by temporal patterns described by Correll and
Gleicher [22]: upward, downward, tent, trough, and background.
In the rst step, we created a matrix of pattern types. In the
beginning, the matrix contained only background pattern types
(Fig. 3.1). We then randomly placed non-target pattern types into the
matrix (Fig. 3.2). We added these non-target patterns as lightweight
distractions and made the nal dataset more realistic. We then
randomly sampled a position for the target pattern type. Further,
to make it easier to locate the target cells, we sampled a cluster of
target pattern types using a 2D Gaussian distribution centered on
the previously determined target pattern type location (Fig. 3.3).
Finally, for each cell, we generated a pattern instance by ran-
domly sampling 100 values from dierent distributions (Table 2)
and aggregated them in a 5-bin histogram. This approach created
patterns instances that dier slightly in shape and magnitude while
still being distinct enough to avoid ambiguousness (Fig. 4). This
approach strikes a balance between predictability and generality.
Figure 4: Pattern Types. Example pattern instances for each
of the ve pattern types: upward, downward, tent, trough,
and background. The instances slightly dier in their shape
and magnitude to mimic realistic data. On the right we plot
the probability density function of each pattern.
3.3 Interactions and Tasks
The participants were asked to interact with the MMV, which by
default showed a slice of our 3D dataset as a univariate matrix
visualization (i.e., a heatmap for one of the ve time instances, see
Sec. 3.2 for details). We used a continuous color schema from white
to black to encode matrix cells. Darker cells indicate higher values.
Such a color scheme is colorblind-friendly. Upon moving the mouse
cursor over the MMV, the lens enlarges an area to show the details
of the time series as a line chart. In each chart, the line connects ve
dots representing the ve values. The dot representing the value
of the background color is additionally highlighted to represent
the currently selected time instance. Participants can switch the
time instance by clicking on a respective dot in an embedded line
chart. To clearly present interactive line charts while still keeping
the context cells legible, we conducted a series of internal tests to
nd an appropriate combination of the parameters for the number
of cells to be enlarged and the magnication factor. We ensure the
size of the enlarged area and each line chart to be consistent across
dierent lenses. For the two data sizes we tested, the enlarged cell
is in the same size: four times the side length as the original cell in
Small data and eight times in Large data. A line chart in such a
size can be reasonably interpreted and interacted by users. We kept
the ratio of the enlarged cells the same as the matrix, i.e., 1:1, and
decided to enlarge 3
×
3matrix cells as the focal area to show their
line charts. Increasing the number of enlarged cells or magnication
factor makes it challenging to interpret the color of the surrounding
cells, even for screens with a standard resolution. For example, on
a Full-HD (or 1080p) screen, we used 800
×
800 pixels to visualize a
100
×
100 matrix for Large data, and the size of a context cell is 5
×
5 pixels in Fisheye,Stretch, and Step when the lens is on top
of the matrix. Some context cells in Cartesian are even smaller.
According to our internal tests, interpreting colors in context cells
smaller than 5
×
5 pixels is dicult. Fig. 2 demonstrates the tested
interaction techniques for enlarging their focal areas.
CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA Yang and Xia, et al.
The most basic interaction for exploring an MMV includes three
steps: rst nding the cell(s) of interest, then moving the cursor
towards them to enlarge them, and nally checking their embedded
details. Additionally, in some cases, users must inspect both the
focal and context areas. Past research in HCI and visualization pro-
posed taxonomies [
47
,
48
,
57
,
61
,
82
,
87
] for these interactions and
conducted studies in various applications (see Sec. 2), but not with
MMV. We analyzed previous work to break down the fundamental
MMV interactions into four components. First,
waynding
is the
process of searching targets cells. Second,
travel
refers to the act of
moving the mouse cursor to the target cells. Third,
interpretation
is the activity of interpreting the targets’ visual encoding. And -
nally,
context-switching
refers to re-interpreting a changed view,
for example, when updating visualization through interaction or
moving the focus to a dierent part of the view. We then designed
three tasks to cover dierent aspects of the identied components.
Since we used the same visual encoding for all conditions (i.e., the
line chart), we did not expect a noticeable performance dierence
in interpretation. Thus, our focus is on evaluating the other three.
In the following, we rst describe the study tasks with practical
examples in the context of multi-year population data for counties
in the United States in an MMV. This data is easily accessible and
understandable. Each matrix cell represents a county and contains
multi-year population data. The cells are typically placed according
to their relative geographic locations, which is similar to the tile
map representation [
56
] used by Wood et al. [
83
]. We then discuss
the rationale and motivation of our task choices.
In the rst task (Locate)
, we asked participants to click on a
specic cell highlighted with an orange outline. Our goal is to test
how the distortion inuences the participants’ perceptual ability to
locate a specic cell. Thus, we remove the highlighting as soon as
the participants move their cursor into the matrix. For accessibility,
the highlighting reappears once the cursor is moved outside the
matrix. Additionally, we followed Blanch et al.’s [
14
] approach
and added visual distractors, i.e., non-target patterns (Sec. 3.2) in
our case. A frequent operation in analyzing population data is to
investigate the temporal trend of a given location, like “what is the
temporal trend of Middlesex County, MA in the last ve years?”
The Locate task was designed to inspect the
travel
component
in interactions. Locating and selecting an element is the most com-
mon task in graphical user interfaces and visualizations and is a
primitive visualization interaction [
57
,
76
]. It is also a standard
task tested in many user studies (e.g., [
42
,
71
]). Fitts’ law provides
a way to quantify the performance of basic target selection [
76
].
However, the standard model does not consider the lenses’ distor-
tion eects. This task aims to investigate how dierent types of
distortion inuence the performance of locating target.
For the second task (Search)
, we asked the participants to
search for the cell with the highest single value among a cluster of
cells, which is a 7
×
7 region for a 3
×
3 lens in the study. Since we
test the ability to locate a cell in the Locate task, we decided to
permanently highlight the search area with an orange outline. To
enforce the use of the lenses, we pre-selected a value of the time
series that does not reveal the target patterns. Only when the user
employs the lens the relevant details of the multivariate pattern
will be visible. An example of this task in population analysis can
be “Within New England (a set of counties), which county has the
largest number of population of a single year in the last ve years?”
The Search task involves both the
travel
and
waynding
com-
ponents. Waynding is an essential step for any high-level visual
analytics task [
57
]. In order to nd the cell with the highest value,
the participants had to inspect and compare the details of multiple
cells. Similar tasks have been tested in other contexts, for example,
by Pietriga et al. [
65
] for multiscale searching and Jakobsen & Horn-
bæk for geographic maps [
71
]. We expect that the dierent lens
distortions will inuence the performance of waynding, especially
in an interactive scenario. It is impractical to only test waynding
performance without physically traveling to the targets. Thus, we
included both these two components in this task.
In the third task (Context)
, we asked the participants to nd
the largest cluster at the time instance where a given cell reaches its
highest value. The participants needed to move the mouse cursor
to a cell highlighted with an orange border and click on the dot
representing the highest value. The representation of MMV (i.e., the
heatmap) will then be updated to the time instance corresponding to
the clicked dot. Subsequently, several clusters in the sizes between
5
×
5 to 7
×
7 of dark cells appeared in the matrix, and participants
were asked to select the largest one. For instance, a practical use
case in population analysis can be “At the year when the population
of Orange County, FL reaches its peak value, where is the largest
region with high population?”
The Context task includes the
travel
,
waynding
, and
context-
switching
components. Context-switching frequently happens in
interactive visualization and multi-scale navigation and has been
tested in various scenarios [
66
,
67
,
71
,
87
], but not with MMV. In
MMV, users have to switch their context in many scenarios, e.g.,
when enlarging the cells to show the line charts, changing the time
instance, and moving their focus between the focal and contex-
tual areas. We expect dierent types of distortion will inuence
the context-switching performance. Again, it is unrealistic to test
context-switching without travel and waynding. Thus, we include
all these three components in this task.
3.4 Experimental Design
We included two factors in the user study: Lens and Size. The Lens
had four dierent lenses, as described in Sec. 3.1. The Size had
two data sizes as described in Sec. 3.2. The experiment followed
a full-factorial within-subject design. We used a Latin square (4
groups) to balance the visualizations but kept the ordering of tasks
consistent: rst Locate, then Search, and nally Context. Each
participant completed 48 study trials: 4 visualizations
×
2 data
sizes
×
3 tasks
×
2 repetitions. The entire study has been tested on
common resolution settings (FHD, QHD and UHD).
Participants.
We recruited 48 participants on Prolic (https:
//www.prolic.co). All participants were located in the US and
spoke English natively. To ensure data quality, we restrict partic-
ipation to workers who had an acceptance rate above 90%. Our
nal participant pool consisted of 19 female, 26 male, and three
non-binary participants. Out of those participants, twelve had a
master’s degree, 16 had a bachelor’s degree, 14 had a high school
degree, and six did not specify their education levels. Finally, 4 par-
ticipants were between 18-20, 17 participants were between the age
of 21-30, 18 participants were between 31-40, ve participants were
The Paern is in the Details CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA
between 41-50, four participants were above 50. We compensated
each participant with 9 USD, for an hourly rate of 12 USD.
Procedures.
Participants were rst presented with the consent
form, which provided information about the study’s purpose and
the procedure. After signing the consent form electronically, the
participants had to watch a short training video (1 minute and 13
seconds) that demonstrated how to read and interact the MMV.
Participants completed the three tasks one by one based on a
Latin square design. Prior to working with a new lens, we showed
a video demonstrating how to interact with the matrix using the
current lens. Each (visualization
×
task) block started with two
training trials followed by study trials. Before each training trial,
we encouraged participants to get familiar with the visualization
condition and explicitly told them they were not timed for the
training. We also ensured that participants submitted the correct
answers in training trials before we allowed them to proceed. Before
starting the study trials, we asked the participants to complete the
trials “as accurately and as quickly as they can, and accuracy is more
important,” and informed them that these trials were timed. To
start a trial, participants had to click on a “start” button placed
in the same location above the MMV. This ensured a consistent
cursor starting point and precisely measured the task duration. The
visualization only appeared after clicking the start button.
After each task, participants were asked to rate each visualiza-
tion’s perceived diculty and write their justications. We collected
the demographic information as the nal step. The average com-
pletion time was around 45 minutes.
Measurements.
We collected the following measurements dur-
ing the user study:
Time.
We measured the time in milliseconds
from the moment the user clicked on the start button until they
selected an answer.
Accuracy.
We measured the participants accu-
racy as the ratio of correct over all answers.
Perceived Diculty
Rating.
After the user completed a task with all four lenses we
asked the participants to rate “how hard was performing the task
with each of the visualizations?” on a 5-point Likert scale ranging
from easy (1) to hard (5). The questionnaire listed visualizations in
the same order as presented in the user study with gures.
Quali-
tative Feedback.
We also asked participants to optionally justify
their perceived diculty ratings in text.
Statistical Analysis.
For dependent variables or their trans-
formed values that met the normality assumption (i.e., time), we
used linear mixed modeling to evaluate the eect of independent
variables on the dependent variables [
8
]. Compared to repeated
measure ANOVA, linear mixed modeling does not have the con-
straint of sphericity [
29
, Ch. 13]. We modeled all independent vari-
ables (four visualization techniques and two data sizes) and their
interactions as xed eects. A within-subject design with random
intercepts was used for all models. We evaluated the signicance of
the inclusion of an independent variable or interaction terms using
log-likelihood ratio. We then performed Tukey’s HSD post-hoc tests
for pair-wise comparisons using the least square means [
52
]. We
used predicted vs. residual and Q—Q plots to graphically evaluate
the homoscedasticity and normality of the Pearson residuals respec-
tively. For other dependent variables that cannot meet the normality
assumption (i.e., accuracy and perceived diculty rating), we used
the Friedman test to evaluate the eect of the independent variable,
Locate:
Search:
Context:
All responses Small Data Large Data
Cartesian Fisheye Stretch Step Comparisons
in dashed lines Effect Size
(Cohen’s d)
Fisheye vs. Stretch 0.23
Fisheye vs. Step 0.34
Cartesian
vs.
Stretch
0.24
Cartesian vs. Step 0.35
Stretch vs. Step 0.18
Fisheye
vs.
Cartesian
0.25
Stretch
vs.
Cartesian
0.12
Step vs. Cartesian 0.23
Figure 5: Time by task and in dierent data sizes. Condence
intervals indicate 95% condence for mean values. Dashed
lines indicate statistical signicance for 𝑝<.
05
. Tables are
showing their eect sizes.
as well as a Wilcoxon-Nemenyi-McDonald-Thompson test for pair-
wise comparisons. Signicance values are reported for
𝑝<.
05
(∗)
,
𝑝<.
01
(∗∗)
, and
𝑝<.
001
(∗ ∗ ∗)
, abbreviated by the number of
stars in parenthesis. Numbers in parentheses indicate mean values
and 95% condence intervals (CI). We also calculated the Cohen’s
d as indicators of eect size for signicant comparisons.
3.5 Results
The accuracy was similarly high across all conditions: on average,
95.3% for Locate, 92.3% for Search, and 78.1% for Context. We
did not nd any signicant dierences between Lens and Size on
accuracy. Therefore, we focus our analysis on the time (Fig. 5),
perceived diculty (Fig. 6), and qualitative feedback.
We found Lens had a signicant eect on time in both Locate
(
∗∗∗
) and Context (
∗∗∗
) tasks, but no signicant eect in the
Search task (
𝑝=
0
.
163). We also found Size had a signicant
eect on time in all tasks (all
∗∗∗
). No signicant eect has been
found in the interaction between Lens and Size for all tasks. For
the perceived diculty ratings, Lens had a signicant eect in the
Locate task (
∗ ∗ ∗
), but not in Search and Context tasks. All
statistical results are included in the supplementary materials.
Quantitative Key Findings.
Fisheye was the best performing technique.
Fisheye (11.8s,
CI=1.4s) and Cartesian (11.7s, CI=1.4s) had a similar performance
in the Locate task, and they both outperformed Stretch (15.3s,
CI=3s) and Step (20.4s, CI=5s) (all
∗∗∗
). The perceived diculty rat-
ings mostly aligned with the performance results. I.e., participants
rated Fisheye (2.19, CI=0.33) easier than Stretch (3, CI=0.33,
∗
) and
Step (3.77, CI=0.34,
∗ ∗ ∗
). Cartesian (2.71, CI=0.39) was also rated
easier than Step (
∗ ∗ ∗
). Fisheye (18s, CI=1.8s) also outperformed
Cartesian (20.7s, CI=1.3s) in the Context task (
∗ ∗ ∗
). Overall,
Fisheye was the best choice for the tested tasks.
Cartesian was not ideal for the Context task.
Cartesian
(20.7s, CI=1.3s) was slower than Fisheye (18s, CI=1.8s,
∗∗∗
), Step
(18.6s, CI=1.3s,
∗∗
), and Stretch (19.5s, CI=1.3s,
∗
). Participants
CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA Yang and Xia, et al.
Figure 6: Perceived diculty ratings by task. Dashed lines
indicate 𝑝<.05.
also tended to consider Cartesian (2.69, CI=0.38) more dicult
than Fisheye (2.27, CI=0.34) and Stretch (2.46, CI=0.32), but not
statistically signicant.
Stretch had advantage over Step in the Locate task.
The
only performance dierence between these two condition is that
Stretch (15.3s, CI=3s) was faster than Step (20.4s, CI=5s) in the Lo-
cate task (
∗∗∗
). Again, the perceived diculty ratings aligned with
the performance, where participants found Stretch (3, CI=0.33)
easier than Step (3.77, CI=0.34) in the Locate task (∗).
All performed similar in the Search task.
We did not nd an
eect of visualization on time or on the perceived diculty rating.
Qualitative Feedback.
We also asked participants to justify their perceived diculty
rating after each task. We analyze the collected feedback to get an
overview of the pros and cons of each lens.
Cartesian
was commented to be “natural” by six participants.
They found it to be intuitive to have cells that are closer to the cur-
sor to be larger. However, 18 participants complained its distortion.
More specically, ve participants found it dicult to know the
cursor’s current location within the matrix. Six found the distortion
results in unexpected “jump” and made it challenging “to get to the
right cell.” One participant also felt “sea-sick”. In the Search task,
one participant found the distortion made it hard to “see the bound-
ary of the highlighted region,” In the Context task, two participants
found it tough to “see far away clusters.”
Fisheye
was commented to be “easy to use” by 18 participants.
More specically, nine found it “easy to follow,” four found it “not
jump so much” and “more in line with the cursor,” two found it
“pinpoint fast,” two found it “easy to locate,” and one found it “easy
to know the current location.” Four participants also found “(cells
are) the same size outside the shseye” and easy to “compare the
clusters at once” in the Context task. However, nine participants
found it “hard to see the surroundings” due to irregular shapes in the
the transition area and they sometimes found it hard to precisely
identify the highlighted box in the Search task.
Stretch
was reported by four participants who found its reg-
ularity to be benecial: “lined up with the boxes” and “(easy) to
keep context in my head.” Three participants explicitly commented
it to be “better than the step.” However, 14 participants found it
disorienting, like “hard to get my bearing” and “alignment o.”
Step
was found positive with its regularity by two participants.
However, ten people found it “disorienting.” Eight also found the
empty space in the enlarged row and column confusing, with one
specically pointed out that “the gap breaks out the clusters” in the
Context task. Four reported it challenging for “precise moves.”
3.6 Discussion
Most lenses performed similarly in the rst user study, with a
few notable dierences. We discuss the potential reasons for these
dierences, and provide guidelines for future lens design in MMV.
Correspondence facilitates precise locating.
Locate is a
fundamental part of many high-level tasks in exploring MMV. In this
task, after moving the mouse cursor into the matrix, the context gets
distorted. Thus, it is important to nd a good entry point to facilitate
this task. A common strategy is to enter at the same row or column
as the target cell. However, due to distortion, the cursor may not
land on the target row or column. We dene the dierence between
the expected and actually hovered row or column after entering
the matrix as correspondence. Higher correspondence means less
oset and gives the user more predictable interactions. To nd out
the lenses’ correspondence, we simulated the cursor moving into
the matrix from the top and scanning the entire boundary with an
incremental one pixel each time. We found Fisheye and Cartesian
have a perfect correspondence. However, for Stretch and Step, the
osets vary from 0 to 3 cells in 50
×
50 matrices and from 0 to 6 cells
in 100
×
100 matrices (see supplementary material for details). In
summary, the ranking of correspondence is: Fisheye
=
Cartesian
>
Stretch
=
Step. The performance and perceived diculty results
align with correspondence, where Fisheye and Cartesian were
faster and generally perceived as easier than Stretch and Step
in the Locate task. Appert et al. [
4
] discussed this in pixel-based
lenses and proposed interaction techniques to improve correspon-
dence. However, it is unclear how to adapt their techniques to MMV.
On the other hand, their evaluation results partially aligned with
our results and conrmed our hypothesis: techniques with higher
correspondence have better locating performance.
Discontinuity aects the performance for precise locat-
ing.
Step was slower than Stretch in the Locate task. The per-
ceived diculty also aligned with the time performance, where
Step was considered more dicult than Stretch in the Locate
task. The only dierence in these two lenses is the way they vi-
sualize the enlarged rows and columns: Stretch stretches them,
while Step aligns the cells in the center and leaves blank space with
discontinuity. We conjectured that this discontinuity hinders the
ability of precise movement in the MMV, thus degrading the per-
formance of Step. This is also reected in participants’ comments,
where eight specically found the “gaps” confusing.
Uniformity facilitates contextualizing patterns.
Cartesian
was the slowest in the Context task. This task had two compo-
nents, where the rst component is similar to the Locate task,
and the second component required identifying the cluster with
most number of cells in the context. The second component started
right after the rst one, which means the visualization was still
distorted by the lenses. For uniform distortion, the participants
only need to compare the areas of the clusters. However, when
the context was distorted non-uniformly, comparing the areas of
clusters may lead to a wrong answer. As a result, participants had to
count the number of cells, which is expected to take longer. Partici-
pants might also rst remove the distortion by moving the cursor
outside, which would prolong the task. From Table 1 and Sec. 3.1,
we can see that the ranking of contextual uniformity is: Fisheye
=
Step
>
Stretch
>
Cartesian. This ranking aligns with the time
performance. In summary, our results suggest that the performance
was proportional to the level of contextual uniformity.
Small regions with irregular distortion might not aect
performance.
Within the lenses, all conditions had perfect regu-
larity, except for the Fisheye, where the cells in the transition area
The Paern is in the Details CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA
were not in a regular grid. Despite this irregularity, Fisheye had
the best overall performance. This does not necessarily mean that
regularity is not important for lenses in MMV, since Fisheye only
has a limited region that is irregular. Further studies are required
to conrm the eect of regularity in other regions (i.e., focal and
contextual regions) and at dierent sizes.
Dierent distortions do not aect coarse locating.
All lenses
had similar performance in the Search task. We believe this is due
to having a large target region (7
×
7) in this task. With a large target,
participants only needed to coarsely locate a region instead of pre-
cisely locating a single cell like in the Locate task. As a result, the
correspondence, discontinuity and other distortion characteristics
do not lead to signicant performance dierence in coarse locating.
4 STUDY 2 — FOCUS+CONTEXT, OVERVIEW+
DETAIL AND PAN&ZOOM IN MMV
This study is intended to address the literature gaps in terms of
identifying which is the best interaction techniques among Focus+
Context,Overview+Detail and Pan&Zoom for MMV. We chose
Fisheye as the representative technique for Focus+Context as it
was the best performing technique from the rst study. We designed
our rst study to be generalizable for testing interaction techniques
in MMV, i.e., the same experimental setups can be used to test
interaction techniques other than just lenses. Therefore, we reused
many materials from the rst study in our second study. Same
as the rst user study, we designed the second user study as an
exploratory study rather than hypothesis testing. This is because
the literature had mixed results for the comparisons of the three
generic interaction techniques and with little empirical knowledge
about the comparison of them in the context of MMV. As a result,
there was not enough guidance to generate reliable hypotheses. We
also pre-registered this study at https://osf.io/q4zp9.
4.1 Experimental Conditions
Same as the rst user study, the tested conditions use dierent ways
to selectively enlarge an ROI of the matrix so that the enlarged cells
have sucient display space to show the multivariate details. Un-
like the rst study, where all conditions superimpose the enlarged
ROI (or focused view) within the matrix (or the contextual view),
dierent conditions use dierent strategies to manage the focused
and contextual views in the second study.
Focus+Context
: we used the same design of Fisheye from
the rst user study (Fig. 2(b)). Focus+Context displays the focused
view inside the contextual view.
Overview+Detail
: we placed a separate view as the detail
view on the right of the overview (the matrix). Some designs place
one view at a xed location (e.g., top right corner) inside the other
view (e.g., in [
71
]). However, such a design is not suitable in our case,
as it will occlude part of the matrix. Thus, we decided to place the
two views side-by-side. In the detail view, the multivariate details
(i.e., lines chart in this study) are rendered for a selected ROI. A red
box is used to indicate the ROI in the matrix. The user can drag
the red box within the matrix, and the detail view will update in
real-time. This tightly coupled design between overview and detail
view is suggested by Hornbæk et al. [
39
]. We set the size of the
detail view and the number of line charts to the same as the Fisheye,
i.e., the detail view always renders 3
×
3 line charts in the same size
as they are in Fisheye. A demonstration of Overview+Detail is
presented in Fig. 7(a). Overview+Detail uses a spatial separation
between the focused and contextual views.
Pan&Zoom
: the participant can scroll the mouse wheel to zoom
in or out an ROI of the matrix continuously. The mouse cursor is
used as the center of zooming, and the transitions are animated.
When the user zooms into a certain level, where the cells’ size is
equal to or larger than a threshold, the line charts will be rendered
inside the cells. We set the threshold as the size of enlarged cells
with line charts in Fisheye. The user can also pan to inspect dif-
ferent parts of the matrix. The design of Pan&Zoom follows the
widespread map interfaces (e.g., Google Maps), and it is a standard
design in many user studies (e.g., in [
65
,
71
,
84
]). A demonstration
of Pan&Zoom is presented in Fig. 7(b). Pan&Zoom uses a temporal
separation between the focused and contextual views, i.e., only one
zoom level can be viewed at a time.
4.2 Experimental Setups
Experimental Design.
Similar to the rst study, we have two
factors: Techniqe (see Fig. 7) and Size. Each participant completed
36 study trials: 3 visualizations
×
2 data sizes
×
3 tasks
×
2 repetitions.
Data and Tasks.
We reused the data from the rst study. To
avoid learning eects, we used a screening tool from Prolic to
limit participants to people who have not seen our rst study. We
slightly modied the Locate task from the rst study to adapt to
the new interaction conditions. The Locate task in the rst study
asked participants to click on a highlighted cell as it is important for
understanding how dierent distortion from lenses aects precise
selection. However, in the second study, Overview+Detail and
Pan&Zoom do not have any distortion. Thus, the previous task can
lead to undesired bias. Instead, in the second study, we asked partic-
ipants to interpret the temporal pattern and select an answer from
ve options (see Fig. 4). With the adapted Locate task, we can com-
pare the eectiveness of interpreting a given cell’s detail in MMV,
which involves locating the target cell and navigating to details.
For the Search and Context tasks, we believe Overview+Detail
and Pan&Zoom do not introduce performance bias. Therefore, we
used the same Search and Context tasks from the rst user study.
Participants.
We recruited 45 participants on Prolic. As men-
tioned, to avoid learning eect, we ltered out participants from
the rst study at screening stage. All participants were located in
the US and spoke English natively. To ensure data quality, we again
restrict participation to workers who had an acceptance rate above
90%. Our nal participant pool consisted of 16 female, and 29 male.
Out of those participants, one had a PhD degree, one had a master
degree, 15 had a bachelor degree, 21 had a high school degree, and
seven did not specify their education levels. Finally, 7 participants
were between the age of 18-20, 22 participants were between the
age of 21-30, 11 participants were between the age of 31-40, one
participant was between the age of 41-50, and four participants
were above 50. We compensated each participant with 7 USD.
Procedures.
We used similar procedures as in the rst study,
except after each task, instead of only rating the perceived di-
culty, we asked participants to rate the overall usability,mental
demand, and physical demand for each visualization. This change is
CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA Yang and Xia, et al.
(a) Overview+Detail (b) Pan&Zoom
Figure 7: Study 2 visualization additional conditions (with 50×50 matrices): (a) Overview+Detail, the detail view on the right
shows the details of the red box in left matrix. The user can drag the red box to update the detail view in real-time. (b) Pan&
Zoom, the user can scroll the mouse wheel to zoom in or out a certain region of the matrix. In addition to Overview+Detail
and Pan&Zoom conditions, we used the same design of Fisheye from the rst user study, as demonstrated in Fig. 2(b). An
interactive demo is available at https://mmvdemo.github.io/, and has been tested with Chrome and Edge browsers.
intended to obtain a more nuanced understanding of the perceived
eectiveness. The average completion time was around 35 minutes.
Measurements and Statistical Analysis.
We collected similar
measures as in the rst study, including time,accuracy, and qualita-
tive feedback. As described in the procedures, we also collected the
subjective ratings of usability,mental demand, and physical demand
for each visualization at each task. We expected that the additional
ratings could help us towards a more nuanced understanding of the
perceived performance of dierent techniques. We used the same
method as in the rst study to analyze the collected data.
4.3 Results
Same as the rst user study, the accuracy was high across all condi-
tions: on average, 98.7% for Locate, 93.0% for Search, and 74.8% for
Context. We did not nd any signicant dierences on accuracy.
Therefore, we focus our analysis on the time (Fig. 8), subjective
ratings (Fig. 9), and qualitative feedback.
We found Techniqe had a signicant eect on time in all tasks:
Locate (
∗ ∗ ∗
), Search (
∗ ∗ ∗
), and Context (
∗
). We also found
Size had a signicant eect on time in Search (
∗
), and a marginal
eect in Context (
𝑝=
0
.
092), but not in Locate (
𝑝=
0
.
172). No
signicant eect has been found in the interaction between Lens
and Size on time for all tasks. In terms of subjective ratings, we
found Techniqe had a signicant eect on usability and mental
demand in tall tasks (all
∗ ∗ ∗
). For physical demand, we found
signicance in the Search (
∗∗∗
) and Context (
∗∗
) tasks. All
statistical results are included in the supplementary materials.
Quantitative Key Findings
Pan&Zoom was the best performing technique.
In the Lo-
cate task, Pan&Zoom (12.1s, CI=1.5s) was faster than Focus+Con-
text (13.8s, CI=1.5s,
𝑝=
0
.
081) and Overview+Detail (17.4s,
CI=3.3s,
∗ ∗ ∗
). In the Search task, Pan&Zoom (14.5s, CI=1.2s) was
faster then Focus+Context (23.0s, CI=1.9s,
∗ ∗ ∗
) and Overview+
Detail (26.3s, CI=1.7s,
∗∗∗
). In the Context task, Pan&Zoom
(16.5s, CI=1.1s) had a similar performance as Overview+Detail
(15.8s, CI=1.6s), and tended to be faster than Focus+Context (18.4s,
CI=2.0s), but not signicant. The subjective ratings mostly aligned
with the performance: participants rated Pan&Zoom with a higher
usability and lower mental demand than Focus+Context in all
tasks, all
∗ ∗ ∗
. Participants also found Pan&Zoom with a higher
Locate:
All responses Small Data Large Data
Focus+Context Overview+Detail Pan&Zoom
Search:
Context:
Comparisons
in dashed lines
Effect Size
(Cohen’s d)
P&Z vs. O+D 0.31
P&Z vs. F+C 0.21
F+C vs. O+D 0.21
P&Z vs. O+D 1.02
P&Z vs. F+C 0.74
F+C vs. O+D 0.23
O+D vs.F+C 0.20
Figure 8: Time by task and in dierent data sizes. Condence
intervals indicate 95% condence for mean values. Dashed
lines indicate statistical signicance for 𝑝<.
05
(black) and
0.05 <𝑝<0.1(gray).
usability, lower mental and physical demand than Overview+De-
tail in the Search task, all
∗∗∗
. Overall, Pan&Zoom was the best
choice for the tested tasks.
Overview+Detail performed well in the Context task.
In
the Context task, Overview+Detail (15.8s, CI=1.6s) was faster
than Focus+Context (18.4s, CI=2.0s,
∗
). It also tended to be slightly
faster than Pan&Zoom (16.5s, CI=1.1s), but that was not statisti-
cally signicant. Again, subjective ratings mostly aligned with the
performance results. Overview+Detail was rated to have a higher
usability (
∗∗∗
), lower mental (
∗∗
) and physical demand (
∗∗
) than
Focus+Context for the Context task. Overview+Detail was
also rated to be marginally less physical demand than Overview+
Detail for the Context task (𝑝=0.090).
Overview+Detail was the slowest technique in the Locate
and Search tasks.
Despite its good performance in the Context
task, Overview+Detail was slower than Pan&Zoom , all
∗ ∗ ∗
.
The Paern is in the Details CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA
Figure 9: Usability,mental demand, and physical demand
ratings by task. Dashed lines indicate 𝑝<.
05
(black) and
0.05 <𝑝<0.1(gray).
Overview+Detail was also slower than Focus+Context (23.0s,
CI=1.9s) in the Search task (
∗∗∗
), and was marginally slower than
Focus+Context (13.8s, CI=1.5s) in the Locate task (𝑝=0.055).
Focus+Context received the worst subjective ratings.
Fo-
cus+Context had the second best performance in the Locate task.
However, it was rated as with the lowest usability and highest men-
tal demand (all
∗∗∗
). For the Search task, it was rated with a lower
usability, higher mental and physical demand than Pan&Zoom (all
∗∗∗
). For the Context task, it was again rated with lowest usability
and highest mental demand (all
>∗∗
), and with a higher physical
demand than Overview+Detail (∗∗).
Qualitative Feedback
Same as the rst study, in addition to quantitative data, we also
asked participants to justify their subjective ratings after each task.
We analyze the collected feedback to get an overview of the pros
and cons of each interaction technique.
Focus+Context
was complained to be “dicult for precise se-
lection” and “hard to get where I wanted to be” by 21 participants.
17 participants also considered it to be “disorienting” as “hard to tell
where I was.” 11 participants did not feel condent with it, and “had
to double check.” Five participants found it “dicult to anticipate the
mapping.” In the Search task, eight participants also found using
it to “scan a large region is dicult,” which “requires high working
memory,” as they need to keep the context in mind. In the Context
task, four participants also commented that the distortion makes it
dicult to identify and inspect close clusters.
Overview+Detail
was reported to be benecial for “clearly
knowing where you are” by four participants. However, 12 par-
ticipants also pointed out it “requires a bit of working memory to
translate the position in the matrix to the detail view.” Five reported
that they “had to double check.” Two participants found it “becomes
more dicult for large matrices.” In the Search task, 13 participants
found using it to “scan a large region is dicult.” Potentially also
because participants need to keep switching between the overview
and the detail view all the time. In the Context task, 11 participants
found “having two view at once” helps complete the task.
Pan&Zoom
was found to be “intuitive” and “familiar” by 15 par-
ticipants. One participant also took advantage of the large number
of cells it can enlarge: “there is no need to precisely zoom in.” In the
Search task, 18 participants reported it can show a large number of
enlarged cells, and “having all at once” makes this task easy. In the
Context task, 12 participants complained about “the extra physical
movements required to zoom in and out.”
5 DISCUSSION
The overarching goal of our studies is to answer the question
“Which is the best interaction technique for exploring MMV?”. Our
results show that Pan&Zoom, was as fast as or faster than the
overall best performing Focus+Context (i.e., the Fisheye) and
Overview+Detail. Participants also rated Pan&Zoom the overall
best option in terms of usability, and mental and physical demand.
5.1 What leads to dierent performance for
focus+context, overview+detail, and
pan&zoom?
Spatial separation of views requires extra time.
Overview+
Detail was the slowest in the Locate and Search tasks. We be-
lieve a potential reason is the spatial separation of two views in
Overview+Detail. In Overview+Detail, the participants had to
interact with the overview, and then inspect the “far away” detail
view. In Focus+Context and Pan&Zoom, the participants have all
the information in just one display space. As a result, Overview+
Detail was likely to require more eye movements, and potentially
introduce extra context-switching cost. Our ndings partially align
with previous studies [
21
], where they also found Overview+De-
tail required more time in some applications.
Spatial separation of views is benecial for contextualiz-
ing details.
Overview+Detail was faster than Focus+Context
in the Context task, and tended to be slightly faster than Pan&
Zoom, but not signicantly. As mentioned earlier, the Context task
has two components, with the rst one similar to the Locate task,
and the second one in identifying the largest cluster. Overview+
Detail was the slowest in the Locate task, which means its good
performance in the Context tasks was mainly from identifying the
clusters. With Overview+Detail, there is no further interaction
needed to nish the second component after the rst one. While,
for Pan&Zoom, participants had to zoom out to complete the sec-
ond component. This is also conrmed by the reported physical
demand ratings, where 33 out of 45 participants found Pan&Zoom
required equal (nine participants) or more physical (24 participants)
movements than Overview+Detail in the Context task. On the
other hand, compared to Overview+Detail, the distortion in Fo-
cus+Context was likely to aect the contextualizing performance,
as participants might require extra eort to interpret the distortion.
This is also conrmed by the usability, mental demand, and physical
demand ratings. In summary, in contextualizing details, the gain of
having spatial separation of views outweighs its loss.
More cells showing details lead to better search perfor-
mance.
In the Search task, Pan&Zoom can show more enlarged
cells with line charts. Pan&Zoom can treat the entire space of MMV
as the focal area, as a result, more enlarged cells showing details can
t in the space. In our user study, a maximum of roughly 10
×
10 cells
can be presented with details. On the other hand, Focus+Context
and Overview+Detail only represent 3
×
3 cells with details in the
study, and more travels (or scanning) was required to complete this
task. This is also conrmed by the subjective rating of usability,
mental demand, and physical demand, where Pan&Zoom clearly
received the best ratings. Increasing the number of cells in detail for
Focus+Context and Overview+Detail can potentially improve
their performance. For Focus+Context, however, a larger focal
CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA Yang and Xia, et al.
area also introduces more distortion. Moreover, it is not possible to
have a focal area as large as the entire matrix like in Pan&Zoom.
On the other hand, it can be straightforward to increase the size
of detail view in Overview+Detail. However, more screen space
will be required, which may not be an option for scenarios with
limited screen estate. Another potential reason might be that the
majority of users are more familiar with Pan&Zoom compared to
other techniques, as it is a standard interaction technique in many
web applications (e.g., Google Maps, photo viewers). Our results
partially aligned with Yang et al [
87
], which found that Pan&Zoom
had better performance than Overview+Detail. Our results dier
from the study by Pietriga et al [
65
], where they found Focus+
Context and Overview+Detail outperformed Pan&Zoom. One
possible reason is that they only consider one navigation task, and
did not consider multivariate details. Interpreting multivariate de-
tails and switching between the focal and contextual areas can
introduce additional eort for dierent conditions.
Distortion results in bad user experience.
Focus+Context
was rated lowest on usability and highest in mental demand for
almost all tasks, despite its generally good performance in the
Locate and Search tasks. An interesting fact is that the Focus+
Context technique used in the second study (i.e., Fisheye) was
rated as the easiest technique in the rst study. However, when
compared to the regularity and uniformity in Overview+Detail
and Pan&Zoom, participants clearly disliked the Fisheye. These
results were not found in previous studies [
9
,
35
,
74
]. A possible
explanation is that prior studies employed applications, where the
regularity and uniformity are not important. However, keeping
rows and columns in a regular grid is critical for matrix visualization
and should be considered for the design of MMV.
5.2 Generalization, Limitations and Future
Work
Interaction Techniques.
In our rst study, we followed Carpen-
dale et al’s taxonomy [
19
], and tested four representative lenses.
In the second study, we compared the best performing lens (fo-
cus+context) to overview+detail, pan&zoom. Those are the most
widely-used techniques, and are likely to be among the rst choices
when designing interactions for MMV. Thus, we believe our selected
techniques cover a wide range of interaction techniques for MMV,
and provide practical guidance on selecting the most eective and
applicable technique. There are other interaction techniques that
can be adapted to MMV, like insets [
50
], editing values, aggregating
values across cells and adapting visualizations to the aggregated
data [
38
] and re-ordering the matrix [
11
]. Our study is meant as a
rst assessment of the fundamental interactions for MMV. Including
these techniques in a future study can obtain a more comprehen-
sive understanding of the eectiveness of interaction techniques in
MMV but beyond the scope of this paper.
Our results and discussion can inspire improvements to existing
approaches and generate potential new techniques. In the rst
study, we found correspondence necessary for precise locating.
TableLenses particularly suered from its low correspondence. One
possible way to increase the correspondence in TableLenses is to
dynamically move the entire matrix based on the mouse cursor to
compensate for its row or column osets. However, such a design
requires extra screen space and may confuse the users. Future
design can also consider adapting 3D distortion and techniques,
like the Perspective Wall [
53
] and Mélange [
28
] to MMV. In the
second user study, we found Pan&Zoom was overall a good option,
but Overview+Detail had a similar performance as Pan&Zoom
and was rated lowest on physical demand in the Context task. To
have the benets of both, the two techniques could be combined.
However, adding an overview to a zooming interface leads to mixed
results in the literature [
39
]: some found it useful for navigation,
and some found it unnecessary [58, 87].
The performance of Focus+Context was not ideal in our stud-
ies. One potential way to improve lenses is to allow the users to
select multiple focal areas, which has been explored in some ap-
plications [
28
,
38
,
50
]. However, as the rst controlled study for
MMV, we decided to have only one focal area to focus on the basic
MMV interactions. Further tests are required to understand the
eectiveness of these techniques. Meanwhile, we believe our re-
sults can be partially generalized to multi-focal interactions. The
tested Locate and Search tasks investigated the waynding and
travel components. We conjectured that adding the multi-focal fea-
ture to our tested conditions would not signicantly change our
results of these two tasks, as they are basic interactions and do
not require participants to investigate multiple areas of interest.
Having multiple focus areas is likely to severely change the distor-
tion for the Context task, and additional investigation is required
for checking the context-switching component. Moreover, one key
motivation of having multiple focus areas is to reduce the num-
ber of travels [
28
,
50
,
87
]. Our tested tasks did not explicitly test
the number of travels component, and it should be systematically
explored in future studies.
Technique Congurations.
We discuss the rationale and limi-
tation of the chosen parameters for the tested techniques:
The size of the focal area. We chose the parameters for lenses to
ensure that the users can interact with the enlarged cells while the
contextual cells are still legible on screens with standard resolutions
(Sec. 3.3). With higher resolution, other settings could be tested,
and we expect larger focal areas to be benecial for some tasks (e.g.,
the Search task). The focal area for Overview+Detail is not as
constrained as Focus+Context, but a larger focal area will require
more screen space, and we intentionally kept their sizes consistent
to reduce confounding factors. One future direction is to investigate
the eect of focal area size on dierent interaction techniques.
Lens on-demand. Providing the ability to switch on and o the
lenses is likely to improve their correspondence. However, one key
motivation for using lenses is interactive exploration [
78
,
79
], where
the location of the targets is not known upfront. Our studies were
designed to investigate the performance of interactive exploration
and simulate dierent interaction components of the exploration
scenario in the tasks. Additionally, allowing the participants to turn
on and o the lenses might bring extra complexities to the interac-
tions, which could potentially aect their performance. Providing
extra training might reduce this side eect but signicantly in-
creases the user study time. However, experts can get familiar with
enabling/disabling lenses with less time constraint in real-world
applications, and its eectiveness should be evaluated.
Dragging interaction in Overview+Detail.There are two ways
to select the focal area in Overview+Detail: point-and-click and
drag-and-drop [
87
]. Point-and-click requires fewer steps, while
The Paern is in the Details CHI ’22, April 29-May 5, 2022, New Orleans, LA, USA
drag-and-drop provides a better estimation of the interaction [
46
].
It is unclear which is a better choice for MMV. We chose drag-and-
drop in our study because the point-and-click method conicts
with our target selection interaction. A future study is desired to
compare the eectiveness of these two methods for MMV.
Embedded Visualization and Tasks.
In our studies, we tested
time series data, one type of widely used multivariate data. Our
tested tasks focus on the interactions to locate, search, and contex-
tualize multivariate details. These tasks were chosen to investigate
the tested conditions’ waynding,travel, and context-switching per-
formance. We intentionally lower the diculty of interpreting the
embedded visualization, so that the participants do not need deep
knowledge about a particular type of visualization and can focus
on the interactions. Changing the embedded visualization is likely
to aect the interpretation performance but will likely bring min-
imum inuence on the waynding,travel, and context-switching
performance. Thus, we expect our ndings on the eectiveness of
dierent interaction techniques to be partially generalized to MMV
with other embedded visualizations. Future studies are required to
conrm our hypothesis. Horak et al [
38
] demonstrated embedding
dierent types of visualizations for dierent cells. Such an adap-
tive design can facilitate complex data analysis process and should
be tested in the future. We also plan to study more specic MMV
applications with more sophisticated and high-level tasks.
Scalability.
We identied three potential eects related to scal-
ability that were not fully investigated in our studies:
The number of data points and pattern types in the line chart. In-
spired by Correll & Gleicher [
23
], we used ve primitive temporal
patterns in our study. We did not include more complicated pat-
terns, as we want to focus on studying the performance of dierent
interactions. We also chose to have ve data points in each cell, as
this is enough for representing all selected temporal patterns while
still allowing interaction within the line chart. Interpreting more
complicated patterns or increasing the number of points in the line
chart is likely to increase the diculty constantly for all testing con-
ditions. Thus, our ndings can still provide helpful guidelines for
selecting the appropriate interaction technique. However, further
investigations are required to conrm this conjecture.
Size of the matrix. We tested two dierent sizes of matrices. We
believe the tested sizes are representative as they can be reasonably
rendered and interacted on a standard screen. We found that the
performance of almost all conditions decreased in the larger data
set. However, we did not nd signicant evidence that one specic
condition resists the increasing data size better than others. Future
studies are required to investigate MMV in larger data sets.
Size of target regions. In the Search task, we used 7
×
7 as the size
of the target regions, which was larger than the size of the lenses,
so that participants had to move the lenses to fully explore it. In
the Context task, we controlled the range of cluster sizes (from
5
×
5 to 7
×
7) to make the task less obvious and more challenging for
participants. We cannot nd any literature indicating a signicant
eect of cluster size, and it should be tested in the future.
6 CONCLUSION
We have presented two studies comparing interaction techniques
for exploring MMV. The ndings extend our understanding of the
dierent interaction techniques’ eectiveness for exploring MMV.
Our results suggest that pan&zoom was the overall best performing
technique, while for contextualizing details, overview+detail can
also be a good choice. We also believe there is potential to improve
the design of lenses in MMV, for example, reducing the inuence
of distortion through lensing on demand. To provide structured
guidelines for future research and design, we discussed the eect of
correspondence, uniformity, irregularity, and continuity of lenses.
Our results indicate that high correspondence, uniformity, and
continuity led to better performance for lenses. Future lens design
should take these metrics into account. Another potential future
direction is to investigate hybrid techniques, such as adding an
overview to a zooming interface or providing interactive zooming
inside the lenses. In summary, we believe there is much unexplored
space in MMV, and our study results and discussion can potentially
lead to improved and novel interaction designs in MMV.
ACKNOWLEDGMENTS
This work was partially supported by NSF grants III-2107328 and
IIS-1901030, NIH grant 5U54CA225088-03, the Harvard Data Sci-
ence Initiative, and a Harvard Physical Sciences and Engineering
Accelerator Award.
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