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Journal of International Technology and Information
Management
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An Innovative Clustering Approach to Market
Segmentation for Improved Price Prediction
Donghui Shi
Anhui Jianzhu University
Jian Guan
University of Louisville
Jozef Zurada
University of Louisville
Alan S. Levitan
University of Lousiville
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Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 15 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
An Innovative Clustering Approach to Market Segmentation for Improved
Price Prediction
Donghui Shi
Department of Computer Engineering
School of Electronics and Information Engineering
Anhui Jianzhu University
CHINA
Universidad Técnica Particular de Loja
ECUADOR
Jian Guan
Department of Computer Information Systems
College of Business
University of Louisville
USA
Jozef Zurada
Department of Computer Information Systems
College of Business
University of Louisville
USA
Alan S. Levitan
School of Accountancy
College of Business
University of Louisville
USA
ABSTRACT
A main obstacle to accurate prediction is often the heterogeneous nature of data. Existing studies
have pointed to data clustering as a potential solution to reduce heterogeneity, and therefore
increase prediction accuracy. This paper describes an innovative clustering approach based on a
novel adaptation of the Fuzzy C-Means algorithm and its application to market segmentation in
real estate. Over 15,000 actual home sales transactions were used to evaluate our approach. The
test results demonstrate that the accuracy in price prediction shows notable improvement for some
clustered market segments. In comparison with existing methods our approach is simple to
implement. It does not require additional collection of data or costly development of models to
incorporate social-economic factors on segmentation. Finally our approach is not market specific
and can be easily applied across different housing markets.
Keywords: Fuzzy c-means clustering, mass assessment, k-means clustering, real estate
submarkets, cluster homogeneity, ANFIS
Journal of International Technology and Information Management Volume 24, Number 1 2015
© International Information Management Association, Inc. 2015 16 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
INTRODUCTION
There is general agreement that a housing market consists of a set of submarkets. Various methods
have been proposed for reliable detection of submarkets. Common methods in determining
submarkets are mostly geographic, administratively determined, or statistics-based.
Administratively determined boundaries, such as those used by local government assessment
offices, can be ineffective (Zurada, Levitan, & Guan, 2011). Though geographic boundaries can
be more effective (Fik, Ling, & Mulligan, 2003), such boundaries also restrict segmentation to
only spatial considerations. As Goodman and Thibodeau (2007) point out, consumers do not
necessarily limit their housing search to spatially contiguous areas when house hunting. Statistical
methods often use specially developed neighborhood characteristics such as quality of schools and
level of public safety. However, the development of such neighborhood characteristics can be
challenging and costly (Goodman & Thibodeau, 2007). This paper explores the feasibility of an
untested approach to construct submarkets with the objective to better disaggregate the properties
in a given market into more homogeneous clusters. The approach is based on an adaptation of the
fuzzy C-means (FCM) algorithm. Our approach is based on a proven and common practice by
humans, uses data features readily available to local governments or appraisal offices, and is
simple to implement without requiring complicated model development. As is common in such
studies, we evaluated the validity of this newly introduced housing segmentation approach by
measuring the accuracy of price prediction in the resulting submarkets. A new input variable, based
on the prices of comparable properties in their cluster, is added to the typical set of housing
characteristics within the newly formed submarkets. Two different methods were used to predict
the prices of properties in the clusters, adaptive neural fuzzy inference system (ANFIS) and the
traditional multiple regression analysis (MRA). The test results, based on actual sales transactions
in Louisville, KY, show that the price prediction accuracy noticeably improves for some of the
resulting clusters.
The paper is organized as follows. The next section provides a brief literature review, which is
followed in section 3 by a presentation of the adapted FCM algorithm and its application to create
homogeneous clusters for properties in a given market. Section 4 provides a description of the data
set used in this study. Section 5 presents and discusses the results of testing using both MRA and
ANFIS. Finally Section 6 provides a summary and conclusions.
RELEVANT LITERATURE
A main obstacle to efforts to obtain an accurate valuation of real estate properties is the
heterogeneous nature of real estate data (Goodman & Thibodeau, 2007; Mark & Goldberg, 1988).
An increasingly common approach to reduce data variability and improve accuracy is to cluster
the data set into submarkets that are more homogeneous (Bourassa, Hamelink, Hoesli, &
MacGregor, 1999; Fletcher, Gallimore, & Mangan, 2000; Goodman & Thibodeau, 1998, 2003,
2007; Wilhelmsson, 2004). It is well recognized in the real estate literature that housing markets
are typically segmented into clusters/submarkets and these clusters/submarkets should be included
in the price prediction process (Wilhelmsson, 2004). A cluster/submarket can be defined as a set
of properties within which implicit pricing and/or property features differ from those of another
area/set (Goodman & Thibodeau, 1998). It is argued that each of these different
clusters/submarkets should have its own price equation/model (Straszheim, 1974). The expectation
is that these separate models should provide better estimates for pricing than an aggregate model
Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 17 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
because an aggregate model will have biased coefficients (Michaels & Smith, 1990). In addition
to improving price prediction accuracy, identification of submarkets also allows researchers to
better model spatial and temporal variation in prices, helps lenders assess risk in home ownership,
and reduces home buyers’ search costs (Goodman & Thibodeau, 2007).
Various methods have been proposed to determine boundaries for clusters and they include
geographical, administrative, and statistically determined boundaries. Dale-Johnson (Dale-
Johnson, 1982) uses factor analysis of property features and pre-defined administrative boundaries
(zip codes) in segmenting his data. Dale-Johnson finds improvement in model predictability but
the study does not use out-of-sample tests. Fletcher et al. (Fletcher et al., 2000) add property type
and age to zip codes in their approach to submarket construction. Though their disaggregated
models yield statistically better price prediction results, the results are not good enough to offer
practical value. Statistical methods, such as principal component analysis and cluster analysis, can
also be used to define submarkets and the resulting submarkets may or may not correspond to
spatially defined submarkets (Bourassa, Cantoni, & Hoesli, 2010). Bourassa et al. (1999) use a
statistical technique to derive clusters/submarkets in which they combine principal component
analysis and cluster analysis. The factors extracted from the principal component analysis are used
in two different clustering methods, k-means and Ward. Their results show an improvement of
about 25% when compared with those of the aggregated model. More recently Bourassa et al.
(2010) confirm the benefit of submarkets in price prediction through a comparative study of
various submarket construction techniques, which include ordinary least squares and geostatistical
methods. Their results confirm that the inclusion of submarket variables improve price prediction
accuracy. Goodman and Thibodeau (2003) use hierarchical linear models to define
clusters/submarkets for the Dallas metropolitan area. They use two different submarket
construction methods, one using zip codes and the other using census tracts. Both methods lead to
improved estimates of property values using regression models. In their more recent study
Goodman and Thibodeau (2007) find that their model based on school quality and public safety
significantly improves price prediction accuracy. However, they also point out that development
of such models can be costly and challenging. More recently Belasco et al. use a finite mixture
model to identify latent submarkets from household survey data (Belasco, Farmer, & Lipscomb,
2012). Their results suggest homogenous preferences of residents within identified submarkets.
In general these submarket construction/clustering studies show that clusters/submarkets in real
estate data exist and property valuation models that incorporate such clusters/submarkets can
potentially result in better price prediction accuracy. Some of these studies use spatial boundaries
in determining clusters/submarkets and these boundaries include zip codes, census tracts, and local
government defined boundaries. If one follows a more general definition of a cluster/submarket as
a set of properties that are relatively close substitutes of one another and poor substitutes for
properties outside the submarket, then spatial boundaries are not necessarily the only way to
segregate real estate data (Bourassa et al., 1999). Zurada et al. (2011) show that administrative
boundaries as used in mass appraisal by local governments may not be effective in segmenting
real estate data. In fact, as Goodman and Thibodeau (2007) point out, consumers do not necessarily
limit their housing search to spatially contiguous areas when house hunting. Consumers are more
driven by price and features as well as location. Development and incorporation of neighborhood
characteristics in cluster/submarket construction provide an alternative approach to geographic and
administrative boundaries but such development can be challenging (Goodman & Thibodeau,
2007).
Journal of International Technology and Information Management Volume 24, Number 1 2015
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This paper introduces a unique clustering method often applied in other fields, the fuzzy c-means
clustering method. The objective is to offer an alternative method to housing market segmentation
and to better understand why certain properties cluster well and others do not. In addition we
incorporated a common and proven practice of using similar properties (“comparables”) by expert
human appraisers in property appraisal. After segmentation by FCM, a comparable properties-
based index is introduced for each property as an additional input in price prediction. Our approach
relies on real estate transactions data readily available in various appraisal contexts and does not
require the development of neighborhood or submarket characteristics. Neither does our approach
require the collection of additional data. Lastly our FCM-based approach is simple to implement.
Often the measure of the effectiveness of a clustering/submarket construction approach is the
improvement in price prediction accuracy (Bourassa et al., 2010; Goodman & Thibodeau, 2007).
The standard and dominant approach to price prediction is MRA-based (McCluskey, Cornia, &
Walters, 2012). The use of MRA in property price prediction has been discussed extensively
because MRA is thought to be a poor model for handling the inherent complexity and high level
of data variability that exist in real estate data (Mark & Goldberg, 1988; Stevenson, 2004). Notable
issues with the application of MRA include non-linearity, multi-collinearity, and
heteroscedasticity (Kilpatrick, 2011; Mark & Goldberg, 1988). Various data mining models have
been proposed and tested (Antipov & Pokryshevskaya, 2012; Do & Grudnitski, 1992; Gonzalez &
Laureano-Ortiz, 1992; Guan, Zurada, & Levitan, 2008; Peterson & Flanagan, 2009; Selim, 2009;
Zurada et al., 2011), but the results are rather mixed. Some studies find data mining methods to be
superior (Antipov & Pokryshevskaya, 2012; Do & Grudnitski, 1992; Peterson & Flanagan, 2009)
but others find little or no improvement when compared to MRA (Guan et al., 2008; Zurada et al.,
2011). A major criticism of the use of data mining methods such as artificial neural networks in
mass appraisal is their lack of interpretability (McCluskey et al., 2012). Guan et al. (2008) propose
the use of ANFIS as ANFIS combines the benefits of neural networks and interpretable results.
The resulting fuzzy rules offer a mechanism to capture the inherent imprecision in mass appraisal
(Bagnoli & Smith, 1998; Byrne, 1995). Therefore in this study we used both MRA and the adaptive
neuro-fuzzy inference system (ANFIS) to test our new approach.
METHODOLOGY
This section describes an alternative approach to group properties into more homogeneous clusters.
FCM is a well-known clustering method popularized by Bezdek (1984). Like most clustering
methods FCM segments data elements (properties in our case) into clusters so that data elements
in the same cluster are as similar as possible and data elements in different clusters are as dissimilar
as possible. FCM belongs to the class of soft clustering methods where a data element can be
assigned to different clusters at the same time. For each cluster to which a data element is assigned,
a value called membership level indicates the degree to which the data element belongs to that
cluster. In the context of housing segmentation a property can belong to more than one segment
through FCM clustering. For each resulting segment FCM finds a level of association of a property
with that segment. Market segments can then be determined by assigning each property to a
segment with which the property has the highest level of association. The level of association can
be determined by any meaningful criterion such as proximity, prices, etc. A more formal
description of FCM for market segmentation follows.
Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 19 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
Let be a set of n properties where each represents a property. The FCM
clustering method returns k clusters and a membership matrix
(1)
where each uij is the degree to which property xi belongs to cluster cj. In FCM the data set is
partitioned into k clusters by minimizing the following objective function
(2)
where m is a weighting exponent, is the Euclidean norm, and
(3)
Minimization of the objective function is an iterative process and consists of the following steps:
1. Select a value for k as the number of clusters, m as the weighting exponent, and ϵ as the
termination threshold.
2. Initialize the membership matrix with random values between 0 and 1
3. Initialize iteration counter t with 0
4. t = t + 1
5. Calculate the cluster centers as follows
6. Update the membership matrix as follows
7. If , stop; otherwise go to step 4.
Although FCM allows each property to belong to one or more clusters, in our study a property
belongs to only one cluster, where its membership in the cluster uij > threshold
1
.
Once the clusters are created, a new input variable, the mean price of comparables, or MPC, is
defined for each property in its cluster to improve prediction accuracy. The MPC index is based
on a common process used by human experts in determining comparables for a given property for
either sales or appraisal purposes. For any given property x, comparables are those properties
whose features and sale prices are most likely to reflect the features and sale price of property x.
The objective of our approach is to group properties into homogeneous clusters so that the most
similar properties are more likely to be used as comparables.
1
The threshold value is 0.8. For details please see the results section.
Journal of International Technology and Information Management Volume 24, Number 1 2015
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Since the use of FCM allows the resulting clusters to become more homogeneous, the resulting
MPC of each property calculated using the k nearest neighbors within a cluster is more likely to
be close to the actual price of the property. The process for calculating MPCs is defined as follows.
For each property in each cluster the k nearest neighbors for the property are first determined by
location and the distance between the property p1 and its neighbor p2 as follows:
(4)
Once the k nearest neighbors are found, the MPC of property using the k nearest neighbors is
calculated as follows:
(5)
where k is the number of neighbors for .
As noted above, the larger the threshold value is, the more homogeneous the resulting clusters
created by FCM will be. However, a larger threshold value also causes a greater number of
properties to remain unassigned to any cluster. As can be seen in Figure 2 the number of properties
assigned to clusters is inversely related to the threshold value. For example if the threshold value
is 0.9, the total number of properties assigned to clusters is 6,422 (or about 38.7% of the total
number properties) but becomes 15,904 (or about 95.8%) if the threshold value is reduced to 0.5.
Figure 1. Relationship between membership degrees and total records in clusters
Therefore, those properties whose membership degree is not greater than or equal to the threshold
are not assigned to any cluster. This paper introduces a modification of the FCM algorithm so that
these unassigned properties are further grouped into additional clusters.
Next we describe the algorithm.
Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 21 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
Input:
Original data set, X;
The initial number of clusters, c; here c=3
The threshold record number of clusters =3000.
Output
C : the set of resulting clusters;
1. Find c clusters using the dataset X using FCM
2. For each of these c clusters find the MPC for each property within each cluster
3. Set Ө = the number of R
4. If Ө < threshold Ө0 retain R as a cluster and Exit
5. Otherwise set X = R
6. Repeat steps 1-5 until the number of properties in R is less than the threshold Ө0
The modified FCM process will create an initial c number of fuzzy clusters (see step1). Then for
each property in each of these newly created clusters the MPC is calculated in step 2. Next the
number of properties in the remaining, unclustered set R, Ө is compared to a threshold size, Ө0, to
determine if R needs to be further segmented into smaller subclusters (steps 3, 4). If the number of
properties in R is less than the threshold Ө0, it is kept as a new cluster and the clustering process
terminates. Otherwise the properties in R will go through another round of clustering. This process
continues until in the number of properties in R is less than the threshold Ө0.
DATA DESCRIPTION
The original data set used in this study contains 20,192 sales transactions of residential properties
in Louisville, Kentucky, US from 2003-2007. The Jefferson County Tax Assessor in Louisville,
Kentucky provided access to the entire database of over 300K properties and 143 variables. About
220K and 80K properties were identified as residential and commercial properties, respectively.
After the removal of commercial properties, the data set was reduced to approximately 200,000
records and included only residential properties with actual sales dates and prices for years 2003–
2007. Vacant lots, properties sold for less than $10,000, properties having less than 500 square
feet on the floors, and several of those built before the year 1800 were excluded. Next the records
were cleansed to eliminate repeated records representing group sales, inconsistent coding, missing
values, and other obvious errors common in any database that large. After the data were
preprocessed to eliminate invalid and incomplete records, 16,592 records remained. Table 2 shows
the fields used in this study. Table 3 shows their descriptive statistics. Each sales record contains
fields describing the typical features of a property, the sale date, and the sale price. The fields
shown in Table 2 are known to have influence on the price of a property and are normally included
in any model of real estate price prediction (Zurada et al., 2011). Since the data set contains sales
records spanning several years the price of each property is CPI-index adjusted by the formula in
Table 1.
YEAR
BASE YEAR 1983
BASE YEAR 2007
Journal of International Technology and Information Management Volume 24, Number 1 2015
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Table 1. CPI-U (Consumer Price Index – All urban consumers)
Variable Name
Sample
Record
Explanation
Sale price [$]
(Dependent variable)
390000
Actual sale price
Year Built
1968
Year in which the property was built
Age
37
Age in years when the property was sold
Square footage in the
basement [Feet]
900
Square feet in basement
Square footage on the
floors [Feet]
2931
Total square feet above basement
Number of fireplaces
1
One fireplace (range 0-3)
Garage size (number of
cars)
2
Two-car garage (range 0-2)
Number of baths
4
0=substandard bath; 1=1 bath; 2=1 ½ baths; 3=2
baths;4=2 ½ baths, etc. up to 6=more than 3 baths
Presence of central air
1
0=no central air; 1=central air is present
Lot type
1
1=up to one-fourth acre; 2=one-fourth to one-half
acre; 3=one-half to 1 acre; 4=over 1 acre
Construction type
3
1=1 story; 2=1 ½ story; 3=2 story; 4=2 ½ story;
5=split-level; 6=bi-level; 7=condominium
Wall type
2
1=frame; 2=brick; 3=other
Basement type
1
0=none; 1=partial; 2=full
Basement code
1
0=none; 1=standard; 2=half standard; 3=walk-out
Garage type
3
0=none; 1=carport; 2=detached; 3=attached;
4=garage in basement; 5=built-in garage
Longitude
-85.573
Degrees west
Latitude
38.216
Degrees north
Table 2. Fields of a property used in the study
Variable
Mean
Std Dev
Minimum
Maximum
Median
Sale price
166562
105585
10700
889220
139674
Year Built
1967
32
1864
2006
1966
Age
38
31.8
-1
141
39
Square footage in the
basement [Feet]
187.8
400.2
0
2952
0
Square footage on the
floors [Feet]
1577.5
649.2
525
7459
1399
Number of fireplaces
0.51
0.50
0.00
1.00
1.00
2003
184.000
1.127
2004
188.900
1.098
2005
195.300
1.062
2006
201.600
1.028
2007
207.342
1.000
Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 23 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
Garage size (number
of cars)
1.13
0.87
0.00
2.00
1.00
Number of baths
2.65
1.49
0.00
6.00
3.00
Presence of central air
2.65
1.49
0.00
6.00
3.00
Lot type
1.18
0.52
1.00
4.00
1.00
Construction Type
1.63
0.82
1.00
3.00
1.00
Wall type
1.59
0.52
1.00
3.00
2.00
Basement type
1.13
0.94
0.00
2.00
2.00
Basement code
0.62
0.49
0.00
1.00
1.00
Garage type
1.82
1.33
0.00
5.00
2.00
Longitude
-85.90
2.86
-157.91
-71.05
-85.65
Latitude
38.15
0.73
21.37
47.12
38.20
Table 3. Descriptive statistics of data set
A careful examination of our data shows that the data are very heterogeneous. As can be seen in
the descriptive statistics several data fields exhibit large variation such as Age (as shown through
Year Built), Sale Price, and Floor Size. This type of large variation in data values may affect
prediction accuracy.
Location is considered a critical data element in real estate property price prediction and is used in
creating clusters of properties, i.e., submarkets, as described in the literature review. Location is
represented by longitudes and latitudes in this study. Another common practice in representing
location is to use administrative boundaries. In the city where the sales data were collected,
administrative boundaries are used to describe each property. The sales records represent
properties belonging to about 20 Tax Assessor (TA) districts. The TA districts are then further
divided into more than 400 TA neighborhoods, which are in turn divided into about 8,000 TA
blocks. One of the ways to assess (or reassess) the value of a property for tax purposes in the city
is to sum the sale prices of all similar properties sold recently in the immediate neighborhood of
the house, divide the sum by the total square footage of these properties. The resulting value is the
price per square foot of similar properties. This price per square foot value is then multiplied by
the square footage of the property to be assessed. This practice is actually very similar to the use
of the so-called comparables. In real estate appraisal the comparables of a property are the nearby
properties with similar features. The mean price of the comparables for a property is often
considered a good predictor of the sale price of the property. However, these comparables are often
manually determined property by property by expert human agents or appraisal experts. Zurada et
al. (2011) show that these administratively determined boundaries may not be very effective in
grouping similar properties and propose the creation of different comparables as a feature to
improve prediction of property values. As discussed in the literature review administrative or
geographical boundaries in general may not be effective in grouping similar properties or
submarkets (Goodman & Thibodeau, 2007).
The use of comparables has proven to be effective when human experts (such as real estate agents)
determine the comparables of a property as the human experts tend to have very intimate
knowledge of the neighborhood of the property. For example there may be several neighborhood
properties that are physically close but vary greatly in price because one such neighborhood
Journal of International Technology and Information Management Volume 24, Number 1 2015
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property has a relatively low price due to aging appliances and/or conditions of the exterior of the
property. Apparently the accuracy of a property’s price prediction is critically dependent on the
correct determination of the comparables for the property. In this study we introduce a new input
variable, MPC, as described in the previous section, to better emulate this human appraisal process.
MPC is computed for each property after clustering, the objective being to use comparables that
are more similar.
TEST RESULTS
This section describes the test results. As consistent with many existing studies on
clustering/segmentation prediction results both before and after segmentation are shown and
compared. The tests were performed with the Matlab software from Math Works. In all the tests
we randomly partitioned the data set into three subsets: training set (40%), validation set (30%),
and test set (30%) (Witten & Frank, 2005). Three performance measures: Mean Absolute
Percentage Error (MAPE), Root Mean-squared Error (RMSE) and Mean Absolute Error (MAE)
were used to measure the performance of the methods on the test sets. The performance measures
are as defined in Table 4. In each of the test scenarios 50 random generations of the training,
validation and test subsets were created and tested and the results are the averages over the 50 runs.
In addition in each of the test scenarios both ANFIS and MRA were used for prediction and their
results are compared in the rest of this section. The results across the different test scenarios are
also compared.
Error Measure
Formula
Root Mean-squared Error (RMSE)
Mean Absolute Error (MAE)
Mean Absolute Percentage Error (MAPE)
Table 4. Error measures
Tables 5 and 6 show the results of price prediction without clustering. Both ANFIS and MRA were
used in the prediction and results of two different test scenarios are shown in the tables. The first
set of results was obtained without MPC as an input variable and the second set of results with
MPC as an input. One can make two observations regarding the results. First, the addition of MPC
as an input variable improved the prediction accuracy for both ANFIS and MRA. For example the
percentage of properties with cumulative MAPE less than or equal to 10% are 38.6% (20.1+18.5)
of all the properties for ANFIS and 34% (17.6+16.4) for MRA. After the MPC was added as an
Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 25 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
input, the prediction results improved to 41.5% for ANFIS and 38.5% for MRA. Second, in both
cases ANFIS outperformed MRA. For example, with MPC added to the input, the percentage of
properties with cumulative MAPE less than or equal to 10% improved from 38.6% to 41.5% for
ANFIS and from 34% to 38.5% for MRA. Similarly for RMSE and MAE the addition of MPC
improves the prediction results and again ANFIS outperformed MRA. See Table 6 for the results.
These results demonstrate that the use of MPC as an input is likely to improve the prediction
accuracy.
%
Without MPC as Input
With MPC as Input
ANFIS
MRA
ANFIS
MRA
≤ 5
MAPE
20.1
17.6
22.3
20.7
(5,10]
MAPE
18.5
16.4
19.2
17.6
(10,15]
MAPE
14.5
13.8
14.6
13.5
(15,20]
MAPE
10.6
10.6
10.4
10.3
(20,25]
MAPE
7.7
8.3
7.6
7.7
>25
MAPE
28.7
33.4
26
30.1
Total
100.0%
100.0%
100.0%
100.0%
Average
MAPE
28.6
30.1
26.8
28.2
Table 5. MAPE prediction results without clustering
$
Without MPC as Input
With MPC as Input
RMSE
MAE
RMSE
MAE
ANFIS
MRA
ANFIS
MRA
ANFIS
MRA
ANFIS
MRA
Average
37742
41345
27805
31147
35289
37763
25747
27957
Max
39146
42094
28551
31687
36427
38740
26202
28687
Min
36904
40121
27107
30185
34399
36931
25103
27342
Std. Dev
519
452
336
368
444
437
272
358
Table 6. RMSE and MAE prediction results without clustering
Next we describe the prediction results after clustering. The modified FCM approach described in
the Methodology section was applied to our dataset and as a result 10 clusters were created. Table
7 shows the descriptive statistics of the 10 clusters. Because of space constraints only the statistics
for a select number of variables are shown. Three variables were used in clustering: Floor Size,
Year-Built, and Basement Size. Other combinations of variables were tried but these three yielded
the best clustering results. One can see that Cluster 1 includes relatively moderately priced houses
with a mean price about $99,355 and with a mean year built of 1959. Cluster 4 contains the most
Journal of International Technology and Information Management Volume 24, Number 1 2015
© International Information Management Association, Inc. 2015 26 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
expensive houses and more recently built houses. Their mean price is around $347,533 and the
average year built is 1999.
Cluster
n
Mean
Sale
Price($)
Mean
MPC($)
Floor
Size
Year-
Built
Basement
Size
Baths
Garage
Size
1
3672
99355
100701
1135
1959
8
1.4
0.8
25240
36667
225
6
51
0.8
0.9
2
4187
215815
217132
1869
2002
12
3.6
1.5
77079
64190
469
4
71
0.7
0.7
3
2209
89539
88014
1322
1913
8
1.6
0.6
61058
45555
386
11
52
0.9
0.8
4
767
347533
352924
2426
1999
1205
5.1
1.9
84533
61462
479
6
239
1.0
0.3
5
812
135317
136655
1372
1980
21
2.5
1.0
39853
26773
301
6
81
0.9
0.9
6
1318
106043
106434
1124
1942
34
1.5
0.8
58943
46082
348
5
108
0.9
0.8
7
233
202665
204627
2166
1962
5
3.4
1.5
63398
37381
250
7
37
0.9
0.8
8
538
138854
140421
1224
1958
703
2.2
1.1
36400
25278
193
5
139
1.0
0.8
9
235
283115
282030
2184
1998
722
4.6
1.9
58193
29115
337
6
83
1.0
0.3
10
2612
224894
223417
1959
1969
567
3.5
1.3
138839
114806
957
28
548
1.6
0.9
Table 7. Descriptive statistics (the means and standard deviations) for clustered data
Table 8 and 9 show the MAPE results of prediction for all 10 clusters. Though only 3 variables
are used in clustering, all 18 variables were used in testing, or price prediction. The tables show
the prediction results for all the 10 clusters with and without the use of MPC as an input variable.
Please note MPC was calculated after clustering using neighboring properties within the cluster.
Table 8 shows the MAPE results for ANFIS and Table 9 shows the MAPE results for MRA.
Freddie Mac’s (the Federal Home Loan Mortgage Corp.) criterion states that on the test data, at
least half of the predicted sale prices should be within 10% of the actual prices (Fik, Ling, and
Mulligan, 2003). The ANFIS MAPE results show that 2 of the 10 clusters meet the Freddie Mac
criterion. These clusters (2 and 4) account for about 30% of the records. Results with MPC are
slightly better than those without MPC as an additional input. Clusters 2 and 4 with MPC as an
additional input have 66.7% and 55.3% of the records in the respective clusters with cumulative
MAPE less than or equal to 10% and the same clusters yield 61.5% and 53.1% without the use of
MPC as an additional input.
Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 27 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
The cumulative MAPE results for MRA produce much better results with 5 clusters meeting the
Freddie Mac criterion when MPC is used as an input. These are clusters 2, 4, 5, 8, and 9, accounting
for about 40% of all the records. The results obtained without MPC as an input are not as good,
with only 3 clusters meeting the Freddie Mac criterion.
%
MAPE Results with MPC as Input (k=10, uij=0.8)
1
2
3
4
5
6
7
8
9
10
Average
18.4
10.9
58.2
17.4
82.9
48.7
84.1
21.0
29.1
22.6
<= 5
22.8
38.3
9.4
30.4
15.6
12.7
12.3
21.3
17.2
20.5
(5,10]
20.8
28.4
9.3
24.9
14.6
12.6
13.2
20.3
15
18.5
(10,15]
16.4
15.7
9
17.7
12
11.6
11.4
17
12.4
16
(15,20]
12.5
8
8.3
10.3
9.6
10.2
10.3
11.9
11.2
12.4
(20,25]
7.8
3.7
7.9
5.7
7.8
8.8
7.8
8.7
8.4
8
>25
19.6
5.9
56
10.9
40.3
44.1
45
20.8
35.7
24.7
Without MPC as Input
Average
21.2
11.8
75.0
15.2
34.0
52.6
80.3
24.1
24.9
23.5
<= 5
20.6
34.1
6.5
28.8
21
10.4
12.6
19.7
24.6
19.1
(5,10]
18.4
27.4
6.8
24.3
18.5
10.8
11.5
18.2
22.7
17.7
(10,15]
14.8
16.7
6.8
19.2
15.7
9.8
12
15
16.2
15.3
(15,20]
11.8
9.5
6.7
11.5
11.3
9.4
9.5
13.4
11.4
12.6
(20,25]
9
4.7
6.9
6
8
8.5
8.4
9.4
6.8
8.6
>25
25.3
7.6
66.2
10.2
25.4
51.1
46
24.3
18.4
26.7
Table 8. MAPE results for clustered data using ANFIS
%
Results with MPC as Input (k=10, uij=0.8)
1
2
3
4
5
6
7
8
9
10
Average
18.2
11.9
56.5
8.9
15.3
34.0
14.2
14.2
7.8
24.1
<= 5
23.1
34
9.7
37.2
27.9
14.2
24.7
26.7
41.5
18.4
(5,10]
21
27.2
10
28.9
22.1
13.9
20.9
23.4
29.2
17.7
(10,15]
16.2
17
9.8
18.3
16.4
12.6
17.3
19.8
15.6
15.3
(15,20]
12.4
10.5
8.8
8.2
12.1
10.8
13.2
11.5
8.2
12.5
(20,25]
8.1
4.4
8.3
3.2
7.7
9.6
9
6.5
3.8
8.5
>25
19.2
6.9
53.4
4.2
13.8
38.9
15
12
1.7
27.7
Results without MPC as Input
Average
20.7
13.0
71.4
10.7
16.1
39.3
15.6
16.3
8.3
25.0
<= 5
20.6
29.7
6.9
30.5
26.1
11.3
22
21.6
40.1
17.2
(5,10]
18.7
24.3
7
26.5
22.3
11.1
19.7
20.7
28.1
15.8
(10,15]
15.5
17.8
7.1
20.5
16.3
11.3
16.2
18
15.9
15.5
(15,20]
12.1
12.2
7.2
10.9
12.1
10.6
13.5
13.9
8
12.6
(20,25]
9.1
6.6
7
4.9
7.6
9.5
10.2
9.2
5.2
9
Journal of International Technology and Information Management Volume 24, Number 1 2015
© International Information Management Association, Inc. 2015 28 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
>25
24.1
9.3
64.8
6.7
15.5
46.2
18.5
16.5
2.7
30
Table 9. MAPE results for clustered data using MRA
Significantly different patterns can be observed when analyzing the RMSE and MAE results with
and without MPC as an additional input to the ANFIS and MRA models for clustered data (Tables
10 and 11). Table 10 shows that the ANFIS models with MPC as input generated the lowest
average RMSE=20966 and MAE=15610 for Cluster 1, and the highest average RMSE=373130
and MAE=131273 for Cluster 7. The average RMSE and MAE over all 10 clusters with MPC are
125989 and 51723, respectively. Table 10 also depicts that the ANFIS models without MPC as
input generated the lowest average RMSE=24252 and MAE=17986 for Cluster 1, and the highest
average RMSE=378183 and MAE=129471 for Cluster 7. The average RMSE and MAE over all
10 clusters without MPC are 107562 and 46504, respectively.
Table 11 shows that for all 10 clusters MRA-based models produce much lower errors than the
same models created with ANFIS. For example, the models with MPC yielded the lowest average
RMSE=20655 and MAE=15429 for Cluster 1, and the highest average RMSE=47538 and
MAE=36584 for Cluster 10; whereas the models without MPC generated the lowest average
RMSE=23092 and MAE=17512 for Cluster 1, and the highest average RMSE=50471 and
MAE=39306 for Cluster 10. The average RMSE and MAE over all 10 clusters with MPC are
31014 and 23691, respectively. The average RMSE and MAE over all 10 clusters without MPC
are 35708 and 27203, respectively.
Thus for clustered data the MRA-based models produce significantly lower minimum, maximum,
and average errors than ANFIS-based models. However, adding MPC as input to the ANFIS and
MRA models reduces the minimum, maximum, and average errors only in the MRA-based models.
ANFIS Results with MPC (k=10, uij=0.8)
1
2
3
4
5
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Avg
20966
15610
27430
19271
39352
29696
177597
53826
341767
96650
Max
21762
16261
29419
20185
42634
31982
1121857
138641
998127
259150
Min
20099
14998
25305
17877
36674
27948
41584
31881
80434
37433
Std.
Dev
427
303
762
470
1483
1014
192772
20332
189901
47211
6
7
8
9
10
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Avg
70400
31606
373130
131273
42061
24902
120484
79628
46707
34771
Max
265738
47729
1968765
527001
245094
59434
637260
298607
50263
37421
Min
34558
25403
49669
39435
24595
18879
53022
38054
44419
32986
Std.
Dev
48703
4941
398401
109298
32450
6182
108661
52797
1396
1022
ANFIS Results without MPC as Input
1
2
3
4
5
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Innovative Clustering Approach to Market Segmentation D. Shi, J. Guan, J. Zurada & A. S. Levitan
© International Information Management Association, Inc. 2015 29 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
Avg
24542
17986
31278
21655
52158
38723
116439
48160
132191
38746
Max
51014
20556
41023
23474
76836
44722
318738
76245
362078
69516
Min
22664
16998
28694
20671
47357
36332
46322
36081
24998
19379
Std.
Dev
4058
597
2534
639
6053
1586
72435
8820
93514
13531
6
7
8
9
10
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Avg
74604
36460
378183
129471
52675
28887
163649
67773
49900
37181
Max
365356
68075
2267246
445391
147917
53655
1194930
368236
55765
40005
Min
39578
29977
53709
38548
27426
20000
31652
25525
46615
34707
Std.
Dev
61183
6657
428252
103042
29659
6797
235130
66197
1825
1157
Table 10. RMSE and MAE results for clustered data using ANFIS
MRA with MPC as Input (k=10, uij=0.8)
1
2
3
4
5
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Avg
20655
15429
28623
20793
37295
28434
38053
29524
22656
17043
Max
21606
16065
30582
21718
39535
29940
43547
33590
26474
19237
Min
19578
14737
26810
19418
34888
26465
34122
26723
19802
15472
Std.
Dev
473
329
799
505
1091
848
1889
1497
1429
880
6
7
8
9
10
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Avg
31309
23763
33935
26560
22658
17285
27416
21497
47538
36584
Max
34440
26275
41069
31796
25805
19672
34241
27039
49773
38321
Min
28527
21848
24542
19261
18687
14823
21130
15669
45506
34836
Std.
Dev
1400
975
3926
3053
1466
1051
2931
2203
1054
903
MRA Results without MPC as Input
1
2
3
4
5
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Avg
23092
17512
32141
23846
46405
36593
44022
34870
24030
18121
Max
23934
18318
33733
25201
48861
38811
47771
38160
27646
19874
Min
22091
16852
30647
22663
44060
34560
39973
31777
21308
16352
Std.
Dev
410
346
731
533
1132
993
1884
1536
1454
892
6
7
8
9
10
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Avg
37228
28880
37983
29704
26136
20337
29269
22863
50471
39306
Max
39545
31186
45698
35691
29685
22813
35171
27945
52914
41382
Min
33959
26818
28489
22468
22858
17990
23032
18704
46981
36305
Std.
Dev
1131
909
3505
2782
1512
1127
2664
2218
1274
1140
Journal of International Technology and Information Management Volume 24, Number 1 2015
© International Information Management Association, Inc. 2015 30 ISSN: 1543-5962-Printed Copy ISSN: 1941-6679-On-line Copy
Table 11. RMSE and MAE results for clustered data using MRA
CONCLUSIONS
Data heterogeneity can reduce the predictive accuracy of data mining methods. Segmentation of a
real estate market has been recognized as a viable method for addressing the issue of data
heterogeneity. This paper proposes an innovative method for data clustering to improve predictive
performance. The existing solutions of using spatial and statistics-based methods to
segment/cluster the data have demonstrated the importance of clustering in improving price
prediction. In this paper an approach based on an adaptation of the FCM algorithm, defined on a
newly introduced homogeneity index, was used to create clusters that are more homogeneous.
These resulting clusters were in turn used to predict sale prices. Two different classification
methods were employed in the testing: the traditional and commonly used MRA approach, and
ANFIS. As discussed in the results section, FCM-based clustering and the use of comparable
properties yielded improved and interesting results. Though the prediction results are not uniform
across all clusters, some clusters yield very good prediction results.
In addition to its promising performance when applied to our dataset this new clustering approach
is also simple to implement. The required data are readily available in any real estate sale
transaction. For example any assessment office in a local government already collects and tracks
the type of property records used in this study. The adaptation of the FCM algorithm and the
implementation of the homogeneity index are straightforward and do not require costly collection
and modeling of data. And unlike those clustering methods that depend on the modeling of
socioeconomic data that can be market specific, this new approach can be easily applied across
different housing markets, thus potentially serving as a common tool for property valuation, risk
assessment for lenders, and a consistent basis for government policy formulation.
Acknowledgment: This work was partially supported by the Prometeo Project of the Secretariat
for Higher Education, Science, Technology and Innovation of the Republic of Ecuador.
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