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Data analysis plays an increasingly valuable role in sports. The better the data that is analysed, the more concise training methods that can be chosen. Several solutions already exist for this purpose in the tennis industry; however, none of them combine data generation with a wristband and classification with a deep convolutional neural network (CNN). In this article, we demonstrate the development of a reliable shot detection trigger and a deep neural network that classifies tennis shots into three and five shot types. We generate a dataset for the training of neural networks with the help of a sensor wristband, which recorded 11 signals, including an inertial measurement unit (IMU). The final dataset included 5682 labelled shots of 16 players of age 13–70 years, predominantly at an amateur level. Two state-of-the-art architectures for time series classification (TSC) are compared, namely a fully convolutional network (FCN) and a residual network (ResNet). Recent advances in the field of machine learning, like the Mish activation function and the Ranger optimizer, are utilized. Training with the rather inhomogeneous dataset led to an F1 score of 96% in classification of the main shots and 94% for the expansion. Consequently, the study yielded a solid base for more complex tennis analysis tools, such as the indication of success rates per shot type.
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Classification of Tennis Shots with a Neural Network Approach
Andreas Ganser 1, Bernhard Hollaus 1,* and Sebastian Stabinger 2
Citation: Ganser, A.; Hollaus, B.;
Stabinger, S. Classification of Tennis
Shots with a Neural Network
Approach. Sensors 2021,21, 5703.
Academic Editor: Anthony Fleury
Received: 15 July 2021
Accepted: 18 August 2021
Published: 24 August 2021
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Attribution (CC BY) license (https://
Department of Mechatronics, MCI, Maximilianstraße 2, 6020 Innsbruck, Austria;
2Deep Opinion, 6020 Innsbruck, Austria;
*Correspondence:; Tel.: +43-(0)-512-2070-3934
Data analysis plays an increasingly valuable role in sports. The better the data that is
analysed, the more concise training methods that can be chosen. Several solutions already exist for
this purpose in the tennis industry; however, none of them combine data generation with a wristband
and classification with a deep convolutional neural network (CNN). In this article, we demonstrate
the development of a reliable shot detection trigger and a deep neural network that classifies tennis
shots into three and five shot types. We generate a dataset for the training of neural networks with the
help of a sensor wristband, which recorded 11 signals, including an inertial measurement unit (IMU).
The final dataset included 5682 labelled shots of 16 players of age 13–70 years, predominantly at an
amateur level. Two state-of-the-art architectures for time series classification (TSC) are compared,
namely a fully convolutional network (FCN) and a residual network (ResNet). Recent advances in
the field of machine learning, like the Mish activation function and the Ranger optimizer, are utilized.
Training with the rather inhomogeneous dataset led to an F
score of 96% in classification of the main
shots and 94% for the expansion. Consequently, the study yielded a solid base for more complex
tennis analysis tools, such as the indication of success rates per shot type.
Keywords: deep learning; wearable computing; activity recognition; tennis shot classification
1. Introduction
In society, interest is growing in monitoring physical performance in everyday life as
well as in sports. Sales of wearable devices, such as fitness trackers or chest straps, have
been growing tremendously over the last decade [
]. The mainstream solutions focus on
supervising heart rate and motion recognition (e.g., step counters or position tracking with
the help of inertial measurement units (IMU) and global positioning systems (GPS) [
As stated in [
], IMUs, in particular, are frequently used to collect information about
training progress and general sports analytics. Analysing this data helps with improving
the training specificity and preventing injuries [8,9].
For training purposes on a competitive level, more advanced sport-specific solutions
are needed. In swing based sports, such as tennis, badminton, and squash, the shot
performance is valuable information to develop better training and game plans. How
interesting would it be if the worn smartwatch could tell the tennis player how fast their
fastest service was during the last match? If this information is combined with the success
rate of the respective shot type, insights for the next training session could be obtained.
The prerequisite for such a sophisticated analysis is the reliable detection and classification
of tennis shots, which is the topic of this study.
1.1. Market Analysis
The market already provides several solutions for tennis shot analysis. They can be
grouped into three categories:
Camera-based analysis tools, such as PlaySight [
], have a high shot recognition rate
and can enable detailed evaluations depending on the complexity of the algorithm.
The drawback of this technology is its high price [
]. Hence, these systems are not
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widespread and are mostly used by players who are on a professional level. Vision
recognition tools are not further considered in this study since the solution should, in
the long run, be available for a broad audience.
Racket integrated solutions, provided by tennis racket manufacturers, are cheaper
than the previous technology, but lack in recognition accuracy [
]. An associated
study [
] using the Pan Tompkins algorithm for shot detection and time warping
for shot classification achieved an accuracy close to 96%. Nevertheless, the sensors
were fixed to a racket and were, therefore, non-mobile. Additionally, the recognition
of topspin and backspin has an accuracy of only 80%. Furthermore, the attachment of
sensors to the racket changes the fine-tuned centre of mass.
Wrist-worn wearables, using the dynamic time warping (DTW) algorithm [
can achieve a shot classification accuracy of up to 99%, but remain close to 80%
for topspin and backspin detection [
]. Another technology for wrist wearables
compared neural network approaches to feature recognition and reached a success
rate of 94% for groundstrokes [
]. A study published in 2017 by [
] generated
data with an IMU, worn at the wrist, and also compared several approaches for
shot classification. In general, the rather classical support-vector machine (SVM)
performed best with an accuracy of 97.4% for the groundstrokes, specifically the
forehand, backhand, service and false shot. Whiteside et al. also implemented a nine-
shot type classifier with a mean accuracy of 93.2%. The SVM classifier distinguishes
between forehand topspin, slice and volley; backhand topspin, slice and volley; serve;
smash; and false shot. The support vector machine is followed by a deep neural
network classifier, reaching an accuracy of 96.6% for the four groundstrokes. The
extended version reaches 90.4% for the nine shot types classifier.
State-of-the-art deep neural networks are well suited for time series classification
(TSC) [
] and give new possibilities in classifying tennis shots. Unfortunately, [
] does
not give deeper insight into the creation and application of the classifier. As the literature
analysis revealed, there are currently few tennis shot recognition solutions with a deep
neural network classifier at the core since this combination is relatively new.
1.2. Biomechanics in Tennis
For a better understanding of the sensor signals, shown in Section 2.1, it is vital to
understand tennis shots anatomically. The focus lies on the upper limb—more specifically
the shot hand. The movement of the upper extremity in tennis sports can be described as a
combination of four basic motions [19]:
1. Pure swing of the upper arm around the shoulder joint: ground swing.
2. Elbow joint flexion and extension: increases the swing.
Forearm pronation and supination: rotation around the forearm longitudinal axis,
responsible for the topspin or backspin.
4. Wrist extension and flexion: tilt of the wrist, also increases the swing.
Additionally, Ref. [
] separates tennis shots into several sequential stages, which are
outlined on the example of a forehand shot in Figure 1:
Figure 1. Sequence of a tennis forehand, subdivided in four parts.
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Preparation/Backswing: the hand starts at resting position, throws the ball up;
at the same time, the racket is guided upwards and down behind the back with
a flexion of the shoulder and the elbow joint; the phase finishes when the racket
reaches the lowest point.
Action phase/Forward swing: the shot forearm and shoulder joint are extended;
the racket is guided upwards and forwards; the impact of ball and racket ideally
occurs at the highest point, so fully extended elbow and wrist, arm showing up-
Follow-through: after the impact, the kinetic energy of the movement has to be
dissipated, which is done by letting the momentum run out by swinging the
shoulder through; usually, the racket stops at a very low point.
Retraction: bringing the shot hand back into a neutral position to be ready for the
next shot.
These four phases are present in all tennis shot types, but differ in the combination of
the anatomical motions, which results in distinguishable sensor signals. The tennis shots
are categorized into three groundstrokes, which are expanded with the spin to five shot
types in total and are described in Table 1.
Table 1.
Division of the tennis shots separated into groundstrokes and their expansion. The abbrevia-
tion for the respective shots is also noted.
Groundstrokes Expansion
Forehand (F) Topspin (FT)
Slice (FS)
Backhand (B) Topspin (BT)
Slice (BS)
Service (S) Service (S)
Slice and volley are combined into one shot as the motion is very similar. The same
applies to service and smash, which are anatomically the same movement with a different
location on the court.
2. Methods
2.1. Shot Detection
To enable shot detection in tennis, a platform to gather data of the shots is needed
and should provide data containing information on the shot type. Other sports have used
wearables successfully to gather such data [
]. We also used this approach using
wearables in this paper.
2.1.1. Hardware
The wearable used for recording the dataset was the SensorTile development kit
(STEVAL-STLKT01V1) of STMicroelectronics, Geneva, Switzerland, which is illustrated in
Figure 2and includes the sensors mentioned in Table 2. The development kit is chosen for
the tennis shot detection task since it has already proved its abilities in a catch detection
application for American Football [
]. Additionally, the sensor kit comprises all relevant
sensors to monitor motion, pressure, and audio in satisfying sample rates and ranges,
which is key for a later classification.
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Table 2.
Sensor properties as set on the development kit. Recording sensor, output data rate (ODR)
and full scale (FS) are assigned to the respective signal. For more information, we refer the reader to
the relevant datasheets [2329].
No. Signal Sensor ODR FS
1 Acceleration aLSM6DSM 1660 Hz 156.96 m/s2
1 Angular velocity ωLSM6DSM 1660 Hz 2000 °/s
2 Magnetic field BLSM303AGR 100 Hz 49.152 G
3 Pressure pLPS22HB 75 Hz 1260 hPa
4 Quantized audio signal MP34DT05-A 8000 Hz 122.5dB SPL
Figure 2.
Sensor tile displayed as (
) the board itself with numbered sensors according to Table 2,
adapted from [24], and (b) the complete wearable with marked sensor axes, worn on the wrist. The
axes for the accelerometer ax,ay, and the gyroscope ωx,ωyare displayed.
2.1.2. Shot Detection Algorithm
The shot detection algorithm is implemented in the programming language Cwith
a finite state machine (FSM) [
]. The FSM, designed for shot detection, is visualized in
Figure 3and is composed of eight states. These states are implemented in the main as well
as three timers. Figure 3shows not only the sequential process but also where the state
is realized.
For example, the triggering procedure, responsible for recognizing the tennis shots,
is located in timer 1 (TIM1), which runs with
1 kHz
. Triggering is done in the states
RUNNING, READY_TO_BE_TRIGGERED, and TRIGGERED and is further described in
Section 2.1.3. The basis for triggering is the accelerometer and gyroscope data, which are
saved as signals in circular buffers [
]. The magnetometer and the pressure signal are
collected in TIM2, which runs with
100 Hz
, since the ODRs of the respective sensors do
not allow faster sampling. An exception is the audio data which is gathered in TIM3 with
the highest sampling rate, namely
8 kHz
, to capture all the expected frequencies during a
tennis shot.
Responsible for accessing the sensor signals and writing them into the respective cir-
cular buffer is the state COLLECT_DATA, which, therefore, has to run in all the above men-
tioned timers. This state is active during the states RUNNING, READY_TO_BE_TRIGGERED
and TRIGGERED since samples have to be collected before and after triggering to save
the complete shot sequence as mentioned in Section 1.2. Several sensor data plots, like
Figure 4a,b
show that
1 s
is sufficient to cover the whole shot. Furthermore, the plots reveal
that the buffer has to be filled with 500 ms of data before and after the trigger.
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Figure 3.
Flowchart of the state machine running on the microcontroller. Note that there is an
annotation about the location of the state.
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t / s
j/ (m/s³)
x 10
triggering window
t / s
ω / (°/s)
Figure 4.
) and angular velocity in y-direction
raw and filtered (
) of a forehand topspin
compared to the trigger thresholds. The time delay of the filtered ωyis clearly visible.
2.1.3. Triggering
Searching for an adequate trigger, which is responsible for recognizing tennis shots
and, therefore, starting the saving process of the sensor values, is one key aspect of this
study. A selective trigger decreases the post-processing effort, since less falsely detected
shots have to be discarded. Optimally, it captures every performed shot, corresponding
to a high sensitivity. Since there is a conflict between sensitivity and selectivity [
], a
suitable trigger algorithm has to be found.
The trigger is realized with two components. A combination of a value modelling
the impact of the ball on the racket and another value representing the specific swing
performed during tennis shots is chosen. In this way, the balance between falsely detected
shots and undetected shots is optimized. On the one hand, the final trigger must capture
all types of shots named in Section 1.2. On the other hand, several scenarios are considered
that should not be detected:
1. A player hitting his racket on the ground to pick up a ball: high impact, low swing.
2. A player swinging his racket without hitting a ball: low impact, high swing.
3. A player sprinting or jumping: mid impact, low swing.
All in all, three triggering solutions are investigated; however, only the finally imple-
mented method is described in more detail. The other two approaches are accessible in
Appendices A.1 and A.2.
The jerk is chosen as the adequate parameter for the impact of the ball on the racket.
The jerk is the change rate of the acceleration with respect to the time. The acceleration is
changing with a high frequency when the ball hits the racket, consequently, with a high
rate of change. Figure 4a shows the high lobes of the jerk during a forehand topspin. The
derivative is taken from the absolute acceleration because the combined signal shows
higher peaks during the vibrations of the racket.
We empirically determined that a jerk threshold of 18,000
led to reliable trigger-
ing. The threshold is compared to a forehand topspin in Figure 4a.
The angular velocity around the y-axis
might be a suitable representative of the
pure swing components as is illustrated in Figure 4b. It exhibits a high peak for all shot
types. Nevertheless,
is also high during shocks which arise, for example, when running
or hitting the racket on the ground. Hence, the threshold is compared to a low-passed
signal. The finite impulse response (FIR) filter is designed to cut frequencies higher than
15 Hz
with an order of
53. It is designed with a Kaiser window function. The filter
coefficients and the magnitude response is illustrated in Figure 5.
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10 20 30 40 50
Frequency/ Hz
Amplitude/ dB
Figure 5. (a) FIR filter coefficients and (b) frequency response of the FIR filter.
As a consequence, the vibrations caused by hard hits or the impact of the ball are
vanished as can be seen in Figure 4b. This configuration adds an delay
to the sensor
signal according to
2fs, (1)
as the sampling frequency. Calculation with
53 and
fs=1000 Hz
yields a
td=26 ms
, which is still in an acceptable range. The threshold is set to
280 ° s1
can be seen in Figure 4b.
Due to the delay of the filter, a window with a size of
50 ms
is implemented. Both
thresholds must be exceeded in the latter; otherwise, the trigger is not set. Figure 4a shows
the triggering window for the first overshooting of the threshold. The window is restarted
after the threshold is surpassed again.
2.2. Generation of the Dataset
Data was collected during training and games of players on a mainly competitive
amateur level. In total 16 players, 6 male and 10 female, from an age of 13 to 70 years old
wore the wristband to cover a wide range of playing styles. The participants were informed
about the MCI ethics assessment and signed a declaration of consent. Additional to the
data collection with the wristband, a camera was used to record the session and to label
the datasets later on.
Before being able to use the data for training and validating the shot classifier, some
pre-processing was performed on the datasets. Neural networks require a feature vector or,
in this case, a tensor as input with all entries having the same amount of samples, but the
collected sensor buffers have different lengths because of the varying sampling frequencies
mentioned in Section 2.1.1. Therefore, the missing sensor samples were interpolated
linearly to match the amount of samples of the audio signal. Moreover, the pressure signal
did not show a remarkable change whenever a shot was performed. This, and the fact that
it was only sampled with a frequency of
100 Hz
led to the decision to exclude the pressure
data from the dataset. The remaining ten sensor buffers, which are displayed in Figure 6,
were extended with the shot hand information encoded as dummy values.
The resulting input feature tensor has a dimensionality of 11
7000 and consists of
Z-Score normalized values. The Z-Score of each sample is derived according to [34]:
σ, (2)
as the current sensor value,
as the standard deviation, and
as the arithmetic
mean value of the respective shot and sensor.
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The output feature tensor contains the one-shot encoded shot type information. After
the labelling process, the datasets are anonymised by shuffling them several times and
renaming them incrementally.
(a) (b)
(c) (d)
Figure 6.
Visualisation of the 10 sensor signals of a forehand topspin with annotated sequences as
mentioned in Section 1.2: (
)x,y,zcomponent of the accelerometer, (
)x,y,zcomponent of the
gyroscope, (c)x,y,zcomponent of the magnetometer, and (d) quantified audio signal.
2.3. Shot Classification with a Deep Convolutional Neural Network
Deep neural networks (DNN) have shown especially promising results in speech
recognition [
] and natural language processing (NLP) [
]. NLP and speech recognition
have the sequential aspect of the data in common, which is also an important feature of the
time series data processed in this study. The authors in [
] saw this as an opportunity to
research deep neural network performance regarding TSC problems. One main question
of his review was whether DNNs could surpass standard classification processes, like
the hierarchical vote collective of transformation-based ensemble (HIVE-COTE) [
] or
dynamic time warping
(DTW) [13,14]
as used in a tennis shots classification approach
by [15], in terms of computational effort and classification accuracy.
Based on the research in [
], the two best-performing architectures were adapted for
the classification problem of tennis shots. The best performers, namely a fully convolutional
network (FCN) and a residual network (ResNet), are categorized as discriminative end-to-
end approaches [
]. End-to-end models do not require any hand-engineered features
of the input training data. The particular architectures learn the feature extraction on their
own while fine-tuning the classifier in the backpropagation process [42,43].
2.3.1. Architecture of the FCN
FCNs were first presented for a time series classification problem in 2016 by [
The FCN for the shot classification is built with four hidden layers, and the input and
output layer. The main components are the three convolution blocks. The first convolution
consists of 128 filters with a length of eight; the second contains 256 filters with a filter
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length equal to five. The last convolution reduces the number of filters back to 128 and
the filter length to three. Every convolution is pursued by a batch normalization [
]. The
output of the batch normalization is fed into a Mish activation function [
]. After the third
convolutional block, a global average pooling (GAP) layer [
] is applied, followed by a
softmax operation [
]. Furthermore, the length of the time series is kept constant with
adequate zero-padding until the GAP layer. Figure 7shows the complete architecture of
the FCN.
Layer 1
128 filters
Layer 2
256 filters
Layer 3
128 filters
11 channels
Layer 4
128 neurons
3 classes
Figure 7. Schematic visualization of the FCN architecture for the three classes model.
2.3.2. Architecture of a ResNet
Residual networks, first published in an image classification competition in 2015
by [
], are convolutional networks with up to 1000 layers that are still trainable. This
deepness is made possible by the so-called “identity shortcut connections”, which skip one
or more layers [
]. Via these connections, the gradient can flow backwards unimpeded.
Thus, the vanishing gradient problem is reduced, making it possible to use deeper networks
that can mimic more complex functions.
In 2016, the researchers in [
] released a relatively deep ResNet for time series
classification. This architecture consists of the indispensable input layer, nine convolutional
layers, and one GAP layer that is fully connected to the output layer with the classical
softmax activation. The nine convolutional layers are dividable into 3
3 blocks of similar
structure: The first of these three blocks consists of three convolutions with 64 filters of size
eight, five, and three. Each convolution is followed by batch normalization and the Mish
activation function, apart from the last one.
After the third filter and batch normalization, the interim result is added to the identity
of a shortcut connection. The sum is activated with a Mish function and then fed into the
next block. The consecutive blocks differ only slightly. The amount of filters is increased
to 128, the rest is kept as before. The shortcut connections take the output of the latter
block instead of the input layer. For a better understanding, the architecture is visualized
in Figure 8.
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Figure 8.
Visualization of the ResNet architecture for the three shot types classification. The first
9 hidden layers are divided into 3
3 similar blocks. Each block has a shortcut connection to the
previous one.
2.3.3. Training of the Deep Neural Network Classifiers
The creation of the classifiers is implemented in Google Colaboratory [
], which is a
cloud service based on Jupyter Notebooks [
]. It offers a free-of-charge use of a graphics
processing unit (GPU) such as an NVIDIA Tesla T4, (NVIDIA, Santa Clara, CA, USA),
which outperforms standard central processing units (CPU) by far [
]. Training sessions
of the tennis shot classification are executed around 25–30-times faster. Another reason for
the use of Google Colab is the out-of-the-box support of the open-source deep-learning
library Keras [54], which runs on Tensorflow [55] as a backend.
A successful training is strongly dependent on the quality of the training and val-
idation set. An important measure is that all the classes are represented as equally as
possible in all sets. The used stratified K-Folds cross validator [
] splits the dataset into n
folds and preserves the percentage of samples for every class. For this application, four
folds are created, meaning that four different models are trained. Figure 9illustrates the
operating principle of stratified K-Folds, which swaps the training and validation sets for
every iteration. The fact that more than one model is created allows creating averages
and standard deviations of several metrics for checking the real capability of the model,
independent from the weight initialization.
Figure 9.
Operating principle of the K-Folds cross validator. The shuffling of the stratified sets leads
to dissimilar models per iteration.
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As an optimizer, Ranger [
] is used. Ranger is a combination of three algorithms,
namely RectifiedAdam (RAdam) [
], Lookahead [
] and Gradient Centralization (GC) [
Ranger is not yet implemented in TensorFlow nor in Keras. Nevertheless, the documenta-
tion of RAdam proposes the integration of the Lookahead optimizer to generate the Ranger
optimizer. This modification is used for the shot classification training. The GC add-on is
left for future work.
Another critical question is the training time, more specifically, how many training
epochs should be used. An exemplary training session is displayed in Figure 10. The train-
ing finished here after 130 epochs, and the results were stable after 60. The training epochs
are fixed to this empirically determined value. The duration of this exemplary training
process was
13 min
, resulting in
6.1 s
per epoch. In conclusion, the settings mentioned
above resulted in stable behaviour.
Figure 10. Training history of (a) accuracy and (b) categorical cross entropy (CCE).
3. Results
3.1. Shot Detection Trigger
The setup described in Section 2.1.3 yielded a 91% success rate of shot detection. The
other investigated solutions were abandoned due to the reasons mentioned in
Appendix A.3
False positives were very rare, only 2%. The trigger was not set in situations that are
closely related to a shot, for example, when a player picks up the ball from the ground by
hitting it several times. However, the time intensive data saving, which takes nearly
2 s
, is
the reason why quick consecutive shots were not captured, for example when one player
was at the net and playing volleys. Furthermore, in rare cases, the backhand slice was not
detected because of the unfavourable orientation of the wearable that resulted in a lower
3.2. Dataset
Overall video material of 18 h resulted in 5682 labelled tennis shots. The distribution
over the shot types is illustrated in Figure 11. The slice version of the shots is, with 6.35%
for backhand and 2.87% for forehand, significantly under-represented, although volley
and slice are already combined. For the groundstroke dataset, the two backhand types
were combined, resulting in 1439 shots that had a 25% contribution to the overall training
set. Additionally, the forehand shots were merged, which yielded 3344 shots or 59%.
Services were the same as before. Another statistic is the division of the dataset into left
and right-handed players. Here, left-handed shots are represented with only 7%.
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Backhand Slice: 361
Backhand Topspin: 1078
Forehand Slice: 163
Forehand Topspin: 3181
Service: 899
Figure 11. Distribution of the shot types in the final training set.
3.3. Shot Classification
The final results of the classifiers are shown for the three classes networks and five
classes networks. First, the three classes model is compared for the FCN and ResNet.
Second, the result of the five classes network is only shown for the ResNet, because of the
reasons mentioned in Section 3.3.1. All following metrics are introduced in [61].
3.3.1. Three Shot Types Classification
The normalized confusion matrices of the respectively best iterations in Figure 12
indicate strong diagonals.
(a) (b)
Figure 12.
Normalized confusion matrix for the FCN (
) and the ResNet (
) comparing the three
classes: backhand (B), forehand (F), and service (S).
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Table 3shows the results in more detail. The F
score for all shot types is in the range
of 94–97%. The recall and precision are constantly high with values between between
Table 3.
Recall (R), precision (P), and F
score (F
) for FCN and ResNet for the respective shot types
of the best model.
FCN ResNet
R P F1R P F1
B 93% 96% 95% 96% 94% 95%
F 98% 96% 97% 98% 97% 98%
S 93% 94% 94% 93% 96% 95%
Average 96% 96% 96 % 96% 96% 96%
Both architectures are well suited for the classification task with the ResNet having
a slightly better performance. Additionally, the optimization of the ResNet architecture
reaches a stable state on average five epochs faster. Moreover, forehand seems to be a little
easier to predict. The reason might be the higher representation of forehands in the dataset.
3.3.2. Five Shot Types Classification
The results of the five classes models are presented only by the ResNet. There is
merely a slight difference in accuracy to the FCN, but the ResNet trained faster.
The confusion matrix in Figure 13 has high percentage values in the diagonal for the
topspin versions and the service, i.e., the standard shots. It has to be mentioned that the
slice variants are less accurately categorized. The wrongly classified samples tend to be
misclassified into the topspin equivalent or as the other ground shot’s topspin. Hence, the
model is overfitted to the ground shots.
Figure 13.
Normalized confusion matrix for the best ResNet comparing the five classes: backhand
slice (BS), backhand topspin (BT), forehand slice (FS), forehand topspin (FT), and service (S).
Table 4illustrates the main metrics for an inhomogenous dataset problem. The results
of the confusion matrix are confirmed. The average is very high, with a percentage of 94%.
The reason for this is the dominating influence of the forehand topspin with nearly 56%
contribution to the whole dataset. Hence, also the low recognition rate of the forehand
slice effects the sample average of the F
score only a little, as it represents only 2.9% of
all samples.
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Table 4. Recall, precision, and F1score for ResNet for the respective shot types of the best model.
R P F1
BS 77% 82% 80%
BT 92% 94% 93%
FS 76% 68% 72%
FT 97% 97% 97%
S 94% 90% 92%
Average 94% 94% 94%
4. Discussion
4.1. Shot Detection Trigger
The shot detection trigger is accurate for the groundstrokes. Improvement lies in the
recognition of the slice variants due to the unfavourable orientation of the wearable. A
possible solution could be a more complex algorithm which includes another trigger value
as representative of slice shots. The data saving time is another bottleneck which does not
allow to capture quick consecutive shots. With these two enhancements, a detection rate of
around 95% can be expected, which lies in the range of the best published research thus
far [
]. As the focus of this study is more shifted towards the generation of a classifier, the
reached accuracy is considered to be sufficient, and optimizations are left for future work.
4.2. Shot Classification
Compared to other approaches, such as dynamic time warping and support vector
machines, mentioned in Section 1, this study reached higher classification accuracies for
the groundstrokes apart from the one mentioned in [
]; however, the less complex and
more module solution justifies the worse recognition rate. The additional distinction
between slice and topspin worsened the performance emphasizing the importance of a
homogeneous dataset.
Furthermore, the classification success was decreased by the limitations of the sensors.
The full scale values of the gyroscope (
2000 ° s1
) and the accelerometer (
156.96 m s2
were exceeded with fast shots. The clipping at the borders adds non-linearities to the
sensor signals. Sensors with a wider measurement range would allow the gathering of
more precise data and could consequently improve the classification accuracy.
4.2.1. Validation of the Dataset Quality
Mislabelled datasets can be a reason for falsely classified shots. During a training
session with 50 iterations, the mispredicted shots were tracked and their unique identifiers
noted. A stratified K-Fold in each iteration ensured that every shot is 50 times in the
validation set. Figure 14 shows how often a shot is falsely classified in how many iterations.
If a shot is incorrectly classified in all fifty iterations, the probability is high that the label is
wrong or it is a complex shot and, therefore, hard to classify.
Note that the histogram in Figure 14 is having its peak at the first two bins. This
indicates that the network is not able to predict these shots in individual iterations. The
uncertainty in the weight distribution of the network is held responsible for this. However,
in 76 of the 5682 shots, located on the far right of Figure 14, the current setup is not capable
of training the DNN to predict certain shots correctly. These are 1.34% of the total dataset.
These shots are either labelled incorrect or seldom occurring and, therefore, hard to train.
Sensors 2021,21, 5703 15 of 20
0 10 20 30 40 50
Amount of misprediction folds
Amount of shots
Figure 14.
The x-axis gives the amount of folds in which a shot is mispredicted. The y-axis is the
amount of shots that occur in the respective bin.
4.2.2. Ablation Study
An ablation study [
] is performed for the three-class ResNet to receive information
about the significance of the input values. The objective is to optimize the input feature
tensor with a simultaneous improvement of the neural network and a possible downsizing
of the sensor board. The mean F
score over four iterations for every configuration is
compared. The sensor values, which are highlighted with a checkmark in Table 5, are left
unchanged, whereas the others are filled with zeroes instead of real values.
Table 5. Ablation study for the input values of the three-class ResNet.
Accelerometer Gyroscope Magnetometer Audio F1-Score
XXX 96.6%
X X X 96.0%
X X X 96.1%
X X X X 96.4%
Interestingly, the ablation study indicates an independence of the DNN classifier
from the audio data. In general, the audio data can be excluded from the feature tensor
and, consequently, also the microphone on the sensor board. Note that the audio data
is sampled with
8 kHz
to capture all the necessary information. If the audio data is not
included, the feature tensor can be reduced considerably. Consequences are a smaller
dataset and network yielding a faster training of the latter.
5. Conclusions and Future Work
This study found that a deep neural network approach reached high accuracies in
tennis shot classification when a rich, homogenous dataset was used. The generation of the
latter one is difficult to obtain when only taking data from games or training sessions since
the groundstrokes are always overrepresented. Data augmentation, including averaging,
amplification, dynamic time warping, addition of noise, etc. [
] is a possibility to
smooth the distribution over the shot types, but was not considered in this study.
Sensors 2021,21, 5703 16 of 20
Nevertheless, high classification rates were achieved with a rather inhomogenous data
set. Recent developments in the architecture of deep learning networks and the newest
research on more stable activation functions and optimizers made this possible.
Furthermore, the results show another capability of deep convolutional neural net-
works for time series classification. The generation of a dataset can be done with much
less domain knowledge because no striking features have to be extracted. Therefore, the
pre-processing effort was reduced drastically.
Triggering with a combination of filtered angular velocity
and jerk
yielded a
reliable detection rate. Since the focus of this study was shifted toward the classification
process, this result is considered sufficiently accurate. The reliability of the triggering
decreased the post-processing effort for labelling the shots, as only few false positives
were detected.
One recommended next step should involve the development of a wearable whose
sensors have adequate full scales. Consequently, the classification accuracy could improve
since the sensor signals will not be clipped. Future work can also focus on better analysis
functions. One suggestion is the development of a real-time shot classification to directly
see information about playing styles—for example, during training sessions or games. The
information could be available in a smartphone application. The used wearable already
has a BlueTooth module, which could be used for the transmission of the data. Valuable
information for the players would also be the quality of the shot and the success rate per
shot. For this purpose, another dataset must be generated. The position of the ball on the
surface of the racket during impact and the success of the shot must be labelled for this.
Furthermore, an implementation of the wearable into a smart-watch would be a step
to create a product that could be offered to a broader audience.
Author Contributions:
Conceptualization, A.G. and B.H.; methodology, A.G. and B.H.; software,
A.G. and B.H.; validation, A.G., B.H. and S.S.; formal analysis, A.G. and B.H.; investigation, A.G., B.H.
and S.S.; resources, A.G.; data curation, A.G.; writing–original draft preparation, A.G.; writing–review
and editing, A.G., B.H. and S.S.; visualization, A.G.; supervision, B.H. and S.S.; project administration,
B.H.; funding acquisition, B.H. All authors have read and agreed to the published version of the
This research received no external funding but was funded within the department of
mechatronics at MCI.
Institutional Review Board Statement:
The study was conducted according to the guidelines of the
Declaration of Helsinki, and approved by the Institutional Ethics Commission of the MCI, Innsbruck,
Austria (protocol code 2020-03-a and date of approval 13 March 2020, statement: Thank you for
submitting the ethics assessment of your work! The MCI Ethics Commission has evaluated your submission
and deemed the therein-described procedure appropriate.”)
Informed Consent Statement:
Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: Samples and code are available from the authors.
The authors would like to thank the MCI for providing the funds to develop
the study and the part-time students for the prework and assistance. Additional thanks goes to the
Tennis Clubs of Innsbruck, especially to the players of the TI Tennis, who played for several hours
with the wearable to generate a vibrant dataset.
Conflicts of Interest: The authors declare no conflict of interest.
The following abbreviations are used in this manuscript:
CNN convolutional neural network
CPU central processing unit
DNN deep neural network
DTW dynamic time warping
Sensors 2021,21, 5703 17 of 20
FCN fully convolutional network
FIR finite impulse response
FS full scale
FSM finite state machine
GAP global average pooling
GPS global positioning system
GPU graphics processing unit
HIVE-COTE hierarchical vote collective of transformation-based ensemble
IMU inertial measurement unit
MCI Management Center Innsbruck
NLP natural language processing
ODR output data rate
ResNet residual network
SVM support vector machine
TSC time series classification
Appendix A. Alternative Triggering Methods
Additional to the triggering method described in Section 2.1.3, two more solutions
were investigated on a small scale. Nevertheless, the authors want to clarify the decision to
use the finally implemented trigger by explaining the other approaches as well.
Appendix A.1. Audio
The idea of triggering with the microphone data was to capture the distinct sound of
the moment when the ball hits the racket. Nevertheless, the audio signal as a trigger failed
because of the disturbing wind generated by the fast movements. The noisy audio signal
of a forehand topspin is shown in Figure 6d. The exact moment of the racket hitting the
ball is not unambiguously recognizable. Trials to protect the device from the wind with a
pop filter [65] were not successful, and therefore, this solution was abandoned.
Appendix A.2. Variation of the Filtered Net Rotational Energy and Jerk
Since tennis is a swing sport, the rotational energy during a shot is relatively high,
resulting in a significant lobe in the
. Hence, the second idea was the triggering via
a modification of the net rotational energy Eω, which is defined as
where Iis the moment of inertia of a body around its rotational axis [16]. Therefore, also
energy =ω2
holds true. This result is smoothed with the filter specified in Section 2.1.3 and compared
to an empirically determined threshold value.
This swing representative is combined with a threshold for the jerk in the same way
as mentioned in Section 2.1.3.
Appendix A.3. Comparison of the Triggers
Table A1 gives an overview about the trigger possibilities. In the end, the
combination was chosen due to its higher selectivity in comparison to the
ωenergy +j
Sensors 2021,21, 5703 18 of 20
Table A1. Advantages and drawbacks of the previously introduced solutions for triggering.
Audio ωenergy +jωy+j
Advantage -
high sensitivity, most of the shots are
detected as the swing in all axes is
high selectivity, false shots are very
rare, for example grabbing a ball from
the ground by hitting the racket on it
Drawback impact not distinguishable
from wind
lacks in selectivity, too many false
some shots are not detected due to
slow angular velocities in the
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... Accordingly, the continued development of these models in sport can benefit coaches and sports medicine staff to monitor athlete training loads and record sport-specific event data. In tennis, wearable sensors positioned on the hitting arm or racquet utilise accurate machine learning models for automated stroke detection [6,7] and present more affordable and accessible technological approaches to monitoring tennis training. However, their placement precludes quantification of runningbased movement [7], which is also a critical component of tennis training and match-play profiles [8]. ...
... This highlights an advantage compared to wrist-worn or racquet-mounted sensors, traditionally used in tennis, that report stroke events but provide limited insight into the locomotor demands of the sport. Whilst emerging evidence in tennis has utilised wrist-worn sensors and classify movement as "sprinting", "running", "walking" and "standing" activities [6], their validity is currently unavailable in the literature. Regardless, exploration of prototype machine learning algorithms from a single commercial cervically mounted wearable sensor to determine both stroke and movement events is currently missing. ...
... Despite this possible limitation, it remains likely that high accuracy classification rates for major strokes remain indicative of the unique trunk rotation and lateral flexion signatures registered from the gyroscope and accelerometer. This could also explain the low (≤3%) false positive rates from the present algorithm and further highlights its suitability for tennis stroke detection given the similarities with results from studies using wrist-worn devices [6]. ...
Full-text available
This study evaluated the accuracy of tennis-specific stroke and movement event detection algorithms from a cervically mounted wearable sensor containing a triaxial accelerometer, gyroscope and magnetometer. Stroke and movement data from up to eight high-performance tennis players were captured in match-play and movement drills. Prototype algorithms classified stroke (i.e., forehand, backhand, serve) and movement (i.e., “Alert”, “Dynamic”, “Running”, “Low Intensity”) events. Manual coding evaluated stroke actions in three classes (i.e., forehand, backhand and serve), with additional descriptors of spin (e.g., slice). Movement data was classified according to the specific locomotion performed (e.g., lateral shuffling). The algorithm output for strokes were analysed against manual coding via absolute (n) and relative (%) error rates. Coded movements were grouped according to their frequency within the algorithm’s four movement classifications. Highest stroke accuracy was evident for serves (98%), followed by groundstrokes (94%). Backhand slice events showed 74% accuracy, while volleys remained mostly undetected (41–44%). Tennis-specific footwork patterns were predominantly grouped as “Dynamic” (63% of total events), alongside successful linear “Running” classifications (74% of running events). Concurrent stroke and movement data from wearable sensors allows detailed and long-term monitoring of tennis training for coaches and players. Improvements in movement classification sensitivity using tennis-specific language appear warranted.
... In other sports such as tennis and American football, the requirements are similar. Based on the paper by [26,27], the sensor platform for this work has been chosen. ...
... After the data-gathering stage, an algorithm had to be developed so the cadence could be derived based on the IMU data. The authors chose a supervised machine-learning approach as found in many other sport-related studies such as [26,27,31], due to their good performance. To this end, the individual pedal strikes that the Hall-effect sensor detects were used as the ground truth. ...
Full-text available
Most commercial cadence-measurement systems in road cycling are strictly limited in their function to the measurement of cadence. Other relevant signals, such as roll angle, inclination or a round kick evaluation, cannot be measured with them. This work proposes an alternative cadence-measurement system with less of the mentioned restrictions, without the need for distinct cadence-measurement apparatus attached to the pedal and shaft of the road bicycle. The proposed design applies an inertial measurement unit (IMU) to the seating pole of the bike. In an experiment, the motion data were gathered. A total of four different road cyclists participated in this study to collect different datasets for neural network training and evaluation. In total, over 10 h of road cycling data were recorded and used to train the neural network. The network’s aim was to detect each revolution of the crank within the data. The evaluation of the data has shown that using pure accelerometer data from all three axes led to the best result in combination with the proposed network architecture. A working proof of concept was achieved with an accuracy of approximately 95% on test data. As the proof of concept can also be seen as a new method for measuring cadence, the method was compared with the ground truth. Comparing the ground truth and the predicted cadence, it can be stated that for the relevant range of 50 rpm and above, the prediction over-predicts the cadence with approximately 0.9 rpm with a standard deviation of 2.05 rpm. The results indicate that the proposed design is fully functioning and can be seen as an alternative method to detect the cadence of a road cyclist.
... Through the control system, the robot moves to the specified position and realizes the action of picking up the ball [8]. Ganser et al. proposed an embedded intelligent ball-picking car, and the scheme uses color and shape recognition algorithm, combined with PID control algorithm, respectively, using motor drive car body movement and steering gear control car ball-picking action, to achieve the function of picking up tennis balls [9,10]. However, this scheme is only a theoretical solution, and the concrete realization remains to be practiced. ...
... (2) Pheromone Update. After searching all the tennis balls, update the pheromone on the path according to Equation (9). ...
Full-text available
Visual recognition and automatic control technology is an important way to realize robot automatic ball picking. Therefore, a tennis robot motion control method based on ant colony algorithm is evaluated. After the camera position was fixed, the motion control system software was designed, and the optimal path was solved by ant colony algorithm. The results show that the two adjacent positioning errors and the current total positioning errors fluctuate around -0.05 mm and -2.29 mm, respectively, and the fluctuation range is less than 3.50 mm. Ant colony algorithm is superior to greedy algorithm in path planning of collecting tennis balls. The number of iterations of ant colony algorithm for optimal path planning of 30 to 50 tennis balls is about 20 to 30 times, and the path length is reduced to reduce the time of collecting tennis balls, which meets the actual work requirements.
... The ANN is a biological brain-inspired technique in which a large number of artificial neurons are strongly interconnected in order to solve complex problems [90]. These models understand the context of a problem by creating multiple transformations on the feature space, followed by non-linearity, to create its simplified representations [91]. Numerous studies have employed ANN models for SMP [38,40,[92][93][94][95]. ...
... It is a layered network where hidden layers use a radial activation function [101,102]. For example, the authors in [91] used the RBF neural network to predict the Shanghai and NASDAQ index by using an extension of LPP (Locality Preserving Projection) known as two-dimensional LPP for the selection of most relevant features for the prediction. The proposed method performed well on both of the market indices. ...
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With the advent of technological marvels like global digitization, the prediction of the stock market has entered a technologically advanced era, revamping the old model of trading. With the ceaseless increase in market capitalization, stock trading has become a center of investment for many financial investors. Many analysts and researchers have developed tools and techniques that predict stock price movements and help investors in proper decision-making. Advanced trading models enable researchers to predict the market using non-traditional textual data from social platforms. The application of advanced machine learning approaches such as text data analytics and ensemble methods have greatly increased the prediction accuracies. Meanwhile, the analysis and prediction of stock markets continue to be one of the most challenging research areas due to dynamic, erratic, and chaotic data. This study explains the systematics of machine learning-based approaches for stock market prediction based on the deployment of a generic framework. Findings from the last decade (2011–2021) were critically analyzed, having been retrieved from online digital libraries and databases like ACM digital library and Scopus. Furthermore, an extensive comparative analysis was carried out to identify the direction of significance. The study would be helpful for emerging researchers to understand the basics and advancements of this emerging area, and thus carry-on further research in promising directions.
... One of the more recent papers, a paper titled Classification of Tennis Shots with a Neural Network Approach was published in 2021. This research paper discusses the use of Neural Networks to classify tennis shots [11]. This paper uses data collected from accelerometers, gyroscopes, magnetometers and audio signals to classify tennis shots in five categories: forehand topspin, forehand slice, backhand topspin, backhand slice, and serve. ...
Conference Paper
Athletes in technical sports often find it difficult to analyze their own technique while they’re playing [1]. Often, athletes look at the technique of professional players to identify problems they may have. Unfortunately, many types of techniques, such as forehand and backhand swings in tennis, are relatively similar between a beginner and a professional, making it more difficult for comparison. On the other hand, techniques that appear different between professionals and casual can also present different challenges. This is especially true for serves in tennis, where the speed of the swing, the motion of the player, and the angle of the camera recording the player all pose a challenge in analyzing differences between professional and learning tennis players [2]. In this paper, we used two machine learning approaches to compare the serves of two players. In addition, we also developed a website that utilizes these approaches to allow for convenient access and a better experience. We found that our algorithm is effective for comparing two serves of different speeds and synchronized the videos effectively.
... Inertial measurement units (IMUs) are sensors used commonly in medical rehabilitation, performance and kinematics analysis in sports [1,2]. In tennis, the use of this type of technology has become increasingly frequent [3], since it is an economical and portable alternative that allows to estimate kinematic parameters such as the body segments' orientation, position and joint angles [4][5][6], the energy transition between segments during the strokes [7] or the ball speed based on a racket-mounted motion sensor [8]. All this makes IMUs suitable to collect data in a natural environment and perform in-field tennis biomechanical analyses, which provide more valid results than laboratory tests [9]. ...
Portable and low-cost motion capture systems are gaining importance for biomechanical analysis. The aim was to determine the concurrent validity and reliability of the NOTCH® inertial sensors to measure the elbow angle during tennis forehand at different sampling frequencies (100, 250 and 500 hertz), using an optical capture system with sub-millimetre accuracy as a reference. 15 competitive players performed forehands wearing NOTCH and an upper body marker-set and the signals from both systems were adjusted and synchronized. The error magnitude was tolerable (5-10°) for all joint-axis and sampling frequencies, increasing significantly at 100 hertz for the flexion-extension and pronation-supination angles (p = 0.002 and 0.023; Cohen d > 0.8). Concordance correlation coefficient was very large (0.7–0.9) in all cases. The within-subject error variation between the test-retest did not show significant differences (p > 0.05). NOTCH® is a valid, reliable and portable alternative to measure elbow angles during tennis forehand.
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Currently, gathering statistics and information for ice hockey training purposes mostly happens by hand, whereas the automated systems that do exist are expensive and difficult to set up. To remedy this, in this paper, we propose and analyse a wearable system that combines player localisation and activity classification to automatically gather information. A stick-worn inertial measurement unit was used to capture acceleration and rotation data from six ice hockey activities. A convolutional neural network was able to distinguish the six activities from an unseen player with a 76% accuracy at a sample frequency of 100 Hz. Using unseen data from players used to train the model, a 99% accuracy was reached. With a peak detection algorithm, activities could be automatically detected and extracted from a complete measurement for classification. Additionally, the feasibility of a time difference of arrival based ultra-wideband system operating at a 25 Hz update rate was determined. We concluded that the system, when the data were filtered and smoothed, provided acceptable accuracy for use in ice hockey. Combining both, it was possible to gather useful information about a wide range of interesting performance measures. This shows that our proposed system is a suitable solution for the analysis of ice hockey.
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Wearable sensors facilitate running kinematics analysis of joint kinematics in real running environments. The use of a few sensors or, ideally, a single inertial measurement unit (IMU) is preferable for accurate gait analysis. This study aimed to use a convolutional neural network (CNN) to predict level-ground running kinematics (measured by four IMUs on the lower extremities) by using treadmill running kinematics training data measured using a single IMU on the anteromedial side of the right tibia and to compare the performance of level-ground running kinematics predictions between raw accelerometer and gyroscope data. The CNN model performed regression for intraparticipant and interparticipant scenarios and predicted running kinematics. Ten recreational runners were recruited. Accelerometer and gyroscope data were collected. Intraparticipant and interparticipant R2 values of actual and predicted running kinematics ranged from 0.85 to 0.96 and from 0.7 to 0.92, respectively. Normalized root mean squared error values of actual and predicted running kinematics ranged from 3.6% to 10.8% and from 7.4% to 10.8% in intraparticipant and interparticipant tests, respectively. Kinematics predictions in the sagittal plane were found to be better for the knee joint than for the hip joint, and predictions using the gyroscope as the regressor were demonstrated to be significantly better than those using the accelerometer as the regressor.
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The use of inertial measurement unit (IMU) has become popular in sports assessment. In the case of velocity-based training (VBT), there is a need to measure barbell velocity in each repetition. The use of IMUs may make the monitoring process easier; however, its validity and reliability should be established. Thus, this systematic review aimed to (1) identify and summarize studies that have examined the validity of wearable wireless IMUs for measuring barbell velocity and (2) identify and summarize studies that have examined the reliability of IMUs for measuring barbell velocity. A systematic review of Cochrane Library, EBSCO, PubMed, Scielo, Scopus, SPORTDiscus, and Web of Science databases was performed according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. From the 161 studies initially identified, 22 were fully reviewed, and their outcome measures were extracted and analyzed. Among the eight different IMU models, seven can be considered valid and reliable for measuring barbell velocity. The great majority of IMUs used for measuring barbell velocity in linear trajectories are valid and reliable, and thus can be used by coaches for external load monitoring.
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Highly efficient training is a must in professional sports. Presently, this means doing exercises in high number and quality with some sort of data logging. In American football many things are logged, but there is no wearable sensor that logs a catch or a drop. Therefore, the goal of this paper was to develop and verify a sensor that is able to do exactly that. In a first step a sensor platform was used to gather nine degrees of freedom motion and audio data of both hands in 759 attempts to catch a pass. After preprocessing, the gathered data was used to train a neural network to classify all attempts, resulting in a classification accuracy of 93%. Additionally, the significance of each sensor signal was analysed. It turned out that the network relies most on acceleration and magnetometer data, neglecting most of the audio and gyroscope data. Besides the results, the paper introduces a new type of dataset and the possibility of autonomous training in American football to the research community.
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The use of wireless sensors to measure motion in non-laboratory settings continues to grow in popularity. Thus far, most validated systems have been applied to measurements in controlled settings and/or for prescribed motions. The aim of this study was to characterize adolescent hip joint motion of elite-level athletes (soccer players) during practice and recreationally active peers (controls) in after-school activities using a magneto-inertial measurement unit (MIMU) system. Opal wireless sensors (APDM Inc., Portland OR, USA) were placed at the sacrum and laterally on each thigh (three sensors total). Hip joint motion was characterized by hip acceleration and hip orientation for one hour of activity on a sports field. Our methods and analysis techniques can be applied to other joints and activities. We also provide recommendations in order to guide future work using MIMUs to pervasively assess joint motions of clinical relevance.
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Artificial noses are broad-spectrum multisensors dedicated to the detection of volatile organic compounds (VOCs). Despite great recent progress, they still suffer from a lack of sensitivity and selectivity. We will review, in a systemic way, the biomimetic strategies for improving these performance criteria, including the design of sensing materials, their immobilization on the sensing surface, the sampling of VOCs, the choice of a transduction method, and the data processing. This reflection could help address new applications in domains where high-performance artificial noses are required such as public security and safety, environment, industry, or healthcare.
2018 Curran Associates Inc.All rights reserved. Batch Normalization (BatchNorm) is a widely adopted technique that enables faster and more stable training of deep neural networks (DNNs). Despite its pervasiveness, the exact reasons for BatchNorm's effectiveness are still poorly understood. The popular belief is that this effectiveness stems from controlling the change of the layers' input distributions during training to reduce the so-called “internal covariate shift”. In this work, we demonstrate that such distributional stability of layer inputs has little to do with the success of BatchNorm. Instead, we uncover a more fundamental impact of BatchNorm on the training process: it makes the optimization landscape significantly smoother. This smoothness induces a more predictive and stable behavior of the gradients, allowing for faster training.
Optimization techniques are of great importance to effectively and efficiently train a deep neural network (DNN). It has been shown that using the first and second order statistics (e.g., mean and variance) to perform Z-score standardization on network activations or weight vectors, such as batch normalization (BN) and weight standardization (WS), can improve the training performance. Different from these existing methods that mostly operate on activations or weights, we present a new optimization technique, namely gradient centralization (GC), which operates directly on gradients by centralizing the gradient vectors to have zero mean. GC can be viewed as a projected gradient descent method with a constrained loss function. We show that GC can regularize both the weight space and output feature space so that it can boost the generalization performance of DNNs. Moreover, GC improves the Lipschitzness of the loss function and its gradient so that the training process becomes more efficient and stable. GC is very simple to implement and it can be embedded into existing gradient based DNN optimizers with only one line of code. Our experiments on various applications, including general image classification, fine-grained image classification, detection and segmentation, demonstrate that GC can consistently improve the performance of DNN learning. The code of GC can be found at