# Constrained Deep One-Class Feature Learning For Classifying Imbalanced
Medical Images ††thanks: Citation:

Long Gao
Department of Radiology
School of Medicine
University of Pittsburgh
Pittsburgh PA, USA, 15260
<EMAIL_ADDRESS>
&Chang Liu
Department of Bioengineering
Swanson School of Engineering
University of Pittsburgh
Pittsburgh PA, USA, 15260
<EMAIL_ADDRESS>
&Dooman Arefan
Department of Radiology
School of Medicine
University of Pittsburgh
Pittsburgh PA, USA, 15260
<EMAIL_ADDRESS>
&Ashok Panigrahy
Department of Radiology
University of Pittsburgh Medical Center
Children’s Hospital of Pittsburgh
Pittsburgh PA, USA, 15260
&Shandong Wu
Intelligent Systems Program
University of Pittsburgh
Pittsburgh PA, USA, 15260
<EMAIL_ADDRESS>

###### Abstract

Purpose: Medical image data are usually imbalanced across different classes.
One-class classification has attracted increasing attention to address the
data imbalance problem by distinguishing the samples of the minority class
from the majority class. Previous methods generally aim to either learn a new
feature space to map training samples together or to fit training samples by
autoencoder-like models. These methods mainly focus on capturing either
compact or descriptive features, where the information of the samples of a
given one class is not sufficiently utilized.

Approach: In this paper, we propose a novel deep learning-based method to
learn compact features by adding constraints on the bottleneck features, and
to preserve descriptive features by training an autoencoder at the same time.
Through jointly optimizing the constraining loss and the autoencoder’s
reconstruction loss, our method can learn more relevant features associated
with the given class, making the majority and minority samples more
distinguishable.

Results: Experimental results on three clinical datasets (including the MRI
breast images, FFDM breast images and chest X-ray images) obtains state-of-art
performance compared to previous methods.

Conclusions: We propose a novel method to address the data imbalance problem.
The proposed method can learn a more compact and descriptive feature space for
the one class classification task.

_K_ eywords Data imbalance $\cdot$ medical imaging $\cdot$ deep learning
$\cdot$ one-class classification

##  1 Introduction

In clinical and biomedical applications, the collected datasets are usually
imbalanced across different classes. Models trained on imbalanced data may
lead to poor or biased performance. To address this issue, One-Class
Classification (OCC) [1] has been proposed to learn single-class-relevant
features from samples belonging to the "majority" class. This method has also
been used for Anomaly Detection (AD) [2, 3], which focuses on distinguishing
the "minority" class samples that have different distribution from the
"majority" class.

The critical problem for OCC is how to learn a high-quality feature space. A
good feature space should be both compact and descriptive [4, 5]. The
compactness means the model can learn a similar representation for different
images belonging to the same class. In this way, samples from the same class
should have lower intra-class distance. The descriptiveness means the model
can learn different representations for images belonging to different classes.
In this way, samples from different classes should have higher inter-class
distance. To optimize the compactness, the model should map images from the
same class to similar representations. On the other hand, to optimize the
descriptiveness, the model should capture features that belong exclusively to
each class. Considering that abnormal samples are unavailable during the
training phase in OCC, we focus on learning more features of the given class
to optimize the descriptiveness. Based on the feature that the model focuses
on, previous methods can be generally split into two categories: learning
compact features or learning descriptive features.

The first scheme is to map features by kernel functions. These methods usually
focus on learning a compact representation by minimizing the intra-class
distance. A representative method is OCSVM [6], which focuses on mapping given
class samples from the original space to a new feature space and maximizing
the distance between the original point and the hyperplane. SVDD [5] attempts
to learn a kernel function, where the given class samples can be mapped into a
hypersphere, and samples belonging to the other classes will be mapped out of
it. Some work also applies these methods to clinical imaging analysis [7, 8,
9]. These methods obtain remarkable performance for small-scale datasets
because the kernel function can map samples into a separable higher
dimensional feature space effectively, but they usually suffer from the "curse
of dimensionality" [10]. To address this issue, D-SVDD [10] is proposed to
learn a hypersphere that encloses the network representations of the data by
an encoder network. These methods can learn a compact representation for the
given class samples, but they neglect the descriptive features of the images.
Thus, these models may learn a trivial solution such as mapping all samples
into zeros.

Another scheme is to fit the distribution of the given class samples by deep
learning models. These methods usually focus on learning descriptive features
by reconstructing images. Deep neural networks have been widely employed in
this scheme because of their powerful feature learning abilities [11, 12].
Example methods include convolutional autoencoders (CAE) [13, 14] and
Generative Adversarial Network (GAN) based models [15, 16, 17]. For example,
Deep Autoencoding Gaussian Mixture Model (DAGMM) [18, 14] is proposed to add a
Gaussian Mixture Model on the output layer to learn more local features.
AnoGAN [13] attempts to generate fake samples with GAN and takes the
discriminator as the classifier to classify samples. Entropy-based loss is
added in the Deep Structured Energy-Based Model (DSEBM) [14] to make samples
belonging to different classes more distinguishable. The study in [19] employs
an inpainting method to detect tumors by calculating the reconstruction loss
of each patch. These methods usually focus on reconstructing input features
and can learn a descriptive model. However, they usually neglect the
compactness of the feature space. Thus, the performance of these algorithms is
limited, especially on clinical image datasets with large variations.

In this paper, a novel method is proposed to learn a compact and descriptive
hypersphere using the autoencoder backbone. The intuition is that ideally, for
a compact representation, all training samples should be mapped into a single
point because they belong to the same class. However, models (such as Deep
SVDD) that only use the encoder part of a network are easy to collapse to a
trivial solution [10] (e.g., map to all zero vectors). With that in mind, we
present a new framework, namely $ConOCC$, to learn a more robust feature
representation by combining a constraining layer and a decoder. The proposed
method not only learns a compact hypersphere by using the constraining layer
to pull all training samples together, but also preserves the descriptive
information to avoid the trivial solution by reconstructing samples with a
decoder. By jointly optimizing the constraining loss and reconstruction loss,
the proposed method can obtain a balance between the compactness and
descriptiveness of features to achieve better performance.

Our contributions can be summarized as follows:

  * •

A novel framework is proposed to learn a representative hypersphere for the
one-class classification task by adding constraints on the features of the
samples from the majority class.

  * •

The proposed method can learn a more compact and descriptive feature space by
jointly optimizing two loss objectives.

  * •

Extensive experiments are performed on three clinical datasets to demonstrate
that the proposed method outperforms the state-of-the-art algorithms.

##  2 Materials and Methods

Definition OCC is to learn a model $M$ from a set of given samples $X$
belonging to a single class $c$. A score $s_{i}$ will be obtained for each
input sample $x_{i}$ by the model, where a lower score means $x_{i}$ is more
likely to belong to the given class.

Motivation Different from the classification of natural images, the
classification of clinical images is usually more depend on the contrast and
brightness features, making the classification of medical images more
sensitive to the reconstruction loss of autoencoder-like models.

Autoencoder has shown powerful ability in learning deep features from medical
images [20], and it has been widely applied in AD tasks [2, 12]. To learn a
more distinguishable hypersphere and to improve the performance, we add
constraints on the bottleneck features. Jointly minimizing the hypersphere and
reconstruction loss will force the encoder to extract the most representative
features of a given class, because the network needs to closely map normal
samples to the center of the hypersphere while preserving the information of
normal samples. The rationale of ConOCC is that, samples from the same class
should ideally be mapped into the same point because they belong to the same
class. In this way, we design ConOCC to pull all training samples to the
center of the hypersphere in the feature space, as described in the following.

###  2.1 Pipeline

Figure 1:  The framework of the proposed method. A constraining layer is added
as a branch for the bottleneck feature to pull all features towards the center
point $\mu$, as shown in the dotted circle. By jointly training the
autoencoder and the constraining layer, the model can learn a compact while
descriptive hypersphere. Samples from the majority class will be mapped into
this hypersphere, while samples from the minority class will be mapped out of
it.

The framework of the proposed method is illustrated in Figure 1. It includes
an encoder $E$ (green), a decoder $D$ (grey), and a $Constraining$ $Layer$
(black).

The function of each component in ConOCC is as follows: The $encoder$ can
reduce the dimension and learn a basic hypersphere from the majority class
samples. The $decoder$ can amplify the difference of features and prevent the
model from mapping all samples into a trivial solution hypersphere (e.g., all
zeros). The $Constraining\ Layer$ can minimize the distance between features
and therefore compress the hypersphere. By selecting appropriate parameters,
the model can obtain a balance between the constraining loss and the
reconstruction loss, thus achieving a better performance.

Suppose $\mu$ is the center point of the hypersphere, $z_{i}$ is the
bottleneck feature generated by an encoder $E$ from the input sample $x_{i}$
of size $m\times m$. The method focuses on minimizing the distance between
$z_{i}$ and $\mu$. The loss objective of the constraining layer can be defined
as:

$L_{con}=||z_{i}-\mu||^{2}=||E(x_{i})-\mu||^{2}$ (1)

Here Mean Square Error (MSE) is employed for the reconstruction loss as
defined in 2:

$L_{AE}=\sum_{j=1}^{j=m\times m}||D(E(x_{i}))-x_{i}||_{2}^{2}$ (2)

To combine the constraining loss and the reconstruction loss together, the
loss function of the whole network can be formulated as:

$L=L_{AE}+\gamma L_{con}$ (3)

where $\gamma$ is the coefficient to balance the influence of $L_{AE}$ and
$L_{con}$. $L_{AE}$ is the reconstruction loss of the autoencoder.

Compared to D-SVDD which penalizes the trivial solution [10], the decoder
employed in ConOCC not only avoids the trivial solution by reconstructing
inputs, but also promotes the encoder to learn descriptive features of the
given class.

Compared to Sparse Autoencoder [21] which also focuses on adding constraints
on bottleneck features, ConOCC aims to minimize the distance of each feature
node, instead of learning sparse representations.

###  2.2 Optimization

The weights of the encoder and the decoder are jointly updated with the
constraining loss and the reconstruction loss. Specifically, the weights of
the decoder $W_{d}$ are updated by:

$W_{d}=W_{d}-\frac{\lambda}{b}\sum_{i=1}^{b}\frac{\partial L_{AE}}{\partial
W_{d}}$ (4)

where $\lambda$ and $b$ are the learning rate and mini-batch size,
respectively. The weights of the encoder are updated by:

$W_{e}=W_{e}-\frac{\lambda}{b}\sum_{i=1}^{b}(\frac{\partial L_{AE}}{\partial
W_{d}}+\gamma\frac{\partial L_{con}}{\partial z_{i}})$ (5)

The center of the hypersphere $\mu$ is set to the mean value of the bottleneck
feature. To stabilize the training procedure, we update $\mu$ after each $T$
epoch of training the whole model.

###  2.3 Score calculation

We use the score of each sample to evaluate how likely each of them belongs to
the given class. The lower the score, the more likely sample $x_{i}$ is to
belong to the given majority class. In this study, the reconstruction loss is
employed as the score. The features extracted from samples of the majority
class will result in a low reconstruction loss, while that of the minority
class will result in a high reconstruction loss. In this way, the model can
distinguish samples from different classes. Specifically, the score of sample
$x_{i}$ can be calculated by the formula:

$s_{i}=\sum_{j=1}^{j=m\times m}||D(E(x_{i}))-x_{i}||_{2}^{2}$ (6)

###  2.4 Datasets

Table 1: Number of samples of each dataset. The "majority" class samples are used for training. We use 2-,5- and 4-fold cross-validation for the MRI, FFDM and ChestX datasets, respectively. Dataset |  Dimension | Training | Majority | Minority | Testing | Cross
---|---|---|---|---|---|---
|  |  (Majority) |  in testing |  in testing |  in total |  validation
MRI |  32$\times$32$\times$1 |  1000 |  946 |  926 |  1872 |  2
FFDM |  64$\times$64$\times$1 |  200 |  52 |  52 |  104 |  5
ChestX |  100$\times$100$\times$1 |  1341 |  234 |  390 |  624 |  4

Three datasets from three modalities are employed for two clinical tasks:
breast tumor detection and pneumonia diagnosis. The sample number of each
dataset is shown in Table 1, some examples from the majority and minority
classes are shown in Figures 2, 3 and 4, and details are as follows.

Breast Magnetic Resonance Imaging (MRI) dataset: This is an MRI dataset
collected at our institution from women diagnosed with breast cancer. 1000
tumor images (majority class) are used for training, and 946 tumor images and
926 normal (suspicious) tissue images are used for testing. As shown in Figure
2, the suspicious patches where tissue biopsy is needed are manually segmented
from original MRI images. For each patient, one tumor/suspicious patch is
used. The mean size of the tumor is about 31$\times$31 pixels. Here all the
tumor patches are resized to 32$\times$32 pixels for all experiments.

Figure 2:  Tumor (majority class) and suspicious (minority class) samples on
the breast tumor MRI dataset. Figure 3:  Tumor (majority class) and suspicious
(minority class) samples on the breast tumor FFDM dataset. Figure 4:  Normal
(majority class) and pneumonia (minority class) samples on the ChestX dataset.

Breast Full-Field Digital Mammography (FFDM) dataset: This is an in-house
X-ray breast imaging dataset for women diagnosed with breast cancer. 200 tumor
(majority class) images are used for training, 52 tumor images and 52 normal
(suspicious) tissue images are used for testing. The patch size ranges from
100 to 500 pixels, all the patches are resized to 64$\times$64 pixels by sub-
sampling (see Figure 3).

ChestX dataset: This is a public chest X-rays dataset from Kaggle111
https://www.kaggle.com/paultimothymooney/chest-xray-pneumonia  for pneumonia
diagnosis. It contains two classes: pneumonia patient samples and normal
samples. 1341 normal CT images are used for training. 234 normal and 390
pneumonia images are used for testing. The original image size ranges from
1000$\sim$2500 pixels. Here all images are resized to 100$\times$100 pixels
(see Figure 4).

###  2.5 Experimental settings and evaluation metrics

Keras [22] is employed on an NVIDIA TITAN GPU to conduct all experiments. Adam
[23] is adopted as the optimizer, with a batch of 128. To make the training
procedure more stable, we train the constraining layer after training the
autoencoder each $T$ epochs. The learning rate $\lambda$ is set to $10^{-3}$,
the coefficient $\gamma$ is set to 10, and the update interval $T$ is set to
60. The details of the encoder and decoder are shown in Figure 1, with the
kernel size set to 3$\times$3, and the bottleneck feature number $n$ set to
256. Note that the OCC task only has the single class samples for training, so
the parameters are unable to be selected using the validation set. Thus,
similar to previous work [10, 12], we train the model for $10^{3}$ epochs for
each experiment, and report the result of the last epoch.

The Area Under the Receiver Operating Characteristic Curve (AUC) and Area
Under Precision-Recall curve (AUPR) are employed to evaluate the performance.
Two types of AUPR can be calculated: taking the majority class as positive
(AUPR-maj), and taking the minority class as positive (AUPR-min).

##  3 Results

In this section, we compare our algorithm to other existing one-class
classification methods to show our algorithm’s superior performance.

###  3.1 Baseline methods

The proposed method is compared with seven previous algorithms: OCSVM [6],
CAE, C-OCSVM, SAE [21], DAGMM [12], AnoGAN [13] and D-SVDD [10]. We run each
algorithm three times, and the average of the performance measures is
reported.

OCSVM This method attempts to learn a mapping to project original samples into
a hyperplane by kernel functions (e.g., linear, RBF). In our experiment, the
RBF kernel is used for the OCSVM and each original image is reshaped into a
vector as the input feature.

CAE To show the effectiveness of adding the constraint to the bottleneck
feature, the performance of CAE is also reported as the baseline. The
structure of CAE is the same as the autoencoder employed in ConOCC, with the
reconstruction loss employed as the score of each sample. The learning rate
$\lambda$ is tested in $\\{10^{-3},10^{-4}\\}$ for CAE, and the best result is
obtained when $\lambda=10^{-4}$.

C-OCSVM This method is a two-stage combination of CAE and OCSVM. First, an
autoencoder (with the same structure as ConOCC) is trained to reduce the
dimension, then the bottleneck feature is used to train the OCSVM. In the
second stage, we use the same procedure as aforementioned in OCSVM.

SAE Sparse autoencoder (SAE) focuses on adding constraints on the bottleneck
feature to learn sparse representations, by which features can be compressed
into fewer nodes. The SAE in [21] is employed with the same structure as
ConOCC for this experiment. The learning rate $\lambda$ is tested in
$\\{10^{-3},10^{-4}\\}$ for SAE, and the best performance is reported.

DAGMM DAGMM employs an autoencoder (with the same structure as ConOCC) to
compress data and obtain a reconstruction loss, which is further fed into a
Gaussian Mixture Model (GMM). By jointly training with GMM, the autoencoder
can escape from local optima and further reduce reconstruction errors of
training samples.

AnoGAN AnoGAN [17] is a GAN-based method for medical image classification.
After training a GAN with samples from the majority class, the model can
generate a latent code for a given testing image, then the difference between
the generated and original image is calculated as the loss. Considering the
sample number of our datasets, here the model provided by the original paper
is used along with data augmentation.

D-SVDD D-SVDD focuses on mapping samples into a hypersphere using a feature
extraction network. Here the encoder of ConOCC is used as the basic model, and
a SVDD-based loss layer is integrated with default parameters for this
experiment.

Table 2: Comparison of ConOCC to seven other previous algorithms. Data | Method | OCSVM | COCSVM | DAGMM | D-SVDD | AnoGAN | SAE | CAE | OURS
---|---|---|---|---|---|---|---|---|---
MRI |  AUC | 0.802 | 0.844 | 0.629 | 0.652 | 0.613 | 0.854 | 0.782 | 0.872
AUPR-maj | 0.831 | 0.866 | 0.545 | 0.675 | 0.611 | 0.855 | 0.825 | 0.879
AUPR-min | 0.784 | 0.826 | 0.692 | 0.614 | 0.590 | 0.859 | 0.713 | 0.871
FFDM |  AUC | 0.771 | 0.710 | 0.563 | 0.622 | 0.676 | 0.779 | 0.675 | 0.791
AUPR-maj | 0.830 | 0.744 | 0.563 | 0.640 | 0.686 | 0.837 | 0.720 | 0.839
AUPR-min | 0.700 | 0.677 | 0.660 | 0.590 | 0.681 | 0.701 | 0.622 | 0.710
ChestX |  AUC | 0.548 | 0.587 | 0.564 | 0.579 | 0.594 | 0.603 | 0.576 | 0.624
AUPR-maj | 0.449 | 0.413 | 0.423 | 0.422 | 0.446 | 0.435 | 0.394 | 0.519
AUPR-min | 0.756 | 0.674 | 0.694 | 0.684 | 0.702 | 0.748 | 0.675 | 0.739
Table 3: Comparison of ConOCC to previous algorithms when using cross-validation. Data | Method | OCSVM | COCSVM | DAGMM | D-SVDD | AnoGAN | SAE | CAE | OURS
---|---|---|---|---|---|---|---|---|---
MRI |  AUC | 0.807 | 0.811 | 0.707 | 0.687 | 0.634 | 0.843 | 0.760 | 0.868
$\pm$std | 0.025 | 0.133 | 0.062 | 0.091 | 0.030 | 0.026 | 0.006 | 0.022
AUPR-maj | 0.834 | 0.798 | 0.660 | 0.503 | 0.578 | 0.813 | 0.785 | 0.865
$\pm$std | 0.016 | 0.166 | 0.021 | 0.208 | 0.079 | 0.041 | 0.011 | 0.020
AUPR-min | 0.793 | 0.817 | 0.777 | 0.465 | 0.674 | 0.825 | 0.726 | 0.878
$\pm$std | 0.036 | 0.110 | 0.036 | 0.139 | 0.023 | 0.016 | 0.011 | 0.024
FFDM |  AUC | 0.772 | 0.683 | 0.607 | 0.662 | 0.705 | 0.786 | 0.650 | 0.827
$\pm$std | 0.069 | 0.042 | 0.109 | 0.105 | 0.077 | 0.062 | 0.042 | 0.044
AUPR-maj | 0.788 | 0.663 | 0.656 | 0.669 | 0.448 | 0.790 | 0.627 | 0.837
$\pm$std | 0.075 | 0.054 | 0.120 | 0.090 | 0.152 | 0.069 | 0.057 | 0.051
AUPR-min | 0.747 | 0.674 | 0.710 | 0.642 | 0.479 | 0.755 | 0.646 | 0.799
$\pm$std | 0.076 | 0.051 | 0.057 | 0.101 | 0.150 | 0.084 | 0.079 | 0.065
ChestX |  AUC | 0.580 | 0.613 | 0.542 | 0.562 | 0.608 | 0.588 | 0.599 | 0.616
$\pm$std | 0.037 | 0.058 | 0.052 | 0.065 | 0.049 | 0.050 | 0.049 | 0.015
AUPR-maj | 0.522 | 0.582 | 0.501 | 0.461 | 0.410 | 0.551 | 0.552 | 0.597
$\pm$std | 0.063 | 0.064 | 0.178 | 0.069 | 0.021 | 0.074 | 0.061 | 0.002
AUPR-min | 0.613 | 0.605 | 0.617 | 0.671 | 0.465 | 0.607 | 0.638 | 0.619
$\pm$std | 0.020 | 0.063 | 0.092 | 0.057 | 0.035 | 0.0432 | 0.023 | 0.021

The average results of running the experiment three times are reported in
Table 2; the average results when using cross-validation are reported in Table
3. Given that the proportion of the minority class samples in the three
datasets is different, we use varying numbers of folds for different datasets
in cross-validation. Specifically, for MRI, FFDM, and ChestX datasets, we use
1020, 200, and 1185 majority class samples for training, and the rest majority
and minority class samples for testing. In the testing set of each fold, the
minority class samples are the same while the majority class samples are
changed alternately, thus the cross-validation fold number is 2, 5, and 4,
respectively. From these two tables we have the following observations.

For models that focus on compactness, we observe that OCSVM and COCSVM are two
relatively effective methods among all datasets. The reason could be that the
kernel-based methods are effective in small-scale datasets[6, 10].

For autoencoder-like models that focus on descriptiveness, we can see that CAE
and SAE outperform other deep learning-based methods, indicating the
reconstruction-based method may be more suitable for learning features of
medical images. Also, SAE outperforms CAE, indicating that adding the
constraint on the bottleneck features is useful for learning better
representations. Autoencoder-like models neglect the compactness of the
features. These models are trained on reconstructing inputs, and they tend to
converge to a local optima for the purpose of reconstruction only, making
their performances limited for anomaly detection.

Our method outperforms all the autoencoder-like models in the three datasets.
Specifically, ConOCC gains a better performance than CAE, indicating that by
adding the compact constraint, ConOCC can learn more distinguishable features
of the given class and the decoder can further amplify the difference of
different classes. ConOCC also outperforms SAE, indicating that the
compactness constraint is better than the sparse constraint.

By jointly optimizing the two loss objectives, ConOCC can simultaneously
minimize the intra-class distance and maximize the inter-class distance. Our
method outperforms the other compared methods in all the tested datasets,
showing that learning both compact and descriptive features together obtains a
better feature representation compared to methods that only focus on one
aspect.

We notice the AUCs of all methods on the ChestX dataset are relatively low.
This is probably because it is hard to learn representations on large-size
images, especially when the training set is small.

##  4 Discussion

In this section, we discuss the following two aspects: 1) analyzing the
influence of coefficients to show the robustness of the proposed method
(Section 4.1); 2) visualizing features to show that the proposed method can
learn a compact hypersphere (Section 4.2).

###  4.1 Robustness analysis

Figure 5:  The influence of $\lambda$, $\gamma$ and interval T. The green
plane is the result of CAE in corresponding learning rate.

To evaluate the influence of the $\lambda$, $\gamma$ and $T$, we take the
breast MRI dataset as an example and report AUCs when setting
$\lambda\in\\{10^{-3},10^{-4}\\}$, $\gamma\in${10-2, 10-1, $\cdots$,
$10^{1}$}, and $T\in\\{20,40,\cdots,100\\}$. In Figure 5, the green plane with
the dotted line is the result of CAE. The histogram is the result of ConOCC in
different settings (run one time). As shown in Figure 5, we can see that CAE
is influenced by the $\lambda$ significantly, whereas ConOCC is robust to
$\lambda$. The proposed method can keep high and stable performance in a
majority of $\gamma$ and $T$.

Figure 6:  Visualized features of training samples for CAE and ConOCC on the
FFDM dataset.

###  4.2 Visualization of features

We take the FFDM dataset as an example to illustrate the distribution of the
bottleneck features. Specifically, we extract features from the training set
and visualize them by reducing into two dimensions with $t$-SNE [24, 25]. As
shown in Figure 6, the proposed method can learn a more compact hypersphere
than CAE, and the sample density increases when samples are close to the
center point. This indicates that the constraining layer can generate a
compact hypersphere.

##  5 Conclusions

To address the data imbalance problem in medical image classification, a
framework is proposed to learn constrained features by integrating a
constraining layer into an autoencoder. The proposed method can jointly learn
a compact while descriptive feature space for the given class samples, making
samples belonging to different classes more distinguishable. The proposed
method is evaluated on three clinical datasets for three detection tasks, and
it exhibits improved performance compared to previous methods. In the future,
we will continue to investigate this framework by integrating potentially
other constraints on the bottleneck features to further improve performance.

## Acknowledgments

This was was supported in part by……

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