Applying Center Loss to Multidimensional Feature Space in Deep Neural

Networks for Open-set Recognition

Daiju Kanaoka

1 a

, Yuichiro Tanaka

2 b

and Hakaru Tamukoh

1,2 c

Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology,

2-4 Hibikino, Wakamatsu-ku, Kitakyushu-shi, Fukuoka, Japan

Research Center for Neuromorphic AI Hardware, Kyushu Institute of Technology,

2-4 Hibikino, Wakamatsu-ku, Kitakyushu-shi, Fukuoka, Japan

Keywords:

Open-set Recognition, Neural Networks, Image Classiﬁcation, Unknown Class.

Abstract:

With the advent of deep learning, signiﬁcant improvements in image recognition performance have been

achieved. In image recognition, it is generally assumed that all the test data are composed of known classes.

This approach is termed as closed-set recognition. In closed-set recognition, when an untrained, unknown class

is input, it is recognized as one of the trained classes. The method whereby an unknown image is recognized

as unknown when it is input is termed as open-set recognition. Although several open-set recognition methods

have been proposed, none of these previous methods excel in terms of all three evaluation items: learning cost,

recognition performance, and scalability from closed-set recognition models. To address this, we propose

an open-set recognition method using the distance between features in the multidimensional feature space of

neural networks. By applying center loss to the feature space, we aim to maintain the classiﬁcation accuracy

of closed-set recognition and improve the unknown detection performance. In our experiments, we achieved

state-of-the-art performance on the MNIST, SVHN, and CIFAR-10 datasets. In addition, the proposed ap-

proach shows excellent performance in terms of the three evaluation items.

1 INTRODUCTION

With the advent of deep learning, image recognition

performance has improved dramatically and has also

been reported to surpass the image recognition per-

formance of a human (He et al., 2016). When tested,

most existing image recognition methods assume that

all the input images belong to known classes. Thus,

they can classify the known classes; however, when

an unknown class is input, these methods classify it as

one of the known classes. This type of image recog-

nition is called closed-set recognition. By contrast,

when an unknown class is input, the image recog-

nition method that recognizes it as an unknown is

termed as open-set recognition (Scheirer et al., 2013).

Figure 1 shows the difference between closed-

set recognition and open-set recognition. For the

dataset distribution shown in (a), closed-set recogni-

tion, shown in (b), calculates a hyperplane that sepa-

rates each class suitably. However, in open-set recog-

https://orcid.org/0000-0003-2300-4189

https://orcid.org/0000-0001-6974-070X

https://orcid.org/0000-0002-3669-1371

nition, shown in (c), an exact region for each class

is set; the region that does not belong to any class,

termed as the open space, is also set. The features

that appear in this open space are recognized as an

unknown class.

Deep learning-based open-set recognition can be

classiﬁed into two categories: discriminative model-

based methods and reconstruction model-based meth-

ods. The discriminative model-based method in-

volves low learning costs and is easily scalable as

its architecture remains the same as that of closed-

set recognition models; nevertheless, its recognition

performance is low. By contrast, the recognition

performance of reconstruction model-based meth-

ods is higher than that of the discriminative model-

based methods; however, the learning costs are higher

and the architecture differs signiﬁcantly from that of

closed-set recognition methods. This makes it difﬁ-

cult to develop an open-set recognition method that

employs closed-set recognition models. Image recog-

nition is often used in embedded systems, where it be-

comes necessary to train additional unknown classes.

Therefore, an open-set recognition model with low

Kanaoka, D., Tanaka, Y. and Tamukoh, H.

Applying Center Loss to Multidimensional Feature Space in Deep Neural Networks for Open-set Recognition.

DOI: 10.5220/0010816600003124

In Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2022) - Volume 5: VISAPP, pages

359-365

ISBN: 978-989-758-555-5; ISSN: 2184-4321

359

Class:1

Class:2

Class:3

Class:4

Unknown

Class:1

Class:2

Class:3

Class:4

Unknown

Class:1

Class:2

Class:3

Class:4

Unknown

(a) Distribution of a dataset

(b) Closed-set recognition

Figure 1: Comparison of closed-set recognition and open-set recognition.

training costs and high recognition performance is

required. In addition, if the pre-trained closed-set

recognition models can be scaled up to open-set

recognition via ﬁne tuning, the learning costs can be

reduced. Consequently, it is necessary to develop an

open-set recognition method with low learning costs,

high recognition performance, and scalability from

closed-set recognition.

Anomaly detection is a research topic similar to

open-set recognition. In a previous study on anomaly

detection, a method using the feature space of a recog-

nition model pre-trained on ImageNet (Deng et al.,

2009), which is a large-scale image dataset, was pro-

posed (Rippel et al., 2020). This study conﬁrmed that

normal images and anomaly images appear at differ-

ent positions in a multidimensional feature space.

Deep metric learning is generally used for face

recognition (Wang and Deng, 2021). In face recog-

nition, there are few changes in the features be-

tween classes; therefore, deep metric learning gener-

ates a feature space with a bias between the classes

by imposing constraints on a feature space, such

that features of the same class are located near each

other, whereas features of different classes are lo-

cated far away. Deep metric learning methods such as

contrastive-loss (Chopra et al., 2005) and triplet-loss

(Wang et al., 2014) are well known. However, the dis-

advantage of these methods is that they require a pair

of classes to be created from the dataset during train-

ing; this results in high learning costs as the number

of classes increases. Center loss (Wen et al., 2016)

is a loss function used in face recognition. Center

loss acts as a constraint to keep features of the same

class close in a given batch during training. Center

loss is not classiﬁed as deep metric learning based

on its properties. It has achieved high performance

in the ﬁeld of face recognition. In addition, unlike

contrastive loss, center loss does not require a pair of

classes to be created from the dataset during training.

Thus, it is easier to incorporate into problems other

than face recognition.

In this paper, we propose an open-set recogni-

tion method that focuses on the multidimensional fea-

ture space formed in the middle layer of neural net-

works. Using center loss for a multidimensional fea-

ture space during training, the distance between fea-

tures of each class in a feature space is made vacant.

In the multidimensional feature space of the trained

classiﬁer, clusters are formed at a certain distance for

each class. When an unknown class is input, it is ex-

pected to appear at a different location from the clus-

ters of each class within the multidimensional feature

space. Thus, we propose a method that calculates the

distance between each cluster and a feature of the in-

put image; this approach estimates a class if the dis-

tance is within a set threshold and recognizes as un-

known class if it exceeds the threshold.

2 RELATED STUDIES

2.1 Open-set Recognition

Open-set recognition can be realized via tradi-

tional machine learning-based methods using SVM

(Scheirer et al., 2013) and the nearest neighbor meth-

ods (Mensink et al., 2013) or via deep learning-based

methods (Geng et al., 2020). In this paper, we dis-

cuss deep learning-based methods, which are the most

popular approaches and exhibit high recognition per-

formance.

2.1.1 Discriminative Model (DM)-based

Methods

Discriminative model-based methods generally use

the probability distribution of each class output from

the classiﬁer (Hendrycks and Gimpel, 2017; Bendale

and Boult, 2016). Figure 2 presents a block diagram

of discriminative model-based methods. For example,

softmax-threshold recognizes an unknown class if the

VISAPP 2022 - 17th International Conference on Computer Vision Theory and Applications

360

Unknown Known

Classiﬁer

Feature

Extraction

Class:5

0.76

Class:5

0.98

>Threshold

Unkown Class:5

Maximum

Probability

Maximum

Probability

condition is satisﬁed

Figure 2: Block diagram of discriminative model-based

methods.

maximum probability of the output probability distri-

bution of each class exceeds a set threshold; alterna-

tively, it estimates a class if this maximum probabil-

ity is less than the threshold (Hendrycks and Gimpel,

2017). The structure of this method is almost identi-

cal to that of closed-set recognition models; it offers

the advantage of low learning costs but suffers from

the disadvantage of a low recognition performance.

2.1.2 Reconstructive Model (RM)-based

Methods

In reconstruction model-based methods, a decoder is

installed in the model to reconstruct the input im-

age and calculate the reconstruction error (Yoshihashi

et al., 2019; Perera et al., 2020; Sun et al., 2020).

Figure 3 depicts the block diagram of reconstruction

model-based methods. If the calculated reconstruc-

tion error exceeds a set threshold, a classiﬁer recog-

nizes it as an unknown; however, if this error is lower

than the threshold, the classiﬁer estimates it as a class.

Although this method affords higher recognition per-

formance than discriminative model-based methods,

it suffers from the disadvantage of higher learning

costs because the reconstruction network needs to be

added to the closed-set recognition model.

Unknown Known

Classiﬁer

Class:5 Class:5

< Threshold

Unknown

Class:5

Latent Features

Encoder

Reconstruct Images

Decoder

Reconstruct

Error

condition is satisﬁed

Figure 3: Block diagram of reconstructive model-based

methods.

2.2 Anomaly Detection using

Multidimensional Feature Space

The anomaly detection method proposed by Rip-

pel et al. focuses on the multidimensional feature

space obtained from each middle layer of Efﬁcient-

Net (Tan and Le, 2019) pre-trained using ImageNet

(Deng et al., 2009) (Rippel et al., 2020). Figure

4 presents the block diagram of the anomaly detec-

tion method. This method is performed without re-

training the pre-trained model. First, the multivariate

Gaussian distribution of normal images is obtained

by applying Gaussian ﬁtting to the multidimensional

features obtained from the middle layer, when nor-

mal images of the training data are input. During

testing, the Mahalanobis distance between the mul-

tidimensional features when the image is input and

the multivariate Gaussian distribution obtained from

the normal images of the training data are calculated.

If the Mahalanobis distance is within the set thresh-

old, the image is classiﬁed as a normal image; how-

ever, if it exceeds the threshold, it is classiﬁed as an

anomaly image. During veriﬁcation using MVTec-

AD (Bergmann et al., 2021), which is a dataset for

anomaly detection, a higher score was achieved, as

compared to previous anomaly detection methods.

2.3 Center Loss

Center loss is a loss function used for face recogni-

tion. A model with center loss learns the center point

of each class of features in a multidimensional feature

space and penalizes the distance between features and

the center point of the class. In this manner, a biased

Applying Center Loss to Multidimensional Feature Space in Deep Neural Networks for Open-set Recognition

361

Anomaly Normal

Classiﬁer

Feature

Extraction

Gaussian distribution

of normal

Multidimensional

Feature Space

Multidimensional

Features

EﬃcientNet pre-trained

with ImageNet

Anomaly

Normal

Distance<Threshold

condition is satisﬁed

Figure 4: Block diagram of anomaly detection using multi-

dimensional feature space.

feature space is formed for each class. Equation 1

shows the loss function of the center loss, where m is

the batch size, x

denotes the features of the input data

in the feature space, and c

is the center point of class

in the feature space.

∑

i=1

− c

(1)

Equation 2, 3 shows the update formula for the

center point c

of class j, Where t is a learning step,

and α is a hyperparameter. Further, δ(condition) = 1

if the condition is satisﬁed; otherwise, δ(condition) =

t+1

= c

− α · ∆c

(2)

∆c

∑

i=1

δ(y

= j) · (c

− x

)

1 +

∑

i=1

δ(y

= j)

(3)

Accordingly, the loss is calculated using Equa-

tion 1, and the center point of each class is up-

dated based on Equation 2, 3. Based on the bench-

marks conducted by the authors on face recognition

datasets, high performance was conﬁrmed even on

small datasets. This also proves that the loss func-

tion is easier to optimize, as compared to the previous

loss functions used for face recognition.

3 PROPOSED METHOD

In this paper, we propose an open-set recognition

method using the multidimensional feature space of

neural networks. We train the neural network on a

dataset comprising only known classes, as in the case

of closed-set recognition. During training, center loss

is applied to the middle layer, immediately before the

output layer of the neural network. In a multidimen-

sional feature space, features of the unknown class are

expected to appear at different positions from features

of the trained classes. By applying center-loss to the

multidimensional feature space, the distance between

features of the trained classes can be shortened, so

that features of the unknown class appear farther from

features of the trained classes compared to the case

where center-loss is not applied. We also calculate

the cross-entropy loss for the probability distributions

of each class, which is the ﬁnal output. The sum of

these values is used in training as the loss of the neu-

ral network. Next, the training data are input to the

trained neural network, and multivariate Gaussian ﬁt-

ting is performed on the clusters of each class that

appear in the feature space.

Figure 5 shows the block diagram for testing.

First, the test data are input, and the classes are es-

timated. Next, we calculate the Mahalanobis dis-

tance between the multivariate Gaussian distribution

of the estimated classes and the test data. Equation 4

presents the formula for calculating the Mahalanobis

distance d(x

x). Here, x

x is a feature in the multidimen-

sional feature space, and µ

and Σ

are the mean and

covariance matrix of the multivariate Gaussian distri-

bution of an estimated class i, respectively.

d(x

x) =

x − µ

)

x − µ

) (4)

When the distance of the 95% conﬁdence interval

of the multivariate Gaussian distribution is set as the

threshold, the model recognizes class as an unknown

if the distance exceeds this threshold.

4 EXPERIMENT

We veriﬁed the performance of the proposed

method on three datasets: MNIST (LeCun et al.,

2010), SVHN (Netzer et al., 2011), and CIFAR-10

(Krizhevsky, 2012). All of these are 10-class datasets.

In open-set recognition, the model is only trained on

certain classes of the dataset; the untrained classes are

then tested as unknown classes, and the performance

is evaluated using macro-F1 scores. Similarly, in this

experiment, we trained the model on 6 randomly se-

lected classes out of the 10 classes in each dataset; the

VISAPP 2022 - 17th International Conference on Computer Vision Theory and Applications

362

Unknown

Known

Classiﬁer

Feature

Extraction

Class:5 Class:5

Class:5

Class:4

Class:6

Unknown

Class:5

Feature

Multidimensional

Feature Space

Distance>Threshold

condition is satisﬁed

Figure 5: Block diagram of proposed method.

remaining 4 classes were used as unknown classes.

We calculated the mean and standard deviation of

the scores after ﬁve trials. All of our experiments

were conducted using AI Bridging Cloud Infrastruc-

ture provided by National Institute of Advanced In-

dustrial Science and Technology. The model was

trained for about 2 hours using 8 cores of Intel Xeon

Platinum 8360Y Processor 2.4 GHz, NVIDIA A100

with 40GB and 32GB RAM. The experimental con-

ditions are shown in Table 1.

Table 2 presents the experimental results. The

scores of the comparison methods were obtained from

(Sun et al., 2020). The experimental results indicate

that the proposed method achieves better scores than

the previous methods on all the datasets.

5 DISCUSSION

The proposed method outperformed the previous

methods on all the datasets; compared to the pre-

vious methods, it achieved 6 points higher on the

MNIST dataset but only 2 points higher on the SVHN

and CIFAR-10 datasets. MNIST is a grayscale hand-

written character dataset; hence, there is little differ-

ence in the shapes of the recognition targets within

the same class; moreover, the color surrounding the

recognition targets remains constant. By contrast,

SVHN and CIFAR-10 are datasets created from ac-

tual environments; hence, the shapes of the recogni-

tion targets vary within the same class, and the sur-

roundings of the recognition targets are also different.

Hence, the low score is attributed to the large variance

in the multidimensional feature space of the neural

network. This suggests that center loss is not as effec-

tive as MNIST for these datasets. Therefore, chang-

ing the method to apply the multidimensional feature

space may be effective for these datasets. Therefore,

we conclude that the proposed method is highly ef-

fective when the recognition target is simple.

Table 3 presents the evaluation results of the pro-

posed method in terms of three evaluation items:

learning cost, recognition performance, and scalabil-

ity from previous closed-set recognition. The learn-

ing cost is expected to be affected by the multivariate

Gaussian ﬁtting and the center loss computation that

were additionally introduced to the network. Multi-

variate Gaussian ﬁtting involves low computational

costs because it can be performed by inputting all the

training data into the model just once. On introduc-

ing center loss to the network, the number of addi-

tional trainable parameters was only 5,120; by con-

trast, the number of trainable parameters in ResNet34

used in the experiment was approximately 20 mil-

lion. Therefore, we concluded that the effects of in-

troducing these additional computations on the learn-

ing cost were signiﬁcantly small. With regard to the

recognition performance, we achieved a score exceed-

ing those of all the previous methods. Finally, the

extension from the closed-set recognition models is

highly effective because it only employs the multidi-

mensional feature space formed in the middle layer

of the classiﬁer and does not alter the structure of the

classiﬁer. To summarize, the proposed method is su-

perior to the previous approaches in terms of the three

evaluation items.

6 FUTURE WORKS

In the future, we aim to improve the recognition per-

formance of the proposed method and to further re-

search incremental learning for open-world recogni-

tion.

In this study, we applied center loss to the mid-

dle layer. However, in the ﬁeld of facial recognition,

several loss functions have been proposed that do not

require the creation of class pairs on datasets, simi-

lar to the center loss (Deng et al., 2019; Liu et al.,

2017; Wang et al., 2018). A model with center loss

learns to locate features of the same class near each

other; however, a model with these methods can learn

to locate features of different classes situated far away

in the multidimensional feature space. Therefore, by

changing the loss function applied in the middle layer,

Applying Center Loss to Multidimensional Feature Space in Deep Neural Networks for Open-set Recognition

363

Table 1: Experiment condition.

Network ResNet34(He et al., 2016)

Training epochs 300

Number of dimensions of multidimensional feature space 512

Optimization method for cross-entropy loss Adam

Optimization method for center loss SGD

Table 2: Macro-F1 scores.

Method MNIST SVHN CIFAR-10

DM-based

methods

Softmax (Hendrycks and Gimpel, 2017) 0.768 ± 0.008 0.725 ± 0.012 0.600 ±0.037

Openmax (Bendale and Boult, 2016) 0.798 ± 0.018 0.737 ± 0.011 0.623 ±0.038

RM-based

methods

CROSR (Yoshihashi et al., 2019) 0.803 ± 0.013 0.753 ± 0.019 0.668 ±0.013

GDFR (Perera et al., 2020) 0.821 ± 0.021 0.716 ± 0.010 0.700 ±0.024

CGDL (Sun et al., 2020) 0.837 ± 0.055 0.776 ± 0.040 0.655 ±0.023

Proposed method 0.901 ± 0.021 0.780 ± 0.006 0.715 ±0.019

Table 3: Performance in terms of three evaluation items.

DM model-based methods RM model-based methods

Proposed method

Learning cost Low High Low

Recognition performance Low High High

Scalability from

closed-set recognition models

 × 

the recognition performance can be improved. The

threshold for recognition as an unknown class was

determined based on the conﬁdence interval. There-

fore, the unknown recognition performance can be

improved by using a different threshold determination

method, instead of the traditional anomaly detection.

The open-set recognition proposed herein does

not learn the additional classes recognized as un-

known classes. The recognition method that in-

cludes incremental learning, whereby classes recog-

nized as unknown in open-set recognition are addi-

tionally learned, is termed as open-world recognition

(Bendale and Boult, 2015). In the future, we aim to

study and apply incremental learning for the proposed

open-set recognition.

7 CONCLUSION

In this work, we developed and veriﬁed an open-set

recognition method using the Mahalanobis distance in

the multidimensional feature space formed at the mid-

dle layer of a neural network. We applied center loss

to the middle layer during training; consequently, fea-

tures of the same class were located near each other in

the multidimensional feature space. The experimental

results show that the proposed method achieves bet-

ter scores than state-of-the-art methods on all datasets

(i.e., MNIST, SVHN, and CIFAR-10). In addition,

the proposed method achieves better results than the

previous methods in terms of three metrics: learning

cost, recognition performance, and scalability from

closed-set recognition models. In the future, we plan

to further improve the recognition performance and

research open-world recognition.

ACKNOWLEDGMENT

This paper is based on results obtained from a

project, JPNP16007, commissioned by the New En-

ergy and Industrial Technology Development Organi-

zation (NEDO).

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