The classification loss functions used in deep neural network classifiers can be split into two categories based on maximizing the margin in either Euclidean or angular spaces. Euclidean distances between sample vectors are used during classification for the methods maximizing the margin in Euclidean spaces whereas the Cosine similarity distance is used during the testing stage for the methods maximizing the margin in the angular spaces. This article introduces a novel classification loss that maximizes the margin in both the Euclidean and angular spaces at the same time. This way, the Euclidean and Cosine distances will produce similar and consistent results and complement each other, which will in turn improve the accuracies. The proposed loss function enforces the samples of classes to cluster around the centers that represent them. The centers approximating classes are chosen from the boundary of a hypersphere, and the pair-wise distances between class centers are always equivalent. This restriction corresponds to choosing centers from the vertices of a regular simplex inscribed in a hypersphere. The proposed loss function can be effortlessly applied to classical classification problems as there is a single hyperparameter that must be set by the user, and setting this parameter is straightforward. Additionally, the proposed method can effectively reject test samples from unfamiliar classes by measuring their distances from the known class centers, which are compactly clustered around their corresponding centers. Therefore, the proposed technique is especially suitable for open set recognition problems. Despite its simplicity, experimental studies have demonstrated that the proposed method outperforms other techniques in both open set recognition and classical classification problems. Interested individuals can access the source code for the proposed approach at https://github.com/Cevikalp/dsc.

Abstract Anomaly detection is a method employed to identify data points or patterns that significantly deviate from expected or normal behaviour within a dataset. This approach aims to detect observations regarded as unusual, erroneous, anomalous, rare, or potentially indicative of fraudulent or malicious activity. Open‐set recognition, also referred to as open‐set identification or open‐set classification, is a pattern recognition task that extends traditional classification by addressing the presence of unknown or novel classes during the testing phase. This approach highlights a strong connection between anomaly detection and open‐set recognition, as both seek to identify samples originating from unknown classes or distributions. Open‐set recognition methods frequently involve modelling both known and unknown classes during training, allowing for the capture of the distribution of known classes while explicitly addressing the space of unknown classes. Techniques in open‐set recognition may include outlier detection, density estimation, or configuring decision boundaries to better differentiate between known and unknown classes. This special issue calls for original contributions introducing novel datasets, innovative architectures, and advanced training methods for tasks related to visual anomaly detection and open‐set recognition.

Abstract In the field of machine learning, clustering has become an increasingly popular research topic due to its critical importance. Many clustering algorithms have been proposed utilizing a variety of approaches. This study focuses on clustering of high-dimensional data using the maximum margin clustering approach. In this paper, two methods are introduced: The first method employs the classical maximum margin clustering approach, which separates data into two clusters with the greatest margin between them. The second method takes cluster compactness into account and searches for two parallel hyperplanes that best fit to the cluster samples while also being as far apart from each other as possible. Additionally, robust variants of these clustering methods are introduced to handle outliers and noise within the data samples. The stochastic gradient algorithm is used to solve the resulting optimization problems, enabling all proposed clustering methods to scale well with large-scale data. Experimental results demonstrate that the proposed methods are more effective than existing maximum margin clustering methods, particularly in high-dimensional clustering problems, highlighting the efficacy of the proposed methods.

This article introduces two methods that find compact deep feature models for approximating images in set based face recognition problems. The proposed method treats each image set as a nonlinear face manifold that is composed of linear components. To find linear components of the face manifold, we first split image sets into subsets containing face images which share similar appearances. Then, our first proposed method approximates each subset by using the center of the deep feature representations of images in those subsets. Centers modeling the subsets are learned by using distance metric learning. The second proposed method uses discriminative common vectors to represent image features in the subsets, and entire subset is approximated with an affine hull in this approach. Discriminative common vectors are subset centers that are projected onto a new feature space where the combined within-class variances coming from all subsets are removed. Our proposed methods can also be considered as distance metric learning methods using triplet loss function where the learned subcluster centers are the selected anchors. This procedure yields to applying distance metric learning to quantized data and brings many advantages over using classical distance metric learning methods. We tested proposed methods on various face recognition problems using image sets and some visual object classification problems. Experimental results show that the proposed methods achieve the state-of-the-art accuracies on the most of the tested image datasets.

The classifiers that return compact acceptance regions are crucial for the success in anomaly detection and open set recognition settings since we have to determine and reject the anomalies and samples coming from the unknown classes. This paper introduces novel methods that approximate the class acceptance regions with compact hypersphere models for anomaly detection and open set recognition. As opposed to the other deep hypersphere classifiers, we treat the hypersphere centers as learnable parameters and update them based on the changing deep feature representations. In addition, we propose novel loss terms that are more robust to the noisy labels within the outlier exposure and background datasets. The proposed methods bear similarity to the deep distance metric learning classifiers using the triplet loss function with the exception that the anchors are set to the hypersphere centers which are updated dynamically. The experimental results show that the proposed methods achieve the state-of-the-art accuracies on the majority of the tested datasets in the context of anomaly detection and open set recognition.

This paper introduces a family of quasi-linear discriminants that outperform current large-margin methods in sliding window visual object detection and open set recognition tasks. In these applications, the classification problems are both numerically imbalanced - positive (object class) training and test windows are much rarer than negative (non-class) ones - and geometrically asymmetric - the positive samples typically form compact, visually-coherent groups while negatives are much more diverse, including anything at all that is not a well-centered sample from the target class. For such tasks, there is a need for discriminants whose decision regions focus on tightly circumscribing the positive class, while still taking account of negatives in zones where the two classes overlap. To this end, we propose a family of quasi-linear “polyhedral conic” discriminants whose positive regions are distorted L1or L2balls. In addition, we also integrated the proposed classification loss into deep neural networks so that both the features and classifier can be learned simultaneously end-to-end fashion to improve the classification accuracies. The methods have properties and run-time complexities comparable to linear Support Vector Machines (SVMs), and they can be trained from either binary or positive-only samples using constrained quadratic programs related to SVMs. Our experiments show that they significantly outperform linear SVMs, deep neural networks using softmax loss function and existing one-class discriminants on a wide range of object detection, face verification, open set recognition and conventional closed-set classification tasks.

A wide range of face appearance variations can be modeled by using set-based recognition approaches effectively, but computational complexity of current methods is highly dependent on the set and class sizes. This paper introduces new video-based classification methods designed for reducing the required disk space of data samples and speed up the testing process in large-scale face recognition systems. In the proposed method, image sets collected from videos are approximated with kernelized convex hulls and it was shown that it is sufficient to use only the samples that participate in shaping the image set boundaries in this setting. The kernelized support vector data description (SVDD) is used to extract those important samples that form the image set boundaries. Moreover, we show that these kernelized hypersphere models can also be used to approximate image sets for classification purposes. Then, we propose a binary hierarchical decision tree approach to improve the speed of the classification system even more. At last, we introduce a new video database that includes 285 people with 8 videos of each person, since the most popular video data sets used for set-based recognition methods include either a few people, or small number of videos per person. The experimental results on varying sized databases show that the proposed methods greatly improve the testing times of the classification system (we obtained speed-ups to a factor of 20) without a significant drop in accuracies.

Majority of the image set based face recognition methods use a generatively learned model for each person that is learned independently by ignoring the other persons in the gallery set. In contrast to these methods, this paper introduces a novel method that searches for discriminative convex models that best fit to an individual's face images but at the same time are as far as possible from the images of other persons in the gallery. We learn discriminative convex models for both affine and convex hulls of image sets. During testing, distances from the query set images to these models are computed efficiently by using simple matrix multiplications, and the query set is assigned to the person in the gallery whose image set is closest to the query images. The proposed method significantly outperforms other methods using generative convex models in terms of both accuracy and testing time, and achieves the state-of-the-art results on four of the five tested datasets. Especially, the accuracy improvement is significant on the challenging PaSC, COX and ESOGU video datasets.

Automatically classifying an image has been a central problem in computer vision for decades. A plethora of models has been proposed, from handcrafted feature solutions to more sophisticated approaches such as deep learning. The authors address the problem of remote sensing image classification, which is an important problem to many real world applications. They introduce a novel deep recurrent architecture that incorporates high‐level feature descriptors to tackle this challenging problem. Their solution is based on the general encoder–decoder framework. To the best of the authors’ knowledge, this is the first study to use a recurrent network structure on this task. The experimental results show that the proposed framework outperforms the previous works in the three datasets widely used in the literature. They have achieved a state‐of‐the‐art accuracy rate of 97.29% on the UC Merced dataset.

In this paper, we propose novel methods that are more suitable than classical large-margin classifiers for open set recognition and object detection tasks. The proposed methods use the best fitting hyperplanes approach, and the main idea is to find the best fitting hyperplanes such that each hyperplane is close to the samples of one of the classes and is as far as possible from the other class samples. To this end, we propose two different classifiers: The first classifier solves a convex quadratic optimization problem, but negative samples can lie on one side of the best fitting hyperplane. The second classifier, however, allows the negative samples to lie on both sides of the fitting hyperplane by using concave-convex procedure. Both methods are extended to the nonlinear case by using the kernel trick. In contrast to the existing hyperplane fitting classifiers in the literature, our proposed methods are suitable for large-scale problems, and they return sparse solutions. The experiments on several databases show that the proposed methods typically outperform other hyperplane fitting classifiers, and they work as good as the SVM classifier in classical recognition tasks. However, the proposed methods significantly outperform SVM in open set recognition and object detection tasks.

In this paper, we propose a novel method that is more appropriate than classical large-margin classifiers for open set recognition and object detection problems. The proposed method uses the best fitting hyper planes approach, and the main idea is to find the best fitting hyper planes such that each hyper plane is close to the samples of one of the two classes and as far as possible from the other class samples. As opposed to the most common hyper plane fitting classifiers in the literature, the proposed classifier allows the negative samples to lie on both sides of the fitting hyper plane and hence it is based on a non-convex optimization problem. We use concave-convex procedure to solve this non-convex problem. Then, the method is extended to the nonlinear case by using the kernel trick. The proposed method is also suitable for large-scale problems, and it returns sparse solutions in contrast to the other hyper plane fitting methods in the literature. The experiments on several databases show that our proposed method typically outperforms other hyper plane fitting classifiers in term of classification accuracy, and it performs as good as the SVM classifier if not any better.

An object detector must detect and localize each instance of the object class of interest in the image. Many recent detectors adopt a sliding window approach, reducing the problem to one of deciding whether the detection window currently contains a valid object instance or background. Machine learning based discriminants such as SVM and boosting are typically used for this, often in the form of classifier cascades to allow more rapid rejection of easy negatives. We argue that “one class” methods - ones that focus mainly on modelling the range of the positive class - are a useful alternative to binary discriminants in such applications, particularly in the early stages of the cascade where one-class approaches may allow simpler classifiers and faster rejection. We implement this in the form of a short cascade of efficient nearest-convex-model one-class classifiers, starting with linear distance-to-affine-hyperplane and interior-of-hypersphere classifiers and finishing with kernelized hypersphere classifiers. We show that our methods have very competitive performance on the Faces in the Wild and ESOGU face detection datasets and state-of-the-art performance on the INRIA Person dataset. As predicted, the one-class formulations provide significant reductions in classifier complexity relative to the corresponding two-class ones.

We introduce a novel method for face recognition from image sets. In our setting each test and training example is a set of images of an individual's face, not just a single image, so recognition decisions need to be based on comparisons of image sets. Methods for this have two main aspects: the models used to represent the individual image sets; and the similarity metric used to compare the models. Here, we represent images as points in a linear or affine feature space and characterize each image set by a convex geometric region (the affine or convex hull) spanned by its feature points. Set dissimilarity is measured by geometric distances (distances of closest approach) between convex models. To reduce the influence of outliers we use robust methods to discard input points that are far from the fitted model. The kernel trick allows the approach to be extended to implicit feature mappings, thus handling complex and nonlinear manifolds of face images. Experiments on two public face datasets show that our proposed methods outperform a number of existing state-of-the-art ones.

This paper introduces a semi-supervised distance metric learning algorithm which uses pair-wise equivalence (similarity and dissimilarity) constraints to improve the original distance metric in lower-dimensional input spaces. We restrict ourselves to pseudo-metrics that are in quadratic forms parameterized by positive semi-definite matrices. The proposed method works in both the input space and kernel induced feature space, and learning distance metric is formulated as a quadratic optimization problem which returns a global optimal solution. Experimental results on several databases show that the learned distance metric improves the performances of the subsequent classification and clustering algorithms.

This paper introduces a geometrically inspired large-margin classifier that can be a better alternative to the Support Vector Machines (SVMs) for the classification problems with limited number of training samples. In contrast to the SVM classifier, we approximate classes with affine hulls of their class samples rather than convex hulls, which may be unrealistically tight in high-dimensional spaces. To find the best separating hyperplane between any pair of classes approximated with the affine hulls, we first compute the closest points on the affine hulls and connect these two points with a line segment. The optimal separating hyperplane is chosen to be the hyperplane that is orthogonal to the line segment and bisects the line. To allow soft margin solutions, we first reduce affine hulls in order to alleviate the effects of outliers and then search for the best separating hyperplane between these reduced models. Multi-class classification problems are dealt with constructing and combining several binary classifiers as in SVM. The experiments on several databases show that the proposed method compares favorably with the SVM classifier.

Nearest neighbour classifiers and related kernel methods often perform poorly in high dimensional problems because it is infeasible to include enough training samples to cover the class regions densely. In such cases, test samples often fall into gaps between training samples where the nearest neighbours are too distant to be good indicators of class membership. One solution is to project the data onto a discriminative lower dimensional subspace. We propose a gap-resistant nonparametric method for finding such subspaces: first the gaps are filled by building a convex model of the region spanned by each class - we test the affine and convex hulls and the bounding disk of the class training samples - then a set of highly discriminative directions is found by building and decomposing a scatter matrix of weighted displacement vectors from training examples to nearby rival class regions. The weights are chosen to focus attention on narrow margin cases while still allowing more diversity and hence more discriminability than the 1D linear Support Vector Machine (SVM) projection. Experimental results on several face and object recognition datasets show that the method finds effective projections, allowing simple classifiers such as nearest neighbours to work well in the low dimensional reduced space.

In high-dimensional classification problems it is infeasible to include enough training samples to cover the class regions densely. Irregularities in the resulting sparse sample distributions cause local classifiers such as Nearest Neighbors (NN) and kernel methods to have irregular decision boundaries. One solution is to "fill in the holes" by building a convex model of the region spanned by the training samples of each class and classifying examples based on their distances to these approximate models. Methods of this kind based on affine and convex hulls and bounding hyperspheres have already been studied. Here we propose a method based on the bounding hyperdisk of each class - the intersection of the affine hull and the smallest bounding hypersphere of its training samples. We argue that in many cases hyperdisks are preferable to affine and convex hulls and hyperspheres: they bound the classes more tightly than affine hulls or hyperspheres while avoiding much of the sample overfitting and computational complexity that is inherent in high-dimensional convex hulls. We show that the hyperdisk method can be kernelized to provide nonlinear classifiers based on non-Euclidean distance metrics. Experiments on several classification problems show promising results.

It has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers. However, how to combine multiple classifiers with various (potentially conflicting) decisions is still an open problem. A rich collection of classifier combination procedures -- many of which are heuristic in nature -- have been developed for this goal. In this brief, we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space. To this end, we use local classifier accuracy estimates to weight classifier outputs. Specifically, we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors, and then use these estimates to find the best weights of classifiers to label the query. The problem is formulated as a convex quadratic optimization problem, which returns optimal nonnegative classifier weights with respect to the chosen objective function, and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample. Experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes, particularly on problems with complex decision boundaries. Hence, the results indicate that local classification-accuracy-based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space.

The common vector (CV) method is a linear subspace classifier method which allows one to discriminate between classes of data sets, such as those arising in image and word recognition. This method utilizes subspaces that represent classes during classification. Each subspace is modeled such that common features of all samples in the corresponding class are extracted. To accomplish this goal, the method eliminates features that are in the direction of the eigenvectors corresponding to the nonzero eigenvalues of the covariance matrix of each class. In this paper, we introduce a variation of the CV method, which will be referred to as the modified CV (MCV) method. Then, a novel approach is proposed to apply the MCV method in a nonlinearly mapped higher dimensional feature space. In this approach, all samples are mapped into a higher dimensional feature space using a kernel mapping function, and then, the MCV method is applied in the mapped space. Under certain conditions, each class gives rise to a unique CV, and the method guarantees a 100% recognition rate with respect to the training set data. Moreover, experiments with several test cases also show that the generalization performance of the proposed kernel method is comparable to the generalization performances of other linear subspace classifier methods as well as the kernel-based nonlinear subspace method. While both the MCV method and its kernel counterpart did not outperform the support vector machine (SVM) classifier in most of the reported experiments, the application of our proposed methods is simpler than that of the multiclass SVM classifier. In addition, it is not necessary to adjust any parameters in our approach.

In some pattern recognition tasks, the dimension of the sample space is larger than the number of samples in the training set. This is known as the "small sample size problem". Linear discriminant analysis (LDA) techniques cannot be applied directly to the small sample size case. The small sample size problem is also encountered when kernel approaches are used for recognition. In this paper, we attempt to answer the question of "How should one choose the optimal projection vectors for feature extraction in the small sample size case?" Based on our findings, we propose a new method called the kernel discriminative common vector method. In this method, we first nonlinearly map the original input space to an implicit higher dimensional feature space, in which the data are hoped to be linearly separable. Then, the optimal projection vectors are computed in this transformed space. The proposed method yields an optimal solution for maximizing a modified Fisher's linear discriminant criterion, discussed in the paper. Thus, under certain conditions, a 100% recognition rate is guaranteed for the training set samples. Experiments on test data also show that, in many situations, the generalization performance of the proposed method compares favorably with other kernel approaches.

In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the within-class scatter matrix is singular and the Linear Discriminant Analysis (LDA) method cannot be applied directly. This problem is known as the "small sample size" problem. In this paper, we propose a new face recognition method called the Discriminative Common Vector method based on a variation of Fisher's Linear Discriminant Analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the within-class scatter matrix of the samples in the training set while the other uses the subspace methods and the Gram-Schmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher's Linear Discriminant criterion given in the paper. Our test results show that the Discriminative Common Vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability.