An Updated OT-PCF Algorithm for One-class Classification of Tensor Datasets
Meiqing Wang, Hou Q., Hao Chen, Xu Y., Gang Zhou · Pacific Journal of Optimization · 2023
(Communicated by Chen Ling) Abstract: Machine learning is one of the most popular topics in recent years, in which the so called one-class classification problem is one of important and interesting problems. The purpose of supervised data classification is to label test data by a classification algorithm based on training data. Different from other classification problems, one-class classification studies a special classification problem that only one class of training samples is available or reliable, while others are either expensive to acquire or difficult to characterize. To the best of our knowledge, the one-class classification problem has many applications such as fault diagnosis, face recognition, the network anomaly detection and text classification etc. Noted that, most one-class classifier such as one-class support vector machines are encoded in vector and matrix spaces. The main idea is to construct a decision boundary around positive data in order to distinguish it from outliers data. However, in many real world applications data are represented more naturally as higher order tensors. For example, sensor data are often organised into the three modes of location, type, and time, while videos are represented as 3D objects corresponding to concatenated frames over time. Thus, with the development of tensor theory, more and more classifiers have been proposed to tensor space. In this paper, we present a new polyhedral conic function (PCF) algorithm to solve the one-class classification problem related with tensor data i.e. named OT-PCF algorithm (“O” means “one class” and “T” means “tensor data”). The corresponding optimization problem is as follows: Here is the given training set including several tensors. By the way, a PCF function will be given to minimize the size of the decision boundaries. The parameter controls the tradeoff between the size of the decision boundaries and the size of the classification error. The variable zi represents the classification error of data object . Since the level set of PCF is polyhedron, only convex decision boundary can be obtained by PCF. However, the target class may have a non-convex structure. To overcome this drawback, by the classicalk-means algorithm, the proposed OT-PCF algorithm divides the target class into k clusters in advance with a fixed center respectively and then a PCF for each cluster can be obtained. The final classifier of the OT-PCF algorithm is given as the minimum of k PCFs to generate non-convex separating surfaces: To show the efficiency of the proposed method, we compare the proposed algorithm with an efficient method in the literature i.e. linear support higher order tensor domain description(LSTDD) algorithm. By testing on real-world datasets including vector data, matrix data and tensor data, experiments show that the proposed algorithm is a promising method for handling one-class classification problems. Furthermore, the OT-PCF is more stable for different parameters k and .