Locality linear fitting one-class SVM with low-rank constraints for outlier detection

Abstract

We propose a novel outlier detection approach in this paper, which learns the most accurate hyperspheres for the normal data through a top-down procedure. Conventional one-class support vector machine (SVM) based approaches aim to find nonlinear global solutions for all the normal data, with the benefit of kernel trick. However, those methods are intractable when data are in large-scale and inaccurate when data are under complex distributions. It's observed that high dimensional data, e.g., features of texts or images, are always sparse, and linear classifier usually performs well. A specific class of data seldom lie in one single subspace. In this paper, we propose to learn multiple discriminative hyper-spheres locally based on the data distributions, and fit them globally to formulate a more discriminative boundary for the normal data. By far, neural mechanisms used by human brain-mind for outlier detection are not known, however, the top-down strategy proposed in this paper would inspire understanding of the human neural mechanisms. The benefits of our model are twofolds. First, the distribution of each local cluster is much simpler than that in a global view, which makes the fitting processing for each individual cluster much easier and insensitive to the choice of kernel. In particular, we adopt low-rank constraints to find multiple clusters automatically. Secondly, the proposed approach trains the model linearly which tackles the largescale problem, substantially reducing training time and memory space. Extensive experimental results on three image databases demonstrate that our approach outperforms several related methods.

Manifold Learning for 3D Shape Description and Classification

“…However, how to find different human shapes from 3D torso data is still an open problem. From this STIR project, we have created a new algorithmic tool set of modeling large-scale high dimensional data [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For uncertainty visual representation, we proposed a class of manifold and subspace learning methods [1] including submanifold decomposition [4], manifold clustering [11], deep learning [14], one-class classification [10], low-rank and discriminative dictionary learning [6], robust low-rank subspace discovery [7], lowrank tensor completion [8] and low-rank transfer subspace learning [3].…”

“…From this STIR project, we have created a new algorithmic tool set of modeling large-scale high dimensional data [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For uncertainty visual representation, we proposed a class of manifold and subspace learning methods [1] including submanifold decomposition [4], manifold clustering [11], deep learning [14], one-class classification [10], low-rank and discriminative dictionary learning [6], robust low-rank subspace discovery [7], lowrank tensor completion [8] and low-rank transfer subspace learning [3]. We also proposed applications of these techniques to analyzing spatial-temporal patterns of human motion, action, and activity [2], 3D hand-gesture recognition [5], expression animation by motion capture [9], 3D human torso shape understanding [11], discriminative pose sub-patterns [12], human gesture in social context [13].…”

Anomaly Detection Using Deep Learning Based Image Completion

“…Learning based anomaly detection methods, that are purely trainable with one-class data, are for example one-class SVMs, which were first introduced by Schölkopf et al [17]. Li et al [18] used them in combination with clustering for outlier detection of face images. Another one-class anomaly detection method was proposed by Zhang et al [19], who used a CNN to map normal instances into a certain feature space, in which the mapped instances were clustered within a hypersphere.…”

Robustness Can Be Cheap: A Highly Efficient Approach to Discover Outliers under High Outlier Ratios

“…In addition, another related topic is low-rank analysis, which is rarely considered in outlier detection. The most relevant works to our knowledge are (Li, Shao, and Fu 2014a;2014b), which embed a low-rank constraint into the classic one-class support vector machine or support vector data description to improve their performance. Besides, (Li, Shao, and Fu 2018) conduct cross-view low-rank analysis to perform multi-view outlier detection.…”