In this paper, we propose a novel method for projecting data from multiple modalities to a new subspace optimized for one-class classification. The proposed method iteratively transforms the data from the original feature space of each modality to a new common feature space along with finding a joint compact description of data coming from all the modalities. For data in each modality, we define a separate transformation to map the data from the corresponding feature space to the new optimized subspace by exploiting the available information from the class of interest only. The data description in the new subspace is obtained by Support Vector Data Description. We also propose different regularization strategies for the proposed method and provide both linear and non-linear formulation. We conduct experiments on two multimodal datasets and compare the proposed approach with baseline and recently proposed one-class classification methods combined with early fusion and also considering each modality separately. We show that the proposed Multimodal Subspace Support Vector Data Description outperforms all the methods using data from a single modality and performs better or equally well than the methods fusing data from all modalities.

An image anomaly localization method based on the successive subspace learning (SSL) framework, called Anomaly-Hop, is proposed in this work. AnomalyHop consists of three modules: 1) feature extraction via successive subspace learning (SSL), 2) normality feature distributions modeling via Gaussian models, and 3) anomaly map generation and fusion. Comparing with state-of-the-art image anomaly localization methods based on deep neural networks (DNNs), AnomalyHop is mathematically transparent, easy to train, and fast in its inference speed. Besides, its area under the ROC curve (ROC-AUC) performance on the MVTec AD dataset is 95.9%, which is among the best of several benchmarking methods. 1

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In this paper, we propose a novel method for transforming data into a low-dimensional space optimized for one-class classification. The proposed method iteratively transforms data into a new subspace optimized for ellipsoidal encapsulation of target class data. We provide both linear and non-linear formulations for the proposed method. The method takes into account the covariance of the data in the subspace; hence, it yields a more generalized solution as compared to the data description in the subspace by hyperspherical encapsulation of target class data. We propose different regularization terms expressing the class variance in the projected space. We compare the results with classic and recently proposed one-class classification methods and achieve competing results and show clear improvement compared to the other support vector based methods. The proposed method is also noticed to converge much faster than recently proposed Subspace Support Vector Data Description.

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