http://www.dsp.utoronto.ca/%7Ehaiping/Publication/SurveyMSL_PR2011.pdf

A survey of multilinear subspace learning for tensor data

Compression of facial images using the K-SVD algorithm

We propose a simple yet effective structural patch decomposition approach for multi-exposure image fusion (MEF) that is robust to ghosting effect. We decompose an image patch into three conceptually independent components: signal strength, signal structure, and mean intensity. Upon fusing these three components separately, we reconstruct a desired patch and place it back into the fused image. This novel patch decomposition approach benefits MEF in many aspects. First, as opposed to most pixel-wise MEF methods, the proposed algorithm does not require post-processing steps to improve visual quality or to reduce spatial artifacts. Second, it handles RGB color channels jointly, and thus produces fused images with more vivid color appearance. Third and most importantly, the direction of the signal structure component in the patch vector space provides ideal information for ghost removal. It allows us to reliably and efficiently reject inconsistent object motions with respect to a chosen reference image without performing computationally expensive motion estimation. We compare the proposed algorithm with 12 MEF methods on 21 static scenes and 12 deghosting schemes on 19 dynamic scenes (with camera and object motion). Extensive experimental results demonstrate that the proposed algorithm not only outperforms previous MEF algorithms on static scenes but also consistently produces high quality fused images with little ghosting artifacts for dynamic scenes. Moreover, it maintains a lower computational cost compared with the state-of-the-art deghosting schemes. 1 1 The MATLAB code of the proposed algorithm will be made available online. Preliminary results of Section III-A [1] were presented at the IEEE International Conference on Image Processing, Canada, 2015.

Robust Multi-Exposure Image Fusion: A Structural Patch Decomposition Approach

The support vector machine (SVM) has provided higher performance than traditional learning machines and has been widely applied in real-world classification problems and nonlinear function estimation problems. Unfortunately, the training process of the SVM is sensitive to the outliers or noises in the training set. In this paper, a common misunderstanding of Gaussian-function-based kernel fuzzy clustering is corrected, and a kernel fuzzy c-means clustering-based fuzzy SVM algorithm (KFCM-FSVM) is developed to deal with the classification problems with outliers or noises. In the KFCM-FSVM algorithm, we first use the FCM clustering to cluster each of two classes from the training set in the high-dimensional feature space. The farthest pair of clusters, where one cluster comes from the positive class and the other from the negative class, is then searched and forms one new training set with membership degrees. Finally, we adopt FSVM to induce the final classification results on this new training set. The computational complexity of the KFCM-FSVM algorithm is analyzed. A set of experiments is conducted on six benchmarking datasets and four artificial datasets for testing the generalization performance of the KFCM-FSVM algorithm. The results indicate that the KFCM-FSVM algorithm is robust for classification problems with outliers or noises.

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A Kernel Fuzzy c-Means Clustering-Based Fuzzy Support Vector Machine Algorithm for Classification Problems With Outliers or Noises

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Sequential fuzzy cluster extraction by a graph spectral method

Recently four non-iterative algorithms for simultaneous low rank approximations of matrices (SLRAM) have been presented by several researchers. In this paper, we show that those algorithms are equivalent to each other because they are reduced to the eigenvalue problems of row-row and column-column covariance matrices of given matrices. Also, we show a relationship between the non-iterative algorithms and another algorithm which is claimed to be an analytical algorithm for the SLRAM. Experimental results show that the analytical algorithm does not necessarily give the optimal solution of the SLRAM.

Equivalence of Non-Iterative Algorithms for Simultaneous Low Rank Approximations of Matrices

Linear discriminant analysis (LDA) is a well-known scheme for feature extraction and dimensionality reduction of labeled data in a vector space. Recently, LDA has been extended to two-dimensional LDA (2DLDA), which is an iterative algorithm for data in matrix representation. In this paper, we propose non-iterative algorithms for 2DLDA. Experimental results show that the non-iterative algorithms achieve competitive recognition rates with the iterative 2DLDA, while they are computationally more efficient than the iterative 2DLDA.

Non-Iterative Two-Dimensional Linear Discriminant Analysis

We propose two methods for robustifying multilinear principal component analysis (MPCA) which is an extension of the conventional PCA for reducing the dimensions of vectors to higher-order tensors For two kinds of outliers, ie, sample outliers and intra-sample outliers, we derive iterative algorithms on the basis of the Lagrange multipliers We also demonstrate that the proposed methods outperform the original MPCA when datasets contain such outliers experimentally

/pdf/robust-multilinear-principal-component-analysis-w8w1qlj0ua.pdf

Robust multilinear principal component analysis

We present a method for extracting arbitrarily shaped clusters buried in uniform noise data. The popular k-means algorithm is firstly fuzzified with addition of entropic terms to the objective function of data partitioning problem. This fuzzy clustering is then kernelized for adapting to the arbitrary shape of clusters. Finally, the Euclidean distance in this kernelized fuzzy clustering is modified to a robust one for avoiding the influence of noisy background data. This robust kernel fuzzy clustering method is shown to outperform every its predecessor: fuzzified k-means, robust fuzzified k-means and kernel fuzzified k-means algorithms.

Kohei Inoue

Papers

Sequential fuzzy cluster extraction by a graph spectral method

Equivalence of Non-Iterative Algorithms for Simultaneous Low Rank Approximations of Matrices

Non-Iterative Two-Dimensional Linear Discriminant Analysis

Robust multilinear principal component analysis

Robust kernel fuzzy clustering