3,269 research outputs found
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
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.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
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.Comment: 232 page
Asymmetric bagging and random subspace for support vector machines-based relevance feedback in image retrieval
Relevance feedback schemes based on support vector machines (SVM) have been widely used in content-based image retrieval (CBIR). However, the performance of SVM-based relevance feedback is often poor when the number of labeled positive feedback samples is small. This is mainly due to three reasons: 1) an SVM classifier is unstable on a small-sized training set, 2) SVM's optimal hyperplane may be biased when the positive feedback samples are much less than the negative feedback samples, and 3) overfitting happens because the number of feature dimensions is much higher than the size of the training set. In this paper, we develop a mechanism to overcome these problems. To address the first two problems, we propose an asymmetric bagging-based SVM (AB-SVM). For the third problem, we combine the random subspace method and SVM for relevance feedback, which is named random subspace SVM (RS-SVM). Finally, by integrating AB-SVM and RS-SVM, an asymmetric bagging and random subspace SVM (ABRS-SVM) is built to solve these three problems and further improve the relevance feedback performance
Learning Using Privileged Information: SVM+ and Weighted SVM
Prior knowledge can be used to improve predictive performance of learning
algorithms or reduce the amount of data required for training. The same goal is
pursued within the learning using privileged information paradigm which was
recently introduced by Vapnik et al. and is aimed at utilizing additional
information available only at training time -- a framework implemented by SVM+.
We relate the privileged information to importance weighting and show that the
prior knowledge expressible with privileged features can also be encoded by
weights associated with every training example. We show that a weighted SVM can
always replicate an SVM+ solution, while the converse is not true and we
construct a counterexample highlighting the limitations of SVM+. Finally, we
touch on the problem of choosing weights for weighted SVMs when privileged
features are not available.Comment: 18 pages, 8 figures; integrated reviewer comments, improved
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