Related papers: A Kernelizable Primal-Dual Formulation of the Mult…

Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to…

In this article, a large dimensional performance analysis of kernel least squares support vector machines (LS-SVMs) is provided under the assumption of a two-class Gaussian mixture model for the input data. Building upon recent advances in…

We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…

Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…

For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically…

Multiple kernel learning (MKL) algorithms combine different base kernels to obtain a more efficient representation in the feature space. Focusing on discriminative tasks, MKL has been used successfully for feature selection and finding the…

Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However,…

We introduce the Singular Value Representation (SVR), a new method to represent the internal state of neural networks using SVD factorization of the weights. This construction yields a new weighted graph connecting what we call spectral…

This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data…

The support vector machines (SVM) is one of the most widely used and practical optimization based classification models in machine learning because of its interpretability and flexibility to produce high quality results. However, the big…

Typically, voice conversion is regarded as an engineering problem with limited training data. The reliance on massive amounts of data hinders the practical applicability of deep learning approaches, which have been extensively researched in…

We evaluate performance of associative memory in a neural network by based on the singular value decomposition (SVD) of image data stored in the network. We consider the situation in which the original image and its highly coarse-grained…

Continual learning in large language models (LLMs) is prone to catastrophic forgetting, where adapting to new tasks significantly degrades performance on previously learned ones. Existing methods typically rely on low-rank,…

Multiple Kernel Learning(MKL) on Support Vector Machines(SVMs) has been a popular front of research in recent times due to its success in application problems like Object Categorization. This success is due to the fact that MKL has the…

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…

A significant challenge to make learning techniques more suitable for general purpose use is to move beyond i) complete supervision, ii) low dimensional data, iii) a single task and single view per instance. Solving these challenges allows…

Support vector machines (SVMs) have been successful in solving many computer vision tasks including image and video category recognition especially for small and mid-scale training problems. The principle of these non-parametric models is…

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…

Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…