Related papers: Class Mean Vector Component and Discriminant Analy…

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…

We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We…

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…

A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…

Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel's scale parameter, also referred to as the kernel's…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…

As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…

Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory.…

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…

We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned…