Related papers: Unified Framework for Spectral Dimensionality Redu…

Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches,…

Machine learning and quantum computing are being progressively explored to shed light on possible computational approaches to deal with hitherto unsolvable problems. Classical methods for machine learning are ubiquitous in pattern…

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with…

We present a novel method to reconstruct a spectral central view and its aligned disparity map from spatio-spectrally coded light fields. Since we do not reconstruct an intermediate full light field from the coded measurement, we refer to…

We introduce a semi-supervised learning estimator which tends to the first kernel principal component as the number of labelled points vanishes. Our approach is based on the notion of optimal target vector, which is defined as follows.…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

In this work, a novel algorithm called SVM with Shape-adaptive Reconstruction and Smoothed Total Variation (SaR-SVM-STV) is introduced to classify hyperspectral images, which makes full use of spatial and spectral information. The…

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…

Kernel adaptive filtering (KAF) integrates traditional linear algorithms with kernel methods to generate nonlinear solutions in the input space. The standard approach relies on the representer theorem and the kernel trick to perform…

This paper presents Universal Vision-Language Dense Retrieval (UniVL-DR), which builds a unified model for multi-modal retrieval. UniVL-DR encodes queries and multi-modality resources in an embedding space for searching candidates from…

Hyperspectral optical imaging provides rich spectral information for estimating continuous environmental and material parameters; however, its high dimensionality and strong feature correlation pose significant challenges for machine…

This is a tutorial and survey paper on metric learning. Algorithms are divided into spectral, probabilistic, and deep metric learning. We first start with the definition of distance metric, Mahalanobis distance, and generalized Mahalanobis…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and…

Representation learning often plays a critical role in reinforcement learning by managing the curse of dimensionality. A representative class of algorithms exploits a spectral decomposition of the stochastic transition dynamics to construct…

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…

Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to…

Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…