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The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Sequential multi-class diagnosis, also known as multi-hypothesis testing, is a classical sequential decision problem with broad applications. However, the optimal solution remains, in general, unknown as the dynamic program suffers from the…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…
Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a…
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…
Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…
This work considers semi-supervised segmentation as a dense prediction problem based on prototype vector correlation and proposes a simple way to represent each segmentation class with multiple prototypes. To avoid degenerate solutions, two…
Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the…
Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…
In self-supervised representation learning, a common idea behind most of the state-of-the-art approaches is to enforce the robustness of the representations to predefined augmentations. A potential issue of this idea is the existence of…
In this paper, we propose a new mathematical optimization model for multiclass classification based on arrangements of hyperplanes. Our approach preserves the core support vector machine (SVM) paradigm of maximizing class separation while…
This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…