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We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

This paper presents a generic pre-processor for expediting conventional template matching techniques. Instead of locating the best matched patch in the reference image to a query template via exhaustive search, the proposed algorithm rules…

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low…

As a fundamental task in natural language processing, word embedding converts each word into a representation in a vector space. A challenge with word embedding is that as the vocabulary grows, the vector space's dimension increases, which…

The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…

We consider the problem of sequential recommendations, where at each step an agent proposes some slate of $N$ distinct items to a user from a much larger catalog of size $K>>N$. The user has unknown preferences towards the recommendations…

Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem…

Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…

In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…

Subdata selection is a study of methods that select a small representative sample of the big data, the analysis of which is fast and statistically efficient. The existing subdata selection methods assume that the big data can be reasonably…

The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…

While variable selection is essential to optimize the learning complexity by prioritizing features, automating the selection process is preferred since it requires laborious efforts with intensive analysis otherwise. However, it is not an…

A novel text data dimension reduction technique, called the tree-structured multi-linear principal component anal- ysis (TMPCA), is proposed in this work. Being different from traditional text dimension reduction methods that deal with the…

Dimension of the encoder output (i.e., the code layer) in an autoencoder is a key hyper-parameter for representing the input data in a proper space. This dimension must be carefully selected in order to guarantee the desired reconstruction…

Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of the data space and then applies a…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Feature selection is a dimensionality reduction technique that selects a subset of representative features from high dimensional data by eliminating irrelevant and redundant features. Recently, feature selection combined with sparse…