相关论文: Dimensionality reduction, and function approximati…

High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…

In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the…

Structured pruning is a widely used technique for reducing the size of pre-trained language models (PLMs), but current methods often overlook the potential of compressing the hidden dimension (d) in PLMs, a dimension critical to model size…

Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and…

The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Single-cell RNA sequencing (scRNA-seq) has revolutionized our ability to analyze gene expression at the cellular level. By providing data on gene expression for each individual cell, scRNA-seq generates large datasets with thousands of…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead…

Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…

Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…

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,…

As the feature size of semiconductor technology shrinks to 10 nm and beyond, the multiple patterning lithography (MPL) attracts more attention from the industry. In this paper, we model the layout decomposition of MPL as a generalized graph…

Most existing structured pruning methods for Large Language Models (LLMs) require substantial computational and data resources for retraining to reestablish the corrupted correlations, making them prohibitively expensive. To address this,…

One of the most interesting tools that have recently entered the data science toolbox is topological data analysis (TDA). With the explosion of available data sizes and dimensions, identifying and extracting the underlying structure of a…

Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such…

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High…

Pruning has recently been widely adopted to reduce the parameter scale and improve the inference efficiency of Large Language Models (LLMs). Mainstream pruning techniques often rely on uniform layerwise pruning strategies, which can lead to…