Related papers: PCA-RAG: Principal Component Analysis for Efficien…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Retrieval-augmented generation (RAG) can enhance the generation quality of large language models (LLMs) by incorporating external token databases. However, retrievals from large databases can constitute a substantial portion of the overall…

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…

Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It primary objective is to identify a subset of disease-causing genes from a vast pool of…

Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…

Retrieval-augmented generation (RAG) has emerged as an approach to augment large language models (LLMs) by reducing their reliance on static knowledge and improving answer factuality. RAG retrieves relevant context snippets and generates an…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

Retrieval-augmented generation (RAG) has become a common strategy for updating large language model (LLM) responses with current, external information. However, models may still rely on memorized training data, bypass the retrieved…

Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…

Retrieval-Augmented Generation (RAG) is an advanced technique designed to address the challenges of Artificial Intelligence-Generated Content (AIGC). By integrating context retrieval into content generation, RAG provides reliable and…

Large language models (LLMs) exhibit remarkable capabilities but often produce inaccurate responses, as they rely solely on their embedded knowledge. Retrieval-Augmented Generation (RAG) enhances LLMs by incorporating an external…

Retrieval-augmented generation (RAG) enhances language models by integrating external knowledge, but its effectiveness is highly dependent on system configuration. Improper retrieval settings can degrade performance, making RAG less…

Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…

Although Large Language Models (LLMs) demonstrate significant capabilities, their reliance on parametric knowledge often leads to inaccuracies. Retrieval Augmented Generation (RAG) mitigates this by incorporating external knowledge, but…

Purpose: Large Language Models (LLMs) hold significant promise for medical applications. Retrieval Augmented Generation (RAG) emerges as a promising approach for customizing domain knowledge in LLMs. This case study presents the development…

Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…