Related papers: PCA-RAG: Principal Component Analysis for Efficien…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
Retrieval-augmented generation (RAG) has emerged as a pivotal method for expanding the knowledge of large language models. To handle complex queries more effectively, researchers developed Adaptive-RAG (A-RAG) to enhance the generated…
Principal component analysis (PCA) is one of the most fundamental tools in machine learning with broad use as a dimensionality reduction and denoising tool. In the later setting, while PCA is known to be effective at subspace recovery and…
In this paper, we present a fast and reliable method based on PCA to select the number of dimensions for word embeddings. First, we train one embedding with a generous upper bound (e.g. 1,000) of dimensions. Then we transform the embeddings…
Principal Component Analysis (PCA) is well known for its capability of dimension reduction and data compression. However, when using PCA for compressing/reconstructing images, images need to be recast to vectors. The vectorization of images…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
With the rapid development of Large Language Models (LLMs), Retrieval-Augmented Generation (RAG) has become a predominant method in the field of professional knowledge-based question answering. Presently, major foundation model companies…
Retrieval-augmented generation (RAG) synergizes the retrieval of pertinent data with the generative capabilities of Large Language Models (LLMs), ensuring that the generated output is not only contextually relevant but also accurate and…
Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant…
Large Language Models (LLMs) have enabled a wide range of applications through their powerful capabilities in language understanding and generation. However, as LLMs are trained on static corpora, they face difficulties in addressing…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
Retrieval-Augmented Generation (RAG) has emerged as a widely adopted approach for knowledge injection during large language model (LLM) inference in recent years. However, due to their limited ability to exploit fine-grained inter-document…
Retrieval-Augmented Generation (RAG) represents a major advancement in natural language processing (NLP), combining large language models (LLMs) with information retrieval systems to enhance factual grounding, accuracy, and contextual…
Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…
Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called REAPER, aims to find the principal components by solving a convex…