Related papers: Efficient Text Classification Using Tree-structure…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…

The t-SVD based Tensor Robust Principal Component Analysis (TRPCA) decomposes low rank multi-linear signal corrupted by gross errors into low multi-rank and sparse component by simultaneously minimizing tensor nuclear norm and l 1 norm. But…

This paper proposes a tree-based convolutional neural network (TBCNN) for discriminative sentence modeling. Our models leverage either constituency trees or dependency trees of sentences. The tree-based convolution process extracts…

Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

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 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,…

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…

This paper develops a method to detect model structural changes by applying a Corrected Kernel Principal Component Analysis (CKPCA) to construct the so-called central distribution deviation subspaces. This approach can efficiently identify…

A generic system for text categorization is presented which uses a representative text corpus to adapt the processing steps: feature extraction, dimension reduction, and classification. Feature extraction automatically learns features from…

Humans can categorize with only a few samples despite the numerous features. To mimic this ability, we propose a novel dimension-reduced category representation using a mixture of probabilistic principal component analyzers (mPPCA). Tests…

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

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…

Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is non-trivial to develop efficient statistical methods due to two main challenges. First, profiles are high-dimensional functional…

Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…

The performance of text classification methods has improved greatly over the last decade for text instances of less than 512 tokens. This limit has been adopted by most state-of-the-research transformer models due to the high computational…

We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse…