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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…

Computational Engineering, Finance, and Science · Computer Science 2021-06-09 Felipe L. Gewers , Gustavo R. Ferreira , Henrique F. de Arruda , Filipi N. Silva , Cesar H. Comin , Diego R. Amancio , Luciano da F. Costa

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…

Computation and Language · Computer Science 2018-02-27 Yuanhang Su , Yuzhong Huang , C. -C. Jay Kuo

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Machine Learning · Statistics 2012-10-29 Youwei Zhang , Laurent El Ghaoui

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,…

Machine Learning · Statistics 2015-05-06 Madeleine Udell , Corinne Horn , Reza Zadeh , Stephen Boyd

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…

Machine Learning · Statistics 2021-06-29 Avishek Chatterjee , Satyaki Mazumder , Koel Das

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

Quantitative Methods · Quantitative Biology 2018-10-18 Luigi Leonardo Palese

Cyber security threats have been growing significantly in both volume and sophistication over the past decade. This poses great challenges to malware detection without considerable automation. In this paper, we have proposed a novel…

Cryptography and Security · Computer Science 2019-02-12 Jason Zhang

Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…

Machine Learning · Computer Science 2024-10-15 Sharon Hendy , Yehuda Dar

Text classification helps analyse texts for semantic meaning and relevance, by mapping the words against this hierarchy. An analysis of various types of texts is invaluable to understanding both their semantic meaning, as well as their…

Machine Learning · Computer Science 2022-11-16 Chaitanya Chadha , Vandit Gupta , Deepak Gupta , Ashish Khanna

We propose to directly compute classification estimates by learning features encoded with their class scores using PCA. Our resulting model has a encoder-decoder structure suitable for supervised learning, it is computationally efficient…

Machine Learning · Computer Science 2022-10-27 Rozenn Dahyot

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…

Machine Learning · Statistics 2020-08-11 Keishi Sando , Hideitsu Hino

Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but (sometimes) poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on…

Machine Learning · Computer Science 2014-04-07 Jonathon Shlens

Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…

Machine Learning · Statistics 2026-01-22 Kexin Wang , Salil Bhate , João M. Pereira , Joe Kileel , Matylda Figlerowicz , Anna Seigal

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…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Machine Learning · Computer Science 2023-01-25 Arpita Gang , Waheed U. Bajwa

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

Methodology · Statistics 2014-01-15 Ngoc Mai Tran , Maria Osipenko , Wolfgang Karl Haerdle

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

Machine Learning · Computer Science 2017-10-27 Gang Wang , Jia Chen , Georgios B. Giannakis

Text Categorization (TC), also known as Text Classification, is the task of automatically classifying a set of text documents into different categories from a predefined set. If a document belongs to exactly one of the categories, it is a…

Information Retrieval · Computer Science 2014-06-09 Vishwanath Bijalwan , Pinki Kumari , Jordan Pascual , Vijay Bhaskar Semwal

Text classification is one of the most widely studied tasks in natural language processing. Motivated by the principle of compositionality, large multilayer neural network models have been employed for this task in an attempt to effectively…

Computation and Language · Computer Science 2018-08-07 Devendra Singh Sachan , Manzil Zaheer , Ruslan Salakhutdinov

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…

Methodology · Statistics 2021-12-09 Martin Schlather , Felix Reinbott
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