Related papers: A Comparative Analysis of Principal Component Anal…

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and…

Principal component analysis (PCA) is an essential algorithm for dimensionality reduction in many data science domains. We address the problem of performing a federated PCA on private data distributed among multiple data providers while…

Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network…

Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear…

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing 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…

This paper presents the modal truncation and singular value decomposition (SVD) technique as two main algorithms for dynamic model reduction of the power system. The significance and accuracy of the proposed methods are investigated with…

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…

Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…

In the age of information explosion, image classification is the key technology of dealing with and organizing a large number of image data. Currently, the classical image classification algorithms are mostly based on RGB images or…

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…