Principal Component Analysis for Big Data

Fan, Jianqing; Sun, Qiang; Zhou, Wen‐Xin; Zhu, Ziwei

doi:10.1002/9781118445112.stat08122

Cited by 35 publications

(21 citation statements)

References 96 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Lan Fu [17] described the Discrimination Analysis of Multivariate Statistical Analysis, Linear Dimensionality Reduction and Nonlinear Dimensionality Reduction Methods in the light of the wide range of applications of high-dimensional data. Zebin Wu [18] developed a parallel and distributed technique for hyperspectral dimensionality reduction and Principal Component Analysis (PCA), of cloud computing architectures. Marco Cavallo [19] proposed a different framework that interacts visually to improve dimensionality reduction based exploratory data analysis.…”

Section: Literature Surveymentioning

confidence: 99%

Evaluation of Various DR Techniques in Massive Patient Datasets using HDFS

Rao¹,

Indukuri²,

Penumatsa³

et al. 2021

IJRTE

View full text Add to dashboard Cite

The objective of comparing various dimensionality techniques is to reduce feature sets in order to group attributes effectively with less computational processing time and utilization of memory. The various reduction algorithms can decrease the dimensionality of dataset consisting of a huge number of interrelated variables, while retaining the dissimilarity present in the dataset as much as possible. In this paper we use, Standard Deviation, Variance, Principal Component Analysis, Linear Discriminant Analysis, Factor Analysis, Positive Region, Information Entropy and Independent Component Analysis reduction algorithms using Hadoop Distributed File System for massive patient datasets to achieve lossless data reduction and to acquire required knowledge. The experimental results demonstrate that the ICA technique can efficiently operate on massive datasets eliminates irrelevant data without loss of accuracy, reduces storage space for the data and also the computation time compared to other techniques.

show abstract

Section: Literature Surveymentioning

confidence: 99%

Evaluation of Various DR Techniques in Massive Patient Datasets using HDFS

Rao¹,

Indukuri²,

Penumatsa³

et al. 2021

IJRTE

View full text Add to dashboard Cite

show abstract

“…Eigenvector computation is a ubiquitous problem in data processing nowadays, such as spectral clustering [Ng et al, 2002;Xu and Ke, 2016a], pagerank computation, dimensionality reduction [Fan et al, 2018], and so on. Classic solvers from numerical algebra are power methods and Lanczos algorithms [Golub and Van Loan, 1996], based on which there has been a recent surge of interest in developing varieties of solvers [Hardt and Price, 2014;Musco and Musco, 2015;Garber et al, 2016;Balcan et al, 2016].…”

Section: Introductionmentioning

confidence: 99%

Convergence Analysis of Gradient Descent for Eigenvector Computation

Cao

Gao

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

View full text Add to dashboard Cite

We present a novel, simple and systematic convergence analysis of gradient descent for eigenvector computation. As a popular, practical, and provable approach to numerous machine learning problems, gradient descent has found successful applications to eigenvector computation as well. However, surprisingly, it lacks a thorough theoretical analysis for the underlying geodesically non-convex problem. In this work, the convergence of the gradient descent solver for the leading eigenvector computation is shown to be at a global rate O(min{ (lambda_1/Delta_p)^2 log(1/epsilon), 1/epsilon }), where Delta_p=lambda_p-lambda_p+1>0 represents the generalized positive eigengap and always exists without loss of generality with lambda_i being the i-th largest eigenvalue of the given real symmetric matrix and p being the multiplicity of lambda_1. The rate is linear at (lambda_1/Delta_p)^2 log(1/epsilon) if (lambda_1/Delta_p)^2=O(1), otherwise sub-linear at O(1/epsilon). We also show that the convergence only logarithmically instead of quadratically depends on the initial iterate. Particularly, this is the first time the linear convergence for the case that the conventionally considered eigengap Delta_1= lambda_1 - lambda_2=0 but the generalized eigengap Delta_p satisfies (lambda_1/Delta_p)^2=O(1), as well as the logarithmic dependence on the initial iterate are established for the gradient descent solver. We are also the first to leverage for analysis the log principal angle between the iterate and the space of globally optimal solutions. Theoretical properties are verified in experiments.

show abstract

“…Complementary work on the fundamental law of active management can be found inClarke et al (2002),Buckle (2004),Ye (2008) andDing et al (2020).6 Following this definition and assuming K common factors with K < N , factor-based methods only need to estimate K(K + 1)∕2 covariance entries and thus do not suffer from the curse of dimensionality.7 This approach is widely spread in the recent financial literature, since it does not require a specific factor model, see, e.g.,Fan et al (2013),Fan et al (2018),Fan et al (2016).…”

mentioning

confidence: 99%

Factor investing: alpha concentration versus diversification

Heinrich¹,

Shivarova

Zurek

2021

J Asset Manag

View full text Add to dashboard Cite

Despite extensive research support, the role of diversification in current factor investing strategies remains neglected. This paper investigates whether well-designed multifactor portfolios should not only be based on firm characteristics, but should also include portfolio diversification effects. While the alpha concentration approach mainly considers factor-specific firm characteristics, the diversified approach utilizes covariance estimators in addition to firm characteristics to account for portfolio diversification. The corresponding out-of-sample results show that including an efficient covariance estimator improves the performance of long-only multifactor portfolios compared to the pure alpha concentration approach. A particular advantage of diversified factor investing strategies can be identified in the significant increase in exposure to the low-volatility factor represented by firm characteristics with high informational content. No significant performance differences are observed for long-short portfolios where the factor exposures of the alpha concentration and diversification approaches are similar with respect to the low-volatility factor.

show abstract

Principal Component Analysis for Big Data

Cited by 35 publications

References 96 publications

Evaluation of Various DR Techniques in Massive Patient Datasets using HDFS

Evaluation of Various DR Techniques in Massive Patient Datasets using HDFS

Convergence Analysis of Gradient Descent for Eigenvector Computation

Factor investing: alpha concentration versus diversification

Contact Info

Product

Resources

About