# Principal Component Analysis and Optimization: A Tutorial

@inproceedings{Reris2015PrincipalCA, title={Principal Component Analysis and Optimization: A Tutorial}, author={Robert Reris and J. Paul Brooks}, year={2015} }

Principal component analysis (PCA) is one of the most widely used multivariate tech- niques in statistics. It is commonly used to reduce the dimensionality of data in order to examine its underlying structure and the covariance/correlation structure of a set of variables. While singular value decomposition provides a simple means for identi- cation of the principal components (PCs) for classical PCA, solutions achieved in this manner may not possess certain desirable properties including…

## 37 Citations

### Sparse kernel feature extraction via support vector learning

- Computer SciencePattern Recognit. Lett.
- 2018

### Robust and Sparse Kernel PCA and Its Outlier Map

- Computer ScienceICBIP '18
- 2018

A two-stage algorithm was proposed: a robust distance was computed to identify the uncontaminated data set, followed by estimating the best-fit ellipsoid to these data for an informative and concise representation, and a kernel PCA outlier map was proposed to display and classify the outliers.

### Feature selection based on star coordinates plots associated with eigenvalue problems

- Computer ScienceVis. Comput.
- 2021

A new feature relevance measure for star coordinates plots associated with the class of linear dimensionality reduction mappings defined through the solutions of eigenvalue problems, such as linear discriminant analysis or principal component analysis is proposed.

### Estimating L 1-Norm Best-Fit Lines for Data

- Computer Science
- 2017

This paper presents a procedure to estimate the L1-norm best-fit onedimensional subspace (a line through the origin) to data in < based on an optimization criterion involving linear programming but which can be performed using simple ratios and sortings.

### Characterizing L1-norm best-fit subspaces

- Computer ScienceCommercial + Scientific Sensing and Imaging
- 2017

The L1-norm best-fit subspace problem is directly formulated as a nonlinear, nonconvex, and nondifferentiable optimization problem that can be solved to global optimality efficiently by solving a series of linear programs.

### Random selection of factors approximately preserves correlation structure in a linear factor model

- Computer Science, Mathematics
- 2017

A statistical factor model is developed, the random factor model, in which factors are chosen at random based on the random projection method, which enables derivation of probabilistic bounds for the accuracy of therandom factor representation of time-series, their cross-correlations and covariances.

### Principal component analysis and singular value decomposition used for a numerical sensitivity analysis of a complex drawn part

- Materials Science
- 2018

The numerical forecasting of car body construction processes is already being used in industry to provide support in the ramp-up process. However, long calculation times are stretching the finite…

### Distributed Maximum Likelihood Principal Component Analysis for Wireless Sensor Network Data

- Computer Science
- 2018

A distributed maximum likelihood PCA algorithm is proposed that is more efficient in finding the principal components from the data containing anomalies and compares it with principal components computed across the network to identify the anomalies.

### Random factor approach for large sets of equity time-series

- Computer Science
- 2016

The developed random factor model, in which factors are chosen at random based on the random projection method, is developed and derives probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances.

### Automatic Baseline extraction based on PCA (Principal Component Analysis) method

- Computer Science
- 2017

An efficient algorithm for robust baseline extraction is proposed; in which the optimal weight vector is computed based on logic distribution function; and, the smooth parameters using PCA method; and the new algorithm has been extended to existing extraction methods.

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