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Principal component analysis: History & Applications

Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.

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Principal component analysis topic overview

The analysis highlights History and Applications as prominent areas in the source structure around Principal component analysis.

Related topics
211
Source areas
14
Connected nodes
225
Extracted relationships
185
Concept neighborhoods
62
Bridge connections
225

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Applications · 48 topics
Overview · 26 topics
Software/source code · 26 topics
Details · 22 topics
Generalizations · 16 topics
Computation using the covariance method · 15 topics
Covariance-free computation · 12 topics
History · 11 topics
Relation with other methods · 10 topics
Properties and limitations · 9 topics
Further considerations · 8 topics
Intuition · 5 topics
Similar techniques · 2 topics
Qualitative variables · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

History

Intuition

Details

Further considerations

Properties and limitations

Computation using the covariance method

Covariance-free computation

Qualitative variables

Applications

Relation with other methods

Generalizations

Similar techniques

Software/source code

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Principal component analysis connects Entity context

The extracted context around Principal component analysis shows recurring relationship patterns in the source. For example, Principal component analysis → ALGLIB, Analysis, Commercial, Contains PCA, Delphi, EigenDecomp, ELKI, ExPosition, Fortran, Free, FreePascal, GNU Octave, Gretl, Implemented, Implements, In, Integrates PCA, Java, Julia, Kernel PCA Another extracted example is Principal component analysis → Chapman, Cite, CiteSeerX, Example Using, Exploratory Multivariate Analysis, Hall/CRC The, Husson François, ISBN, Jackson, Jolliffe, Jérôme, London, Lê Sébastien, Multiple Factor Analysis, New York, Pagès Jérôme, Principal Components, Series, Series London, Springer Series. Use these groups to spot repeated connection types before inspecting the individual relationships.

Principal component analysis

Top relations

related to Software/source code · 59
Principal component analysis → ALGLIB, Analysis, Commercial, Contains PCA, Delphi, EigenDecomp, ELKI, ExPosition, Fortran, Free, FreePascal, GNU Octave, Gretl, Implemented, Implements, In, Integrates PCA, Java, Julia, Kernel PCA
related to Further reading · 24
Principal component analysis → Chapman, Cite, CiteSeerX, Example Using, Exploratory Multivariate Analysis, Hall/CRC The, Husson François, ISBN, Jackson, Jolliffe, Jérôme, London, Lê Sébastien, Multiple Factor Analysis, New York, Pagès Jérôme, Principal Components, Series, Series London, Springer Series
related to history · 21
Principal component analysis → Brooks, Ch, Depending, Eckart, EOF, EVD, Harman, Harold Hotelling, Hotelling, Jolliffe's Principal Component Analysis, Karhunen, Karl Pearson, KLT, Lorenz, Loève, PCA, POD, Sirovich, SVD, XTX
related to External links · 14
Principal component analysis → Andrew Ng, Copenhagen, PCA, Principal Component AnalysisA, Rasmus Bro, Software, Stack OverflowSee, StatQuest, Step-by-Step, University, YouTube, YouTubeA Tutorial, YouTubeLayman's, YouTubeStanford University
see also · 13
Principal component analysis → Canonical, Correspondence, Detrended, Factor, Factorial, Multiple, PCA, PCAL1-norm, PCATransform, Principal, SVD, Wikibooks, Wikiversity
related to Factor analysis · 10
Principal component analysis → Different, Factor, However, If, In, PCA, Principal, Results, The, The PCA
related to Correspondence analysis · 8
Principal component analysis → Because CA, CA, Correspondence, It, Jean-Paul Benzécri, One, PCA, Several
related to Sparse PCA · 5
Principal component analysis → Bayesian, It, PCA, Several, Sparse PCA
related to Independent component analysis · 2
Principal component analysis → ICA, Independent

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

pca matrix principal data components analysis displaystyle component variables covariance variance first eigenvectors used also eigenvalues mathbf vector factor value

Principal component analysis relationships Subject–Predicate–Object triples

TTTA extracted 185 structured relationships around Principal component analysis. Examples in this analysis include population genetics → instance of → Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points.Principal compon… and XTX is that the quotient's maximum possible value is the largest eigenvalue of the matrix → instance of → A standard result for a positive semidefinite matrix. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
population geneticsinstance ofMany studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points.Principal compon…0.80text
microbiome studiesinstance ofMany studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points.Principal compon…0.80text
and atmospheric scienceinstance ofMany studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points.Principal compon…0.80text
XTX is that the quotient's maximum possible value is the largest eigenvalue of the matrixinstance ofA standard result for a positive semidefinite matrix0.80text
which occurs when w is the corresponding eigenvector.With winstance ofA standard result for a positive semidefinite matrix0.80text
astronomyinstance ofIn fields0.80text
all the signals are non-negativeinstance ofIn fields0.80text
and the mean-removal process will force the mean of some astrophysical exposures to be zeroinstance ofIn fields0.80text
which consequently creates unphysical negative fluxesinstance ofIn fields0.80text
and forward modeling has to be performed to recover the true magnitude of the signalsinstance ofIn fields0.80text
FactoMineRinstance ofthe method is available in the R environment through packages0.80text
spatial intelligenceinstance ofIt was believed that intelligence had various uncorrelated components0.80text

Related concept clusters Concept neighborhoods

The concept neighborhoods around Principal component analysis bring nearby vocabulary together. In this analysis, examples include Principal, Components and Analysis. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Principal component analysis
    • Principal
    • Components
    • Analysis
    • Component
    • Data
    • First
    • Variables
    • Matrix
    • Variance
    • Original
    • Covariance
    • Decomposition
  • principal component analysis
    • Principal
    • Components
    • Factor
    • Analysis
    • Component
    • Data
    • First
    • Variables
    • Pca
    • Variance
    • Used
    • Matrix
  • dimensionality reduction
    • Reduction
    • Method
    • Pca
    • Variables
    • Dataset
    • Linear
    • Decomposition
    • May
    • Variance
    • First
    • Data
    • One
  • exploratory data analysis
    • Factor
    • Component
    • Principal
    • Displaystyle
    • Matrix
    • Variables
    • Pca
    • First
    • Used
    • Components
    • Vector
    • Mathbf
  • data preprocessing
    • Principal
    • Displaystyle
    • Matrix
    • Variables
    • Pca
    • First
    • Components
    • Vector
    • Mathbf
    • Mean
    • Points
    • Given
  • unit vectors
    • Value
    • Displaystyle
    • Eigenvectors
    • Orthogonal
    • Mathbf
    • Column
    • Decomposition
    • Given
    • Matrix
    • Eigenvalues
    • Data
    • Eigenvalue
  • covariance matrix
    • Matrix
    • Eigenvectors
    • Mathbf
    • Displaystyle
    • Value
    • Column
    • Eigenvalues
    • Principal
    • Eigenvalue
    • Dataset
    • Also
    • Vector
  • singular value decomposition
    • Value
    • Vectors
    • Factor
    • Orthogonal
    • Also
    • Matrix
    • Using
    • Principal
    • Vector
    • Dimensionality
    • Column
    • Eigenvector

Connections between topic areas Semantic bridges

For Principal component analysis, one of the stronger structural bridges in this analysis connects Principal component analysis with Applications. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Principal component analysisApplications · splits 177 ⟂ 49
Principal component analysisOverview · splits 199 ⟂ 27
Principal component analysisSoftware/source code · splits 199 ⟂ 27
Principal component analysisDetails · splits 203 ⟂ 23
Principal component analysisGeneralizations · splits 209 ⟂ 17
Principal component analysisComputation using the covariance method · splits 210 ⟂ 16
Principal component analysisCovariance-free computation · splits 213 ⟂ 13
Principal component analysisHistory · splits 214 ⟂ 12
Principal component analysisRelation with other methods · splits 215 ⟂ 11
Principal component analysisProperties and limitations · splits 216 ⟂ 10
Principal component analysisFurther considerations · splits 217 ⟂ 9
Principal component analysisIntuition · splits 220 ⟂ 6
Principal component analysisSimilar techniques · splits 223 ⟂ 3

Map overview Semantic statistics

Principal component analysis

Nodes226
Edges225
Triples185
Avg. degree1.99
Density0.00885
Components1

Source & methodology

TTTA analyzes the structure around Principal component analysis to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History & Applications, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Principal component analysis · EN edition · Analysis: TopicsToTalkAbout

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