Onnowpurbo at 20:09, 22 February 2020

2020-02-22T20:09:58Z

← Older revision		Revision as of 20:09, 22 February 2020
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	PCA can reduce number of variables by eliminating correlations between them: A more realistic example		PCA can reduce number of variables by eliminating correlations between them: A more realistic example

			[[File:PCA 2.png\|center\|600px\|thumb]]

	Figure 2 (A) Data set of gene expression level in different tissues. (B) Gene expression level is a n-dimensional function. (C) PCA process. (D) After PCA, gene expression level becomes a k-dimensional function (k<n). (E) Data set is "compressed" with no information lost.		Figure 2 (A) Data set of gene expression level in different tissues. (B) Gene expression level is a n-dimensional function. (C) PCA process. (D) After PCA, gene expression level becomes a k-dimensional function (k<n). (E) Data set is "compressed" with no information lost.


	Suppose we measure expression levels of N genes in M tissues. We will get a data set of M*N matrix (see Figure 2A). Mathematically, we can describe the data set as:		Suppose we measure expression levels of N genes in M tissues. We will get a data set of M*N matrix (see Figure 2A). Mathematically, we can describe the data set as:

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	PCA has limitations : example of failures		PCA has limitations : example of failures

			[[File:PCA 3.png\|center\|600px\|thumb]]

	Figure 3. (A) PCA on non-Gaussian source data. (B) Principal components given by PCA may still be correlated in a non-linear way. Prior knowledge could help us to find out the best principal components.		Figure 3. (A) PCA on non-Gaussian source data. (B) Principal components given by PCA may still be correlated in a non-linear way. Prior knowledge could help us to find out the best principal components.

	Any algorithm could fail when its assumptions are not satisfied. PCA makes "the largest variance" assumption. If the data does not follow a multidimensional normal (Gaussian) distribution, PCA may not give the best principal components (see Figure 3A). For non-Gaussian source data, we will need independent component analysis (ICA) to separate data into additive, mutual statistical independent sub-components.		Any algorithm could fail when its assumptions are not satisfied. PCA makes "the largest variance" assumption. If the data does not follow a multidimensional normal (Gaussian) distribution, PCA may not give the best principal components (see Figure 3A). For non-Gaussian source data, we will need independent component analysis (ICA) to separate data into additive, mutual statistical independent sub-components.

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	PCA implementations : eigenvalue decomposition (EVD) and singular value decomposition (SVD)		PCA implementations : eigenvalue decomposition (EVD) and singular value decomposition (SVD)

			[[File:PCA 4.png\|center\|600px\|thumb]]

	Figure 4		Figure 4
	As a conceptual framework, PCA could have different implementations. May be the most popular ones are eigenvalue decomposition (EVD) and singular value decomposition (SVD). They both can be used to find principal components and will give same results in most cases.		As a conceptual framework, PCA could have different implementations. May be the most popular ones are eigenvalue decomposition (EVD) and singular value decomposition (SVD). They both can be used to find principal components and will give same results in most cases.

Onnowpurbo at 20:06, 22 February 2020

2020-02-22T20:06:51Z

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2020-02-22T20:05:23Z

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==Referensi==

* http://mengnote.blogspot.com/2013/05/an-intuitive-explanation-of-pca.html

==Pranala Menarik==

* [[Orange]]
* [[Orange: Principal Component Analysis]]

Principal Component Analysis (PCA) - Revision history

Onnowpurbo at 20:09, 22 February 2020

Onnowpurbo at 20:06, 22 February 2020

Onnowpurbo: Created page with "Sumber: http://mengnote.blogspot.com/2013/05/an-intuitive-explanation-of-pca.html ==Referensi== * http://mengnote.blogspot.com/2013/05/an-intuitive-explanation-of-pca.h..."