Principal component analysis - Revision history

Sebastian at 20:07, 24 March 2020

2020-03-24T20:07:48Z

← Older revision		Revision as of 20:07, 24 March 2020
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	* What is PCA good for? compressing data, dimensionality reduction/preprocessing step before passing to another learning algorithm, visualization, etc.		* What is PCA good for? compressing data, dimensionality reduction/preprocessing step before passing to another learning algorithm, visualization, etc.
	* When does PCA not work so well?		* When does PCA not work so well?

			== References ==

Sebastian at 20:05, 24 March 2020

2020-03-24T20:05:13Z

← Older revision		Revision as of 20:05, 24 March 2020
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	Principal component analysis (PCA) is the prime linear method among the various methods used for [[dimensionality reduction]]. ~~Its method~~ consists in constructing the covariance matrix of the data, and computing the eigenvectors of the matrix.<ref>[https://data-flair.training/blogs/dimensionality-reduction-tutorial/ What is Dimensionality Reduction – Techniques, Methods, Components]</ref>		Principal component analysis (PCA) is the prime linear method among the various methods used for [[dimensionality reduction]]. It consists in constructing the covariance matrix of the data, and computing the eigenvectors of the matrix.<ref>[https://data-flair.training/blogs/dimensionality-reduction-tutorial/ What is Dimensionality Reduction – Techniques, Methods, Components]</ref>

	==Questions/things to explain==		==Questions/things to explain==

Sebastian at 20:03, 24 March 2020

2020-03-24T20:03:49Z

← Older revision		Revision as of 20:03, 24 March 2020
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	Principal component analysis (PCA) is the prime linear method among the various methods used for [[dimensionality reduction]].		Principal component analysis (PCA) is the prime linear method among the various methods used for [[dimensionality reduction]]. Its method consists in constructing the covariance matrix of the data, and computing the eigenvectors of the matrix.<ref>[https://data-flair.training/blogs/dimensionality-reduction-tutorial/ What is Dimensionality Reduction – Techniques, Methods, Components]</ref>

	==Questions/things to explain==		==Questions/things to explain==

Sebastian at 20:01, 24 March 2020

2020-03-24T20:01:34Z

← Older revision		Revision as of 20:01, 24 March 2020
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			Principal component analysis (PCA) is the prime linear method among the various methods used for [[dimensionality reduction]].

	==Questions/things to explain==		==Questions/things to explain==

IssaRice: /* Questions/things to explain */

2018-07-14T06:04:04Z

Questions/things to explain

← Older revision		Revision as of 06:04, 14 July 2018
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	** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].		** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].
	* once you've done PCA, how do you calculate the percentage of variance captured by a principal component? what is the relationship between the percentage variance and the size of the eigenvalue (the larger the eigenvalue, the larger the variance, but what is the specific relationship)?		* once you've done PCA, how do you calculate the percentage of variance captured by a principal component? what is the relationship between the percentage variance and the size of the eigenvalue (the larger the eigenvalue, the larger the variance, but what is the specific relationship)?
			* What is PCA good for? compressing data, dimensionality reduction/preprocessing step before passing to another learning algorithm, visualization, etc.
			* When does PCA not work so well?

IssaRice at 04:33, 14 July 2018

2018-07-14T04:33:22Z

← Older revision		Revision as of 04:33, 14 July 2018
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	** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?		** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?
	** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].		** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].
	** once you've done PCA, how do you calculate the percentage of variance captured by a principal component? what is the relationship between the percentage variance and the size of the eigenvalue (the larger the eigenvalue, the larger the variance, but what is the specific relationship)?		* once you've done PCA, how do you calculate the percentage of variance captured by a principal component? what is the relationship between the percentage variance and the size of the eigenvalue (the larger the eigenvalue, the larger the variance, but what is the specific relationship)?

IssaRice at 04:33, 14 July 2018

2018-07-14T04:33:06Z

← Older revision		Revision as of 04:33, 14 July 2018
Line 9:		Line 9:
	** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?		** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?
	** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].		** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].
	** once you've done PCA, how do you calculate the percentage of variance captured by a principal component? what is the relationship between the percentage variance and the size of the eigenvalue?		** once you've done PCA, how do you calculate the percentage of variance captured by a principal component? what is the relationship between the percentage variance and the size of the eigenvalue (the larger the eigenvalue, the larger the variance, but what is the specific relationship)?

IssaRice: /* Questions/things to explain */

2018-07-14T04:25:24Z

Questions/things to explain

← Older revision		Revision as of 04:25, 14 July 2018
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	** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?		** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?
	** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].		** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].
	** once you've done PCA, how do you calculate the percentage of variance captured by a principal component?		** once you've done PCA, how do you calculate the percentage of variance captured by a principal component? what is the relationship between the percentage variance and the size of the eigenvalue?

IssaRice: /* Questions/things to explain */

2018-07-14T04:24:56Z

Questions/things to explain

← Older revision		Revision as of 04:24, 14 July 2018
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	** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?		** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?
	** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].		** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].
			** once you've done PCA, how do you calculate the percentage of variance captured by a principal component?

IssaRice: /* Questions/things to explain */

2018-07-14T04:20:23Z

Questions/things to explain

← Older revision		Revision as of 04:20, 14 July 2018
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	** minimum-error (see Bishop)		** minimum-error (see Bishop)
	** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?		** the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?
	** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]		** maximum-variance and minimum-error are related by the Pythagorean theorem, see [https://drive.google.com/file/d/0B3-japQ2zgG_MGM3cHdzdGRyMm8/view page 16 of these slides]. There's a similar picture in [https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ this post].