Difference between revisions of "Principal Component Analysis (PCA)"
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===The spatial principle of a PCA=== | ===The spatial principle of a PCA=== | ||
In a space of 3 dimensions, that are for instance income in x, savings in y and consumption in z, we have let’s say 12 vectors that represent our 12 similar variables that were measured in the field. Those vectors combined together create a cloud in 3D. That cloud has 3 principal directions; the first 2 like the sticks of a kite, and a 3rd stick at 90 degrees from the first 2. Well, the longest of the sticks that represent the cloud, is the Principal Component. | In a space of 3 dimensions, that are for instance income in x, savings in y and consumption in z, we have let’s say 12 vectors that represent our 12 similar variables that were measured in the field. Those vectors combined together create a cloud in 3D. That cloud has 3 principal directions; the first 2 like the sticks of a kite, and a 3rd stick at 90 degrees from the first 2. Well, the longest of the sticks that represent the cloud, is the Principal Component. | ||
Thus, the PCA provides us with the information that similar variables have the most in common, but drops the rest. Therefore, the PCA ''really must be used only on variables that have a lot in common, or else a lot of information will be lost''. | |||
===Subsection 2=== | ===Subsection 2=== | ||
Revision as of 23:30, 7 February 2017
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PCA, is a way to create an index from a group of variables that are similar in the information that they provide. This allows maximizing the information we keep, without using variables that will cause multicolinearity, and without having to choose one variables among many.
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The spatial principle of a PCA
In a space of 3 dimensions, that are for instance income in x, savings in y and consumption in z, we have let’s say 12 vectors that represent our 12 similar variables that were measured in the field. Those vectors combined together create a cloud in 3D. That cloud has 3 principal directions; the first 2 like the sticks of a kite, and a 3rd stick at 90 degrees from the first 2. Well, the longest of the sticks that represent the cloud, is the Principal Component.
Thus, the PCA provides us with the information that similar variables have the most in common, but drops the rest. Therefore, the PCA really must be used only on variables that have a lot in common, or else a lot of information will be lost.
Subsection 2
Subsection 3
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This article is part of the topic Data Analysis
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