Re: About Principle Components Analysis

On Feb 17, 1:36 pm, dtian.ty...@xxxxxxxxxxxxxx wrote:
Hello,

I am a little confused about the projection operation of PCA. It is
defined as E*X where E is an eigenvector;

Normally the vector E is normalized, that is ||E|| = 1

X is a data point and * is
the matrix multiplication operator. In the linear algebra textbooks
such as "Linear Algebra (Schaum's Outlines)" by Seymour Lipschutz,
projection of a vector u on a vector v is
[(u dotproduct v)/(square of magnitude of v)] v

For two Vectors u and v the dotproduct is identical to the
matrix multiplication if u is written as a row-vector. So,
if your E has unit length, both definitions are identical.

Greetings, Uwe.
.

Relevant Pages

  • Re: About Principle Components Analysis
    ... I am a little confused about the projection operation of PCA. ... such as "Linear Algebra " by Seymour Lipschutz, ... If E is an eigenvector, then so is tE for any scalar t. ...
    (sci.stat.math)
  • About Principle Components Analysis
    ... I am a little confused about the projection operation of PCA. ... defined as E*X where E is an eigenvector; X is a data point and * is ... such as "Linear Algebra " by Seymour Lipschutz, ...
    (sci.stat.math)
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