Relationship To Principal Components
The first principal component about the mean of a set of points can be represented by that line which most closely approaches the data points (as measured by squared distance of closest approach, i.e. perpendicular to the line). In contrast, linear least squares tries to minimize the distance in the direction only. Thus, although the two use a similar error metric, linear least squares is a method that treats one dimension of the data preferentially, while PCA treats all dimensions equally.
Read more about this topic: Least Squares
Famous quotes containing the words relationship to, relationship, principal and/or components:
“Film music should have the same relationship to the film drama that somebodys piano playing in my living room has to the book I am reading.”
—Igor Stravinsky (18821971)
“But the relationship of morality and power is a very subtle one. Because ultimately power without morality is no longer power.”
—James Baldwin (19241987)
“Rather than have it the principal thing in my sons mind, I would gladly have him think that the sun went round the earth, and that the stars were so many spangles set in the bright blue firmament.”
—Thomas Arnold (17951842)
“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
—Noam Chomsky (b. 1928)