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:
“Artists have a double relationship towards nature: they are her master and her slave at the same time. They are her slave in so far as they must work with means of this world so as to be understood; her master in so far as they subject these means to their higher goals and make them subservient to them.”
—Johann Wolfgang Von Goethe (17491832)
“Most childhood problems dont result from bad parenting, but are the inevitable result of the growing that parents and children do together. The point isnt to head off these problems or find ways around them, but rather to work through them together and in doing so to develop a relationship of mutual trust to rely on when the next problem comes along.”
—Fred Rogers (20th century)
“Today, only a fool would offer herself as the singular role model for the Good Mother. Most of us know not to tempt the fates. The moment I felt sure I had everything under control would invariably be the moment right before the principal called to report that one of my sons had just driven somebodys motorcycle through the high school gymnasium.”
—Mary Kay Blakely (20th century)
“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)