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 (1749–1832)
“Our mother gives us our earliest lessons in love—and its partner, hate. Our father—our “second other”Melaborates on them. Offering us an alternative to the mother-baby relationship . . . presenting a masculine model which can supplement and contrast with the feminine. And providing us with further and perhaps quite different meanings of lovable and loving and being loved.”
—Judith Viorst (20th century)
“In our country today, very few children are raised to believe that their principal destiny is to serve their family, their country, or God.”
—Benjamin Spock (b. 1903)
“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)