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:
“Poetry is above all a concentration of the power of language, which is the power of our ultimate relationship to everything in the universe.”
—Adrienne Rich (b. 1929)
“... the Wall became a magnet for citizens of every generation, class, race, and relationship to the war perhaps because it is the only great public monument that allows the anesthetized holes in the heart to fill with a truly national grief.”
—Adrienne Rich (b. 1929)
“We must reserve a back shop all our own, entirely free, in which to establish our real liberty and our principal retreat and solitude.”
—Michel de Montaigne (1533–1592)
“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)