{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ohdatamineDISC2 - DATA MINING Susan Holmes Stats202 Lecture...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
. . . . . . DATA MINING Susan Holmes © Stats202 Lecture 15 Fall 2010 A B a b c d f g h i e j kl
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
. . . . . . Special Announcements I All requests should be sent to [email protected] . I Homework, the deadline is Tuesday 5.00pm, all hw not within the deadline is rejected (we have an automatic system). Please don't forget to add your sunet id to your hw file name (at the end). I Midterm, you can bring a one page cheatsheet, no cellphones, no laptops.
Background image of page 2
. . . . . . Last Time:Alternative Classification Methods I Rule Based. I Instance Based Methods and Nearest Neighbors (knn). Today: Discriminant Analysis: for continuous explanatory variables only.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
. . . . . . Discrimination for Continuous Explanatory Variables Discriminant functions are the essence of the output from a discriminant analysis. Discriminant functions are the linear combinations of the standardised independent variables which yield the biggest mean differences between the groups. If the response is a dichotomy(only two classes to be predicted) there is one discriminant function; if the reponse variable has k levels(ie there are k classes to predict), up to k-1 discriminant functions can be extracted, and we can test how many are worth extracting.
Background image of page 4
. . . . . . Discriminant Functions Successive discriminant functions are orthogonal to one another, like principal components, but they are not the same as the principal components you would obtain if you just did a principal components analysis on the independent variables, because they are constructed to maximise the differences between the values of the response, not the total variance, but the variance between classes. The initial input data do not have to be centered or standardized before the analysis as is the case in principal components, the outcome of the final discriminant analysis will not be affected by the scaling.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
. . . . . . Discriminant Functions A discriminant function, also called a canonical root, is a latent variable which is created as a linear combination of discriminating (independent) variables, such that L = b 1 x 1 + b 2 x 2 + ... + b p x p + c, where the b's are discriminant coefficients, the x's are discriminating variables, and c is a constant. This is similar to multiple regression, but the b's are discriminant coefficients which maximize the distance between the means of the criterion (dependent) variable. Note that the foregoing assumes the discriminant function is estimated using ordinary least-squares, the traditional method, but there is also a version involving maximum likelihood estimation.
Background image of page 6
. . . . . . Least Squares Method of estimation of Discriminant Functions The variance covariances matrix can be decomposed into two parts: one is the variance within each class and the other the variability between clases, or we can decompose the sum of squares and cross products (the same up to a constant factor) T = B + W T = X ( I n - P 1 n ) X B = X ( Pg - P 1 n ) X between-class W = X ( I n - Pg ) X within I n is the identity matrix. P1n is the orthogonal projection in the space 1 n . (i.e. P 1 n = 1 n 1 n / n ). Such that ( I n - P 1 n ) X is the matrix of centered cases.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}