LEC 3: Fisher Discriminant Analysis (FDA)

The discriminant function coefficients denote the unique contribution of each variable to the discriminant function, while the structure coefficients denote the simple correlations between the variables and the functions Summary To summarize, when interpreting multiple discriminant functions, which arise

COSC522–MachineLearning Discriminant Functions

3 8/27 Discriminant Function - MD Proj1 - Supervised Learning 9/10 4 9/1 Parametric Learning - MLE 5 9/3 Non-parametric Learning - kNN 6 9/8 Unsupervised Learning - kmeans HW2 9/15 7 9/10 Dimensionality Reduction - FLD Proj2 - Unsupervised Learning and DR 9/24 8 9/15 Dimentionality Reduction - PCA 9 9/17 Linear Regression

Understanding the Discriminant Date Period

Find the value of the discriminant of each quadratic equation 1) 6 p2 − 2p − 3 = 0 76 2) −2x2 − x − 1 = 0 −7 3) −4m2 − 4m + 5 = 0 96 4) 5b2 + b − 2 = 0 41 5) r2 + 5r + 2 = 0 17 6) 2p2 + 5p − 4 = 0 57 Find the discriminant of each quadratic equation then state the numberof real and imaginary solutions 7) 9n2 − 3n − 8

The DISCRIM Procedure

a discriminant criterion to classify each observation into one of the groups The de-rived discriminant criterion from this data set can be applied to a second data set during the same execution of PROC DISCRIM The data set that PROC DISCRIM uses to derive the discriminant criterion is called the training or calibration data set

Discriminant Function Analysis - USDA

of similar types (groups) of flowers, and then perform a discriminant function analysis to determine the set of characteristics that allows for the best discrimination between the types To index Computational Approach Computationally, discriminant function analysis is very similar to analysis of variance (ANOVA ) Let us consider a simple example

LEC 4: Discriminant Analysis for Classiﬁcation

Discriminant Analysis for Classiﬁcation Probabilistic models We introduce a mixture model to the training data: We model the distribution of each training class Ci by a pdf fi(x) We assume that for a fraction πi of the time, x is sampled from Ci The Law of Total Probability implies that the mixture distribution has a pdf f(x) = ∑ f(x x

Logistic Regression and Discriminant Analysis

Discriminant Function Analysis •Discriminant function analysis (DFA) builds a predictive model for group membership •The model is composed of a discriminant function based on linear combinations of predictor variables •Those predictor variables provide the best discrimination between groups