homework for

Linear Discriminant Analysis




EE 8993: Fundamentals of Speech Recognition


March 11, 1999


submitted to:

Dr. Joseph Picone

Department of Electrical and Computer Engineering
413 Simrall, Hardy Rd.
Mississippi State University
Box 9	571
MS State, MS 39762


submitted by:

Janna Shaffer













I.	Original Data Set Calculations
This homework assignment applies linear discriminant analysis(LDA) to a classification problem. The data sets in Figure 1 were hand drawn using a MATLAB graphical user interface. The means for the two sets are and . The test set consists of the points , , , and.

Figure 1.   Data sets and test set used for LDA

After the data and test sets were defined, the Euclidean distances between each point in the test set and the data set means were calculated. Set membership was based upon this distance. The results for both set independent and specific LDA are shown in the next section of this report.













II.	LDA
In order to find a better classification of the test data, linear discriminant analysis was applied to the data sets and test sets [1]. 


Class Independent LDA:

	Distance from mean 1	Distance from mean 2
x1	2.8452	 2.8113
x2	2.8283	 2.8282
x3	2.8198	 2.8367
x4	3.5353	2.1212

Table 1:  Euclidean Distances Between Test Sets and Data Set Means (bold represents set membership)



Table 2:  Plot of the Decision Line from Class Independent LDA



Class Specific LDA:

	Distance from mean 1	Distance from mean 2
x1	2.9069	3.0550
x2	2.8236	2.7707
x3	2.7819	2.6285
x4	3.5294	2.0780

Table 3:  Euclidean Distances Between Test Sets and Data Set Means (bold denotes set membership)


Table 4:  Plot of the Decision Line from Class Specific LDA

III.	REFERENCES 
[1]	Brown, S. Balakrishnama, J. Picone, "Scenic Beauty Estimation using Linear Discriminant Analysis," MS State ECE 4773 Semester Project December 11, 1997.