Generate Training and Test samples from a Mixture of Gaussians with three Gaussian mixtures given by: N(µ1,R1),N(µ2,R2),N(µ3,R3). Corresponding mixture coefficients are π1=0.4,π2=0.3,π3=0.3. Assuming that the samples are drawn from the second and third Gaussian corresponds to features representing a singular object. Implement LDA and PCA algorithms. Evaluate the performance of this two algorithms including their sensitivity to the number of training samples, outliners and susceptibility to Over-Fitting.
The parameters of Gaussian distributions are given as follows:
µ1 = [0.2 1.4] R1 = [24.08 4.62
4.62 1.92]
µ2 = [-7.5 0.5] R2 = [1.92 4.62
4.62 24.08]
µ3 = [2.5 5] R3 = [24.08 4.62
4.62 1.92]
Illustrate followings,
[1] Sampling from the mixture of Gaussian [2] Implementation of the Linnear Discriminant Analysis. [3] Implementation of the Principal Component Analysis. [4] Performance analysis
References,
- Bishop, C. M. (2006), Pattern Recognition and Machine Learning, Springer, ISBN-10:0-387-31073-8
- Theodoridis, S. and Koutroumbas, K. (2008), Pattern Recognition, Academic Press (4th Edition) , ISBN: 978-1-59749-272-0