I. Principal Component Analysis

Represent a set of n d-dimensional samples by a single vector xo, where xo minimizes the sum of squared distances between xo and various xk.  PCA tries to find the best representation of the data by reducing the dimensionality of the feature space so this might be a good method since I am trying to model the different pressure patterns for each posture.

Steps:
• zero-mean the data.

• calculate covariance matrix of sample data to form the scatter matrix.  Since the dimension of my data is large, I used the eigenface trick for numrows >> numcols to calculate A'*A instead of A*A'.

• select eigenvectors corresponding to the largest eigenvalues in the scatter matrix.

• project each data class onto the eigenvectors.

• calculate mahalanobis distance between projected test data and projected train data to classify (in other words, find probability that test data belongs to each class)

...but, but...how many eigenvectors should we use???

 Number of Eigenvectors % Recognition 10 55.33% 20 65.67% 30 65.00% 40 73.33% 50 69.67% 60 67.00%

Table 1: Comparison of Different Numbers of Eigenvectors Used for Classification

.Results.

 Total % Recognition 86.45%

Table 2: Using k-fold Cross Validation, k = 10

 Number Correct % Recognition Upright 47 94% Leaning Forward 32 64% Leaning Left 44 88% Leaning Right 35 70% Leaning Back 41 82% Slouching 21 42% Total Recognition 73.33%

Table 3: Using 40 Eigenvectors on 10 New Test Subjects