Multi – feature discriminant analysis Essay

MULTI-FEATURE DISCRIMINANT ANALYSIS
The MFDA is an extension and improvement of the LDA using multiple features combined with two different random sampling methods in feature and sample spaces. The MFDA is proposed specifically for handling multiple feature sets with large dimensionality and with different scales and measurements.
3.1 Procedure for MFDA
Algorithm for MFDA has the following steps
Input SIFT feature vectors and MLBP feature vectors.
Output C_j {1or 2 ...or m}, the class to which the input pattern Z is finally assigned.
Break the SIFT and MLBP feature sets into slices with feature from the patches of the same row in the image as one slice. The parameter values used in the feature representation as shown in Table 1.
Apply PCA on each slice, compute eigenvalues and eigenvectors with non zero eigenvalues.
Construct random subspace {S^i }_(i=1)^10 by keeping eigenvectors with non zero eigenvalues.
Compute within-class scatter matrix S_w
S_w= _(i=1)^c_(X_j C_i)(X_j- _i) (X_j- _i)^T (7)
where _i denotes the mean of the class C_i.
Compute the whitened data matrix W and whitening transform Aw,
W= A_(w )^T S_w (8)
A_w= ^(-1/2) (9)
where is the eigenvector matrix of S_w , is the eigenvalue matrix of S_w and I is the identity matrix.
Generate inter-class pairs from the whitened data matrix W ,such that (x_k1 , x_k2) is the kth inter-class pair.
Compute the pair-wise distances by using Euclidean distance method
d=(x_s- y_t ) (x_s- y_t)' (10)
Compute between-class scatter matrices
{S_b^j }_(j=1)^5 = _k^2000((x_k1- x_k2 ) (x_k1- x_k2)^T)/x_k1- x_k2 ^2 (11)
where (x_k1 , x_k2) is the kth selected inter-class pair from the subset of the 10,000 inter-class pairs with the smallest distances.
Construct the classifiers
C_i= S_b^i W_j (12)
where, i = 1 to 5 and j = 1 to 10.
Normalize the classification outputs using min-max normalization scheme,
S_k^'= (S_k- min)/max- min (13)
where {S_k}, k=1,2...n is a set of matching scores.
Combine outputs by using score-sum based fusion rule and assigns the input pattern to class c such that
C= argmaxj_(i=1)^RP(C_j(x_i )) (14)
where, P(C_j(x_i )) is the posterior probability of class C_j for classifier (x_i ) .
Table 1 Total slices for each sample [5]
SIFT Feature 1 SIFT Feature 2 MLBP Feature 1 MLBP Feature 2
Patch size 16 16 32 32 16 16 32 32
Number of patches 408 88 408 88
Number of slices 24 11 24 11
Number of total slices for each sample 70
Generate multiple subspaces with lower dimensionalities by applying the random subspace technique to sample the feature space. It will reduce the feature dimensionality. In the bagging technique, generate the inter-class sample pairs with small distances to generate multiple inter-class sample pair subsets. Then select specific sample pair subset to compute the between-class scatter matrix and the discriminant subspace. The inter-class sample pairs near the classification boundary contain more discriminatory information. By combing the random subspace and bagging techniques, a random sampling based classification method, called MFDA is developed.