Multi – feature discriminant analysis, **499 words** essay example

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.

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.

Forget about stressful night

With our academic essay writing service

Popular categories

- Academic writing
- Article writing service
- best thesis writing service
- Buy a Research Papers
- Buy coursework
- Buy dissertation online
- Buy essay online
- Buy speeches online
- Buy thesis paper
- college essay writing
- Coursework writing help
- Custom dissertation writing
- Custom essay writing service
- Custom Research Paper
- Custom term paper
- Dissertation writing help
- Dissertation writing services
- Do my essay for me
- Essay writer
- Essay writing help
- Essay writing service
- Essays for sale
- Help writing college papers
- homework help
- Original essay writing
- Paper writing help
- Paper writing service
- Pay for essay
- Professional dissertation writer
- Research paper help
- Speech help
- Term paper writing help
- Thesis writing service
- Type my essay online
- Write my essay
- Write My Paper
- Write my research paper
- Write My Term Paper
- Write papers for money
- Writing a dissertation
- Writing a thesis
- Сheap essay writing service