Data driven frequency mapping for kernels used in support vector machines

1. A method for selecting frequency features to be used for binary classification of data using a linear classifier, comprising the steps of:

determining a set of hypotheses in a d-dimensional space using d-dimensional labeled training data, wherein a magnitude of each hypothesis vector is a spatial combing frequency;

constructing a mapping function for each hypothesis;

applying the mapping functions to the training data to generate frequency features;

selecting iteratively a subset of the frequency features; and

training the linear classifier using the subset of frequency features and labels of the training data, wherein the steps are performed in a processor.

2. The method of claim 1 , wherein the training data include a first subset of positive training data with positive labels and a second subset of negative training data with negative labels, and basis vectors define a separating boundary between the first and second subsets of training data.

3. The method of claim 1 , wherein each hypothesis is a vector ω for the training data.

4. The method of claim 1 , further comprising;

extracting separate probability distribution functions ρ+ and ρ− from the training data, wherein ρ+ is a probability distribution function of the positive labeled data, and ρ− is the probability distribution function of the subset of negative training data points;

sampling M data points for each of distributions to construct point pairs

{( x − ,x + )} {1 . . . M}

where x − is a data point from the distribution ρ− and x + is a data from the distribution ρ−; and

assigning the hypothesis ω was the vector that connects the point pairs.

5. The method of claim 4 , wherein a weighted discriminant constraint is applied while extracting the probability density functions ρ+ and ρ−.

6. The method of claim 4 , wherein a mapping function is defined by

z ω ( x )=√{square root over (2)} cos(ω T x+b )

where T is a vector transpose operator, and b is a phase-shift parameter.

7. The method of claim 4 , wherein the mapping function from R d →R z is defined by

z ω ( x )=[cos(ω T ( x ))sin(ω T ( x )] T

where T is a vector transpose operator.

8. The method of claim 6 , wherein the phase-shift is b=−ω T x + .

9. The method of claim 1 , wherein the subset of frequency features is selected by a boosting method.

10. The method of claim 9 , wherein the selection is repeated until a desired performance level for the linear classifier is achieved.

11. The method of claim 9 , wherein the selection is repeated until an upper bound on a computational load is reached.

12. The method of claim 1 , wherein the linear classifier is a support vector machine with linear kernel.

13. The method of claim 1 , wherein the set of hypotheses selected by random sampling.

14. The method of claim 1 , wherein the training data has multiple classes.

15. The method of claim 1 further comprising:

determining the frequency features for test data; and

applying the linear classifier to the frequency features to obtain final labels that classify the test data.

16. A system for selecting frequency features to be used for binary classification of data using a linear classifier, comprising a processor for:

determining a set of hypotheses in a d-dimensional space using d-dimensional labeled training data;

constructing a mapping function for each hypothesis, wherein each hypothesis is a vector, and a magnitude of each hypothesis vector is a spatial combing frequency;

applying the mapping functions to the training data to generate frequency features;

selecting iteratively a subset of the frequency features; and

training the linear classifier using the subset of frequency features and labels of the training data.