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In order to make KSVD applicable to nonlinear structured data, kernel methods[9] have been introduced in this article.
Different sources of data can be encoded into different types of data kernel [ 2], which we denote by K(x i 1, x i 2).
Two distinct base kernels may be different pairwise kernels representing the same source of data (i.e., the same data kernel) or they could be the same type of pairwise kernel applied to two different sources of data.
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No pairwise kernel uses more than five of the component data kernels.
Of the three sequence data kernels, the Pfam kernel (K P ) achieves the highest weight for the TPPK kernel K ¯ P 1.
In Figure 3 we plot the test accuracy (as a fraction) versus the p-value cutoff (a) when using all the above mentioned pairwise and data kernels.
Borrowing notation from these authors, we used three data kernels based on sets of amino acid sequences (spectrum (K S ) [ 4], motif (K M ) [ 16], and Pfam (K P )) [ 17] and three diffusion data kernels based on interaction networks from the BioGRID database [ 18] (yeast two-hybrid assay (KYH), genetic interactions (KGI), and affinity capture-MS (KMS)) [ 1].
For contrast calculations, data kernels (0.6 x 0.4 mm) for the signal and background ROIs were chosen in order to obtain kernels containing only the respective signal and background measurements.
Examples include diffusion kernels or standard kernels such as linear or Gaussian kernels [ 2] for encoding the similarity between data objects x i 1 and x i 2. These data kernels are, in turn, embedded in pairwise kernels, as described in the previous section.
Thirdly, for each pairwise kernel, we established performance using MKL over these six different data kernels and then compared this with the performance of MKL, when using all five different types of pairwise kernel and taken over all six different types of data; that is, the algorithm could use a weighted combination of 30 different types of kernel.
(4) Translate the data to kernel matrix according to the kernel function.
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