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Figure 3 Definition of a transform kernel value.
A kernel value of one is only obtained for identical (by means of the kernel) molecules.
The obtained limit is the expectation of the sequence set similarity and is taken as the kernel value.
Thus, the latter can be obtained using the identity of the kernel value for an object pair (x, y) ∈ X × X and the inner product of the respective feature space projection φ (x) for x ∈ X: (5).
The final kernel value is obtained as the sum of the similarities of the assigned atoms normalized by the self-similarities (i.e., the kernel similarities) of the respective molecules.
Such data, which corresponds to the absolute value of the considered transform kernel entry, is then used to control the operation of the specialized multiplication circuit that is embedded in the PE arithmetic module, as it is described below and is represented in Figure 2. Finally, the sign information of the kernel value is computed by considering the two most significant bits of f ′.
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This involves 80 distinct transform kernel values in the range of −90 to +90.
The normalization ensures that the kernel values are always in the interval [0,1].
Together, they generate all the multiplier values corresponding to all the kernel values of the considered transforms.
In the following design step, a 10-bit control word was defined for each one of the considered kernel values.
This data is disposed in the same manner as its corresponding kernel values in the first column of the transform kernel matrix.
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