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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).
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 ′.
The kernel value between two images x i and x j is computed as follows: Kleft({x}_i,{x}_jright)=sum limits_{k=1}^m{pi}_kleft({x}_i^kright){pi}_kleft({x}_j^kright){K}_kleft({x}_i^k,{x}_j^kright) (4 where ( {x}_i^k ) is a representation of training sample x i corresponding to the k th feature.
Then, this partial value is updated with the result of the multiplication involving X in and the kernel value corresponding to the multiplier control word stored in the internal standing-data register of the PE, by also taking into consideration the sign information bit stored in the same internal standing-data register.
This kernel has several parameters: the gap opening and extension penalty parameters d and e, the amino acid mutation matrix s, and the factor β which controls the influence of suboptimal alignments in the kernel value.
Similar(52)
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.
The rationale behind the algorithm that was implemented to generate the kernel values for any given DCT results from the observation that only N−1 different basis values exist in a N×N transform kernel [6].
The convolution normalized with the sum of the kernel values was computed and the results of the CPU implementation and the GPU implementation, both in single precision, were compared.
This case required about 600 GB of memory, mostly to store the kernel values for the wave fronts, where the kernel storage to the memory greatly reduces the computation time for the convolution although FDPM works also without the memory storage (see Ando (2016) for technical details).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com