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Efficient computation of gapped substring kernels on large alphabets
 Journal of Machine Leaning Research
, 2005
"... We present a sparse dynamic programming algorithm that, given two strings s and t, a gap penalty λ, and an integer p, computes the value of the gapweighted lengthp subsequences kernel. The algorithm works in time O(pMlogt), where M = {(i, j)si = t j} is the set of matches of characters in the ..."
Abstract

Cited by 13 (1 self)
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We present a sparse dynamic programming algorithm that, given two strings s and t, a gap penalty λ, and an integer p, computes the value of the gapweighted lengthp subsequences kernel. The algorithm works in time O(pMlogt), where M = {(i, j)si = t j} is the set of matches of characters in the two sequences. The algorithm is easily adapted to handle bounded length subsequences and different gappenalty schemes, including penalizing by the total length of gaps and the number of gaps as well as incorporating characterspecific match/gap penalties. The new algorithm is empirically evaluated against a full dynamic programming approach and a triebased algorithm both on synthetic and newswire article data. Based on the experiments, the full dynamic programming approach is the fastest on short strings, and on long strings if the alphabet is small. On large alphabets, the new sparse dynamic programming algorithm is the most efficient. On mediumsized alphabets the triebased approach is best if the maximum number of allowed gaps is strongly restricted.
Computing rank convolutions with a mask
, 2006
"... Rankconvolutions have important applications in a variety of areas such as signal processing and computer vision. We define a “mask ” as a function taking only values zero and infinity. Rankconvolutions with masks are of special interest to image processing. We show how to compute the rankk convo ..."
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Cited by 3 (0 self)
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Rankconvolutions have important applications in a variety of areas such as signal processing and computer vision. We define a “mask ” as a function taking only values zero and infinity. Rankconvolutions with masks are of special interest to image processing. We show how to compute the rankk convolution of a function over an interval of length n with an arbitrary mask of length m in O(n √ m log m) time. The result generalizes to the ddimensional case. Previously no algorithm performing significantly better than the brute force O(nm) bound was known. Our algorithm seems to perform well in practice. We describe an implementation, illustrating its application to a problem in image processing. Already on relatively small images, our experiments show a signficant speedup compared to brute force.