# Learning the Kernel Matrix with Semidefinite Programming

##### Citations

11,357 citations

### Cites background or methods from "Learning the Kernel Matrix with Sem..."

...Lanckriet et al. [2004] show that if K is a convex combination of Gram matrices Ki so that K = ∑ i νiKi with νi ≥ 0 for all i then the optimization of the alignment score w....

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...The subset of datapoints (SD) method for GPC was proposed in Lawrence et al. [2003], using an EP-style approximation of the posterior, and the differential entropy score (see section 8....

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7,767 citations

### Cites background from "Learning the Kernel Matrix with Sem..."

...This question also motivated much research (Lanckriet, Cristianini, Bartlett, El Gahoui, & Jordan, 2002; Wang & Chan, 2002; Cristianini, Shawe-Taylor, Elisseeff, & Kandola, 200 ), and deep architectures can be viewed as a promising development in this direction....

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...…to construct a supervised classifier, and in that case the unsupervised learning component can clearly be seen as a regularizer or a prior (Ng & Jordan, 2002; Lasserre et al., 2006; Liang & Jordan, 2008; Erhan et al., 2009) that forces the resulting parameters to make sense not only to model…...

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...(discriminant models) (Ng & Jordan, 2002; Liang & Jordan, 2008)....

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4,433 citations

3,773 citations

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##### References

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33,341 citations

13,736 citations

### "Learning the Kernel Matrix with Sem..." refers background or methods in this paper

...Kernel-based learning algorithms (see, for example, Cristianini and Shawe-Taylor, 2000; Schölkopf and Smola, 2002) work by embedding the data into a Hilbert space, and searching for linear relations in such a space....

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...(See, for example, Cristianini and Shawe-Taylor, 2000; Schölkopf and Smola, 2002)....

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...With a fixed kernel, all of these criteria give upper bounds on misclassification probability (see, for example, Chapter 4 of Cristianini and Shawe-Taylor, 2000)....

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12,059 citations

### "Learning the Kernel Matrix with Sem..." refers background in this paper

...The flrst kernelK1 is derived as a linear kernel from the \bag-of-words" representation of the difierent documents, capturing information about the frequency of terms in the difierent documents ( Salton and McGill, 1983 )....

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10,262 citations

### "Learning the Kernel Matrix with Sem..." refers methods in this paper

...Moreover, an additional kernel matrix is constructed by applying the Smith-Waterman (SW) pairwise sequence comparison algorithm ( Smith and Waterman, 1981 ) to the yeast protein sequences and applying the empirical kernel map (Tsuda, 1999)....

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7,655 citations

### "Learning the Kernel Matrix with Sem..." refers background or methods in this paper

...A general-purpose program such as SeDuMi ( Sturm, 1999 ) handles those problems e‐ciently....

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...Note also that the optimal weights µi, i = 1, . . . , m, can be recovered from the primal-dual solution found by standard software such as SeDuMi (Sturm, 1999)....

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...General-purpose programs such as SeDuMi (Sturm, 1999) use interior-point methods to solve SDP problems (Nesterov and Nemirovsky, 1994); they are polynomial time, but have a worst-case complexity O(n4....

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...A general-purpose program such as SeDuMi (Sturm, 1999) handles those problems efficiently....

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...…weights {µi}3i=1 are optimized according to a hard margin, a 1-norm soft margin and a 2-norm soft margin criterion, respectively; the semi-definite programs (27), (32) and (38) are solved using the general-purpose optimization software SeDuMi (Sturm, 1999), leading to optimal weights {µ∗i }3i=1....

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