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22
Fast Neighborhood Subgraph Pairwise Distance Kernel
"... We introduce a novel graph kernel called the Neighborhood Subgraph Pairwise Distance Kernel. The kernel decomposes a graph into all pairs of neighborhood subgraphs of small radius at increasing distances. We show that using a fast graph invariant we obtain significant speedups in the Gram matrix co ..."
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Cited by 24 (10 self)
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We introduce a novel graph kernel called the Neighborhood Subgraph Pairwise Distance Kernel. The kernel decomposes a graph into all pairs of neighborhood subgraphs of small radius at increasing distances. We show that using a fast graph invariant we obtain significant speedups in the Gram matrix computation. Finally, we test the novel kernel on a wide range of chemoinformatics tasks, from antiviral to anticarcinogenic to toxicological activity prediction, and observe competitive performance when compared against several recent graph kernel methods. 1.
Distances and (indefinite) kernels for sets of objects
 In ICDM
, 2006
"... For various classification problems involving complex data, it is most natural to represent each training example as a set of vectors. While several distance measures for sets have been proposed, only a few kernels over these structures exist since it is difficult in general to design a positive sem ..."
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Cited by 15 (2 self)
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For various classification problems involving complex data, it is most natural to represent each training example as a set of vectors. While several distance measures for sets have been proposed, only a few kernels over these structures exist since it is difficult in general to design a positive semidefinite (PSD) similarity function. The main disadvantage of most existing set kernels is that they are based on averaging, which might be inappropriate for problems where only specific elements of the two sets should determine the overall similarity. In this paper we propose a class of kernels for sets of vectors directly exploiting set distance measures and, hence, incorporating various semantics into set kernels and lending the power of regularization to learning in structural domains where natural distance functions exist. These kernels belong to two groups: (i) kernels in the proximity space induced by set distances and (ii) set distance substitution kernels (nonPSD in general). We report experimental results which show that our kernels compare favorably with kernels based on averaging and achieve results similar to other stateoftheart methods. At the same time our kernels bring systematically improvement over the naive way of exploiting distances. 1
A generalization of haussler’s convolution kernel: mapping kernel
 Proceeding of the International Conference on Machine Learning
, 2008
"... Haussler’s convolution kernel provides a successful framework for engineering new positive semidefinite kernels, and has been applied to a wide range of data types and applications. In the framework, each data object represents a finite set of finer grained components. Then, Haussler’s convolution k ..."
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Cited by 11 (0 self)
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Haussler’s convolution kernel provides a successful framework for engineering new positive semidefinite kernels, and has been applied to a wide range of data types and applications. In the framework, each data object represents a finite set of finer grained components. Then, Haussler’s convolution kernel takes a pair of data objects as input, and returns the sum of the return values of the predetermined primitive positive semidefinite kernel calculated for all the possible pairs of the components of the input data objects. On the other hand, the mapping kernel that we introduce in this paper is a natural generalization of Haussler’s convolution kernel, in that the input to the primitive kernel moves over a predetermined subset rather than the entire cross product. Although we have plural instances of the mapping kernel in the literature, their positive semidefiniteness was investigated in casebycase manners, and worse yet, was sometimes incorrectly concluded. In fact, there exists a simple and easily checkable necessary and sufficient condition, which is generic in the sense that it enables us to investigate the positive semidefiniteness of an arbitrary instance of the mapping kernel. This is the first paper that presents and proves the validity of the condition. In addition, we introduce two important instances of the mapping kernel, which we refer to as the sizeofindexstructuredistribution kernel and the editcostdistribution kernel. Both of them are naturally derived from well known (dis)similarity measurements in the literature (e.g. the maximum agreement tree, the edit distance), and are reasonably expected to improve the performance of the existing measures by evaluating their distributional features rather than their peak (maximum/minimum) features.
Ghash: towards fast kernelbased similarity search in large graph databases
 In EDBT
, 2009
"... Structured data including sets, sequences, trees and graphs, pose significant challenges to fundamental aspects of data management such as efficient storage, indexing, and similarity search. With the fast accumulation of graph databases, similarity search in graph databases has emerged as an impor ..."
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Cited by 10 (0 self)
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Structured data including sets, sequences, trees and graphs, pose significant challenges to fundamental aspects of data management such as efficient storage, indexing, and similarity search. With the fast accumulation of graph databases, similarity search in graph databases has emerged as an important research topic. Graph similarity search has applications in a wide range of domains including cheminformatics, bioinformatics, sensor network management, social network management, and XML documents, among others. Most of the current graph indexing methods focus on subgraph query processing, i.e. determining the set of database graphs that contains the query graph and hence do not directly support similarity search. In data mining and machine learning, various graph kernel functions have been designed
Kernels on Prolog Proof Trees: Statistical Learning in the ILP Setting
, 2006
"... We develop kernels for measuring the similarity between relational instances using background knowledge expressed in firstorder logic. The method allows us to bridge the gap between traditional inductive logic programming (ILP) representations and statistical approaches to supervised learning. L ..."
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Cited by 9 (3 self)
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We develop kernels for measuring the similarity between relational instances using background knowledge expressed in firstorder logic. The method allows us to bridge the gap between traditional inductive logic programming (ILP) representations and statistical approaches to supervised learning. Logic programs are first used to generate proofs of given visitor programs that use predicates declared in the available background knowledge. A kernel is then defined over pairs of proof trees. The method can be used for supervised learning tasks and is suitable for classification as well as regression. We report positive empirical results on Bongardlike and MofN problems that are difficult or impossible to solve with traditional ILP techniques, as well as on real bioinformatics and chemoinformatics data sets.
Classification of small molecules by two and threedimensional decomposition kernels
 BIOINFORMATICS
, 2007
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Graphlet Kernels for Prediction of Functional Residues in Protein Structures
"... In this study we introduce a novel graph‐based kernel method for annotating functional residues in protein structures. A structure is first modeled as a protein contact graph, where nodes correspond to residues and edges connect spatially neighboring residues. Each vertex in the protein contact grap ..."
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Cited by 7 (2 self)
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In this study we introduce a novel graph‐based kernel method for annotating functional residues in protein structures. A structure is first modeled as a protein contact graph, where nodes correspond to residues and edges connect spatially neighboring residues. Each vertex in the protein contact graph is then represented as a vector of counts of labeled non‐isomorphic subgraphs (called graph‐ lets), centered on the vertex of interest. A similarity measure between two vertices is expressed as the inner product of their respective count vectors and is used in a supervised learning framework to classify protein residues. We evaluated our method on two function prediction problems: identi‐ fication of catalytic residues in proteins, which is a well‐studied problem suitable for benchmark‐ ing, and a much less explored problem of predicting phosphorylation sites in protein structures. We compared the graphlet kernel approach against two alternative methods, a sequence‐based predic‐ tor and our implementation of the FEATURE framework. On both function prediction tasks the graphlet kernel performed favorably compared to the alternatives; however, the margin of differ‐ ence was considerably higher on the problem of phosphorylation site prediction. While there is both computational and experimental evidence that phosphorylation sites are preferentially posi‐
Learning with kernels and logical representations
 In Probabilistic inductive logic programming
, 2008
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Fast Kernel Methods for SVM Sequence Classifiers
"... Abstract. In this work we study string kernel methods for sequence analysis and focus on the problem of specieslevel identification based on short DNA fragments known as barcodes. We introduce efficient sortingbased algorithms for exact string kmer kernels and then describe a divideandconquer t ..."
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Cited by 3 (0 self)
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Abstract. In this work we study string kernel methods for sequence analysis and focus on the problem of specieslevel identification based on short DNA fragments known as barcodes. We introduce efficient sortingbased algorithms for exact string kmer kernels and then describe a divideandconquer technique for kernels with mismatches. Our algorithms for mismatch kernel matrix computations improve currently known time bounds for these computations. We then consider the mismatch kernel problem with feature selection, and present efficient algorithms for it. Our experimental results show that, for string kernels with mismatches, kernel matrices can be computed 100200 times faster than traditional approaches. Kernel vector evaluations on new sequences show similar computational improvements. On several DNA barcode datasets, kmer string kernels considerably improve identification accuracy compared to prior results. String kernels with feature selection demonstrate competitive performance with substantially fewer computations. 1
Adaptive matching based kernels for labelled graphs
 IN: MINING AND LEARNING WITH GRAPHS (MLG 2006), WITH ECML/PKDD
, 2006
"... Several kernels over labelled graphs have been proposed in the literature so far. Most of them are based on the Cross Product (CP) Kernel applied on decompositions of graphs into subgraphs of specific types. This approach has two main limitations: (i) it is difficult to choose apriori the appropr ..."
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Cited by 2 (0 self)
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Several kernels over labelled graphs have been proposed in the literature so far. Most of them are based on the Cross Product (CP) Kernel applied on decompositions of graphs into subgraphs of specific types. This approach has two main limitations: (i) it is difficult to choose apriori the appropriate type of subgraphs for a given problem and (ii) all the subgraphs of a decomposition participate in the computation of the CP kernel even though many of them might be poorly correlated with the class variable. To tackle these problems we propose a class of graph kernels constructed on the proximity space induced by the graph distances. These graph distances address the aforementioned limitations by learning combinations of different types of graph decompositions and by flexible matching the elements of the decompositions. Experiments performed on a number of graph classification problems demonstrate the effectiveness of the proposed approach.