Kilho Shin

A generalization of Haussler's convolution kernel: mapping kernel

Hausslers 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, Hausslers 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 Hausslers 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 case-by-case 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 size-of-index-structure-distribution kernel and the editcost-distribution 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.

A theoretical analysis of alignment and edit problems for trees

The problem of comparing two tree structures emerges across a wide range of applications in computational biology, pattern recognition, and many others. A number of tree edit methods have been proposed to find a structural similarity between trees. The alignment of trees is one of these methods, introduced as a natural extension of the alignment of strings, which gives a common supertree pattern of two trees, whereas tree edit gives a common subtree pattern. It is well known that alignment and edit are two equivalent notions for strings from the computational point of view. This equivalence, however, does not hold for trees. The lack of a theoretical formulation of these notions has lead to confusion. In this paper, we give a theoretical analysis of alignment and edit methods, and show an important relationship, which is the equivalence between the the alignment of trees and a variant of tree edit, called less-constrained edit.

Kernels Based on Distributions of Agreement Subtrees

The MAST (maximum agreement subtrees) problem has been extensively studied, and the size of the maximum agreement subtrees between two trees represents their similarity. This similarity measure, however, only takes advantage of a very small portion of the agreement subtrees, that is, the maximum agreement subtrees, and agreement subtrees of smaller size are neglected at all. On the other hand, it is reasonable to consider that the distributions of the sizes of the agreement subtrees may carry useful information with respect to similarity. Based on the notion of the size-of-index-structure-distribution kernel introduced by Shin and Kuboyama, the present paper introduces positive semidefinite tree-kernels, which evaluate distributional features of the sizes of agreement subtrees, and shows efficient dynamic programming algorithms to calculate the kernels. In fact, the algorithms are of O (|x | ·|y |)-time for labeled and ordered trees x and y . In addition, the algorithms are designed so that the agreement subtrees have roots and leaves with labels from predetermined sub-domains of an alphabet. This design will be very useful for important applications such as the XML documents.

A Consistency-Constrained Feature Selection Algorithm with the Steepest Descent Method

This paper proposes a new consistency-based feature selection algorithm, which presents a new balance to the fundamental tradeoff between the quality of outputs of feature selection algorithms and their efficiency. Consistency represents the extent of corrective relevance of features to classification, and hence, consistency-based feature selection algorithms such as INTERACT, LCC and CCC can select relevant features more correctly by taking interaction among features into account. INTERACT and LCC are fast by employing the linear search strategy. By contrast, CCC is slow, since it is based on the complete search strategy, but can output feature subsets of higher quality. The algorithm that we propose in this paper, on the other hand, takes the steepest descent method as the search strategy. Consequently, it can find better solutions than INTERACT and LCC, and simultaneously restrains the increase in computational complexity within a reasonable level: it evaluates

Provably secure anonymous access control for heterogeneous trusts

(|{\mathcal F}| + |{\tilde {\mathcal F}}|)(|{\mathcal F}| - |{\tilde {\mathcal F}}| + 1)/2

Position-aware string kernels with weighted shifts and a general framework to apply string kernels to other structured data

feature subsets to output

Practical Anonymous Access Control Protocols for Ubiquitous Computing

{\tilde {\mathcal F}}

Practical access control protocol for secure sensor networks

. We prove effectiveness of the new algorithm through experiments.

Polynomial summaries of positive semidefinite kernels

Privacy has been a central concern of ubiquitous (pervasive) computing. Although the boundary between privacy and publicity dynamically moves depending on the context in which the issue is considered, access control, which is one of the most fundamental functionality constituting ubiquitous computing, is required to support perfect privacy, that is, anonymity and unlinkability. This paper presents a concrete protocol for anonymous access control that supports compliance to the distributed trust management model introduced by Blaze et al, efficiency for continual verification and provable security. In addition, the protocol is based on a practical trust model that models the heterogeneous structure of trust in the real world. The model defines a service provider, a service appliance, users and a device that users carry or wear as independent players, and further assumes that trust between them is independently established only based on their arbitrary mutual agreements.

Polynomial Summaries of Positive Semidefinite Kernels

In combination with efficient kernel-base learning machines such as Support Vector Machine (SVM), string kernels have proven to be significantly effective in a wide range of research areas (e.g. bioinformatics, text analysis, voice analysis). Many of the string kernels proposed so far take advantage of simpler kernels such as trivial comparison of characters and/or substrings, and are classified into two classes: the positionaware string kernel which takes advantage of positional information of characters/substrings in their parent strings, and the position-unaware string kernel which does not. Although the positive semidefiniteness of kernels is a critical prerequisite for learning machines to work properly, a little has been known about the positive semidefiniteness of the positionaware string kernel. The present paper is the first paper that presents easily checkable sufficient conditions for the positive semidefiniteness of a certain useful subclass of the position-aware string kernel: the similarity/ matching of pairs of characters/substrings is evaluated with weights determined according to shifts (the differences in the positions of characters/ substrings). Such string kernels have been studied in the literature but insufficiently. In addition, by presenting a general framework for converting positive semidefinite string kernels into those for richer data structures such as trees and graphs, we generalize our results.