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Pattern analysis 3 1.1 Patterns in data 4 1.2 Pattern analysis algorithms 12 1.3 Exploiting patterns 17 1.4 Summary 22 1.5 Further reading and advanced topics 23 2 Kernel methods: an overview 25 2.1 The overall picture 26 2.2 Linear regression in a feature space 27 2.3 Other examples 36 2.4 The modularity of kernel methods 42 2.5 Roadmap of the book 43 2.6 Summary 44 2.7 Further reading and advanced topics 45 3 Properties of kernels 47 3.1 Inner products and positive semi-definite matrices 48 3.2 Characterisation of kernels 60 3.3 The kernel matrix 68 3.4 Kernel construction 74 3.5 Summary 82 3.6 Further reading and advanced topics 82 4 Detecting stable patterns 85 4.1 Concentration inequalities 86 4.2 Capacity and regularisation: Rademacher theory 93 v vi Contents

Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.

We present a general method using kernel Canonical Correlation Analysis to learn a semantic representation to web images and their associated text. The semantic space provides a common representation and enables a comparison between the text and images. In the experiments we look at two approaches of retrieving images based only on their content from a text query. We compare the approaches against a standard cross-representation retrieval technique known as the Generalised Vector Space Model.

International audienceThe PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not pre-segmented objects). Four object classes were selected: motorbikes, bicycles, cars and people. Twelve teams entered the challenge. In this chapter we provide details of the datasets, algorithms used by the teams, evaluation criteria, and results achieved