A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classi?cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation.

An overview of the theory and application of kernel classification methods. Linear classifiers in kernel spaces have emerged as a major topic within the field of machine learning. The kernel technique takes the linear classifier—a limited, but well-established and comprehensively studied model—and extends its applicability to a wide range of nonlinear pattern-recognition tasks such as natural language processing, machine vision, and biological sequence analysis. This book provides the first comprehensive overview of both the theory and algorithms of kernel classifiers, including the most recent developments. It begins by describing the major algorithmic advances: kernel perceptron learning, kernel Fisher discriminants, support vector machines, relevance vector machines, Gaussian processes, and Bayes point machines. Then follows a detailed introduction to learning theory, including VC and PAC-Bayesian theory, data-dependent structural risk minimization, and compression bounds. Throughout, the book emphasizes the interaction between theory and algorithms: how learning algorithms work and why. The book includes many examples, complete pseudo code of the algorithms presented, and an extensive source code library.

Parallelism and Programming in Classifier Systems deals with the computational properties of the underlying parallel machine, including computational completeness, programming and representation techniques, and efficiency of algorithms. In particular, efficient classifier system implementations of symbolic data structures and reasoning procedures are presented and analyzed in detail. The book shows how classifier systems can be used to implement a set of useful operations for the classification of knowledge in semantic networks. A subset of the KL-ONE language was chosen to demonstrate these operations. Specifically, the system performs the following tasks: (1) given the KL-ONE description of a particular semantic network, the system produces a set of production rules (classifiers) that represent the network; and (2) given the description of a new term, the system determines the proper location of the new term in the existing network. These two parts of the system are described in detail. The implementation reveals certain computational properties of classifier systems, including completeness, operations that are particularly natural and efficient, and those that are quite awkward. The book shows how high-level symbolic structures can be built up from classifier systems, and it demonstrates that the parallelism of classifier systems can be exploited to implement them efficiently. This is significant since classifier systems must construct large sophisticated models and reason about them if they are to be truly ""intelligent."" Parallel organizations are of interest to many areas of computer science, such as hardware specification, programming language design, configuration of networks of separate machines, and artificial intelligence This book concentrates on a particular type of parallel organization and a particular problem in the area of AI, but the principles that are elucidated are applicable in the wider setting of computer science.