By Vladimir S. Cherkassky, Filip Mulier
An interdisciplinary framework for studying methodologies—covering records, neural networks, and fuzzy good judgment, this publication offers a unified remedy of the foundations and strategies for studying dependencies from facts. It establishes a basic conceptual framework within which a variety of studying tools from information, neural networks, and fuzzy good judgment should be applied—showing few basic rules underlie so much new equipment being proposed this day in facts, engineering, and laptop technological know-how. entire with over 100 illustrations, case experiences, and examples making this a useful textual content.
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Extra info for Learning from Data: Concepts, Theory, and Methods, Second Edition
Example text
20) using only the training data x1 ; . . ; xn leads to the density estimate f ðx; o0 Þ. Clustering and Vector Quantization Say, the goal is optimal partitioning of the unknown distribution in x-space into a prespecified number of regions (clusters) so that future samples drawn from a particular region can be approximated by a single point (cluster center or local prototype). Here the set of vector-valued functions fðx; oÞ, o 2 , are vector quantizers. cðxÞ; ð2:21Þ where cðxÞ denotes the cluster center coordinates.
The general learning scenario involves three components (Fig. 1): a Generator of random input vectors, a System that returns an output for a given input vector, and the Learning Machine that estimates an unknown (input, output) mapping of the System from the observed (input, output) samples. This formulation is very general and describes many practical learning problems found in engineering and statistics, such as interpolation, regression, classification, clustering, and density estimation. Before we look at the learning machine in detail, let us clearly describe the roles of each component in mathematical terms: Generator: The generator (or sampling distribution) produces random vectors x 2 Classical theory focuses on the problem of estimation and sidesteps the issue of specification. Classical approaches to the learning problem depend on much stricter assumptions than those posed in the general learning formulation because they assume that functions are specified up to a fixed number of parameters. The two inductive principles that are most commonly used in the classical learning process are Empirical Risk Minimization (ERM) and Maximum Likelihood (ML). ML is a specific form of the more general ERM principle obtained when using particular loss functions.