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Let X be a random element in a metric space (F,d), and let Y be a random variable with value 0 or 1. Y is
called the class, or the label, of X. Let (Xi,Yi)1 ≤ i ≤ n be an observed i.i.d. sample having the same law as (X,Y). The problem of classification is to
predict the label of a new random element X. The k-nearest
neighbor classifier is the simple following rule: look at
the k nearest neighbors of X in the trial sample and choose 0 or 1 for its label
according to the majority vote. When ,
Stone...
For general Bayes decision rules there are considered perceptron approximations based on sufficient statistics inputs. A particular attention is paid to Bayes discrimination and classification. In the case of exponentially distributed data with known model it is shown that a perceptron with one hidden layer is sufficient and the learning is restricted to synaptic weights of the output neuron. If only the dimension of the exponential model is known, then the number of hidden layers will increase...
We summarize the main results on probabilistic neural networks recently published in a series of papers. Considering the framework of statistical pattern recognition we assume approximation of class-conditional distributions by finite mixtures of product components. The probabilistic neurons correspond to mixture components and can be interpreted in neurophysiological terms. In this way we can find possible theoretical background of the functional properties of neurons. For example, the general...
The problem of missing data is particularly present in archaeological research where, because of the fragmentariness of the finds, only a part of the characteristics of the whole object can be observed. The performance of various dissimilarity indices differently weighting missing values is studied on archaeological data via a simulation. An alternative solution consisting in randomly substituting missing values with character sets is also examined. Gower's dissimilarity coefficient seems to be...
The paper gives an overview of feature selection techniques in statistical pattern recognition with particular emphasis on methods developed within the Institute of Information Theory and Automation research team throughout recent years. Besides discussing the advances in methodology since times of Perez’s pioneering work the paper attempts to put the methods into a taxonomical framework. The methods discussed include the latest variants of the optimal algorithms, enhanced sub-optimal techniques...
Numerical taxonomy, which uses numerical methods to classify and relate items whose properties are non-numerical, is suggested as both an advantageous tool to support case-based reasoning and a means for agents to exploit knowledge that is best expressed in cases. The basic features of numerical taxonomy are explained, and discussed in application to a problem where human agents with differing views obtain solutions by negotiation and by reference to knowledge that is essentially case-like: allocation...
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