In many pattern recognition/classification problem the true class conditional model and class probabilities are approximated for reasons of reducing complexity and/or of statistical estimation. The approximated classifier is expected to have worse performance, here measured by the probability of correct classification. We present an analysis valid in general, and easily computable formulas for estimating the degradation in probability of correct classification when compared to the optimal classifier. An example of an approximation is the Naïve Bayes classifier. We show that the performance of the Naïve Bayes depends on the degree of functional dependence between the features and labels. We provide a sufficient condition for zero loss of performance, too.

MOTIVATION: Previously, Rantanen et al. (2001; J. Mol. Biol., 313, 197-214) constructed a protein atom-ligand fragment interaction library embodying experimentally solved, high-resolution three-dimensional (3D) structural data from the Protein Data Bank (PDB). The spatial locations of protein atoms that surround ligand fragments were modeled with Gaussian mixture models, the parameters of which were estimated with the expectation-maximization (EM) algorithm. In the validation analysis of this library, there was strong indication that the protein atom classification, 24 classes, was too large and that a reduction in the classes would lead to improved predictions. RESULTS: Here, a dissimilarity (distance) matrix that is suitable for comparison and fusion of 24 pre-defined protein atom classes has been derived. Jeffreys' distances between Gaussian mixture models are used as a basis to estimate dissimilarities between protein atom classes. The dissimilarity data are analyzed both with a hierarchical clustering method and independently by using multidimensional scaling analysis. The results provide additional insight into the relationships between different protein atom classes, giving us guidance on, for example, how to readjust protein atom classification and, thus, they will help us to improve protein--ligand interaction predictions. CONTACT: [email protected]

Local searching (LS) has proven to be an efficient optimization technique in clustering applications when minimizing stochastic complexity. In this paper, we propose a method for organizing LS in this context - the adaptive multi-operator local search (AMOLS) - and compare its performance to the non-adaptive multi-operator LS (MOLS) method. Both of these methods use several different LS operators to solve problems. MOLS applies the operators randomly, whereas AMOLS adapts itself to favour those operators which manage to improve the results more frequently. We use a large database of binary vectors representing strains of bacteria belonging to the family Enterobacteriaceae and a binary image as our test materials. The results show the benefits of self-adaptation.

The principle of minimum entropy of error estimation (MEEE) is formulated for discrete random variables. In the case when the random variable to be estimated is binary, we show that the MEEE is given by a Neyman-Pearson-type strictly monotonous test. In addition, the asymptotic behavior of the error probabilities is proved to be equivalent to that of the Bayesian test.

Representations and statistical properties of the process .>

Combined linear-Viterbi equalizer (CLVE) is a term often used for a class of digital receivers reducing the complexity of the Viterbi detector by assuming an approximate channel model together with linear pre-equalization of the received data. The authors reconsider a weighted least squares design technique for CLVEs by introducing a minimax criterion for suppressing the strongest component of the residual intersymbol interference. Odling (1993) studied the performance of some proposed CLVE design methods and evaluated them by simulated bit error rates. The present authors investigate the performance of the minimax design and of the CLVE designs found in literature for two GSM test channels. They also present a comparison of the CLVE designs based on a common quadratic optimization criterion for the selection of the channel prefilter and the desired impulse response.>

Explicit expression are derived for the conditional expectation and variance of the encoder in a predictive DPCM coder with an N-level quantizer, when a stationary Ornstein-Uhlenbeck process is a source. A representation of the encoder in terms of a stochastic integral is presented. These expressions yield a nonlinear stochastic difference equation for the decoding error process and a stochastic differential equation (SDE) as a weak limit for the error process. The statistical properties of the error obtained as a solution of the limiting SDE are interpreted in terms of the slope overload error.>

A sharp upper bound is derived for the exponential entropy in the class of absolutely continuous distributions with specific standard deviation and an exact description of the extremal distributions. This result is interpreted as determining the least favorable cases for certain methods of quantization of analog sources. It is known that for a large class of quantizers (both zero-memory and vector) the rth power distortion, as well as some other distortion criteria, are bounded below by a constant, depending on r, multiplied by a certain integral of the source's probability density. It is pointed out that this bound can be rewritten in terms of the exponential entropy. The exponential entropy measures the quantitative extent or range of the source distribution. This fact gives a physical interpretation of the indicated limits of quantizer performance, further elucidated by the main result.>