Urszula Libal

Multistage classification of signals with the use of multiscale wavelet representation

The aim of signal decomposition in wavelet bases is to represent a signal as a sequence of wavelet coefficients sets. There is proposed a multistage classification rule using on every stage only one set of the signal coefficients. The hierarchical construction of wavelet multiresolution analysis was an inspiration for the multistage classification rule. The algorithm makes an optimal decision for every set of coefficients and its main advantage is a smaller dimension of classification problem on every stage.

Multistage pattern recognition of signals represented in wavelet bases with reject option

We propose a multistage pattern recognition algorithm with a reject option. On every stage, the presented algorithm chooses a class of signal or rejects the signal, i.e. refuses to make a decision. If a class is assigned to the signal on some stage, then the algorithm stops. In the opposite case of a signal rejection, the decision of assigning to a class is made on the next stage. The multiresolution signal representation in wavelet bases allows to take a more accurate signal representation on every following stage. Our approach saves the computation time, when the algorithm selects a class on an early stage basing on a coarse wavelet representation. If the inaccurate representation is insufficient to point out one of classes (e.g. when the a posteriori probability of every class is lower than a fixed bound, in case of Bayesian classifier), the reject option protects from choosing a wrong class. We show that a risk of misclassification for the Bayesian decision rule with a reject option is lower or equal to a risk of the one-stage optimal Bayesian rule.

Feature selection for pattern recognition by LASSO and thresholding methods - a comparison

For high-dimensional data processing, like pattern recognition, it seems desirable to precede with a reduction of the number of describing features. Our aim is a comparison of various feature selection methods for pattern recognition. We consider two-class supervised classification problem for signals decomposed in wavelet bases. We test kNN classification rule with soft and hard thresholding, performed in two stages: (1) wavelet detail coefficient thresholding (noise reduction) and (2) searching for the most differentiating coefficients between classes (selection of discriminating coefficients). We present a new classification rule based on LARS/LASSO. We compare criteria for L1-norm regularization of wavelet coefficients: AIC, BIC and the thresh derived for kNN rule. There were performed simulations for noisy signals with SNR in the range from 0 to 22 [dB], approximated for all possible wavelet resolutions. The quality of pattern recognition for the presented algorithms was measured by the estimated recognition risk and the size of reduced model.

Wavelet Algorithm for Hierarchical Pattern Recognition

The idea, presented in this article, is based on a combination of hierarchical classifier with multiresolution representation of signals in the Daubechies wavelet bases. The paper concerns a multi-class recognition of random signals. It presents a multistage classifier with a hierarchical tree structure, based on a multiscale representation of signals in wavelet bases. Classes are hierarchically grouped in macro-classes and the established aggregation defines a decision tree. In each macro-class, the existence of deterministic pattern of signals is assumed. A global loss function with reject option is proposed for the multistage classifier and two strategies for the choice of loss function parameters are discussed. An analysis of risk is performed for a local (binary) attraction-limited minimum distance classifier for wavelet approximation of signals. This leads to proposals, relating to the upper estimate of the risk, called the guaranteed risk. Its value depends on the several parameters as the wavelet scale of signal representation, the support length of wavelet function, or the variance of the random noise in the macro-class. Finally, the guaranteed risk of the multistage classifier is derived.