Supervised classification is one of the most active areas of machine learning research. Most work has focused on classification in static domains, where an instantaneous snapshot of attributes is meaningful. In many domains, attributes are not static; in fact, it is the way they vary temporally that can make classification possible. Examples of such domains include speech recognition, gesture recognition and electrocardiograph classification. While it is possible to use ad hoc, domain-specific techniques for "flattening " the time series to a learner-friendly representation, this fails to take into account both the special problems and special heuristics applicable to temporal data and often results in unreadable concept descriptions. Though traditional time series techniques can sometimes produce accurate classifiers, few can provide comprehensible descriptions. We propose a general architecture for classification and description of multivariate time series. It employs event primitive...

There has been much recent interest in adapting data mining algorithms to time series databases. Most of these algorithms need to compare time series. Typically some variation of Euclidean distance is used. However, as we demonstrate in this paper, Euclidean distance can be an extremely brittle distance measure. Dynamic time warping (DTW) has been suggested as a technique to allow more robust distance calculations, however it is computationally expensive. In this paper we introduce a modification of DTW which operates on a higher level abstraction of the data, in particular, a Piecewise Aggregate Approximation (PAA). Our approach allows us to outperform DTW by one to two orders of magnitude, with no loss of accuracy.

We describe an extension to the "best-basis" method to construct an orthonormal basis which maximizes a class separability for signal classification problems. This algorithm reduces the dimensionality of these problems by using basis functions which are well localized in time-frequency plane as feature extractors. We tested our method using two synthetic datasets: extracted features (expansion coefficients of input signals in these basis functions), supplied them to the conventional pattern classifiers, then computed the misclassification rates. These examples show the superiority of our method over the direct application of these classifiers on the input signals. As a further application, we also describe a method to extract signal component from data consisting of signal and textured background. keywords: wavelet packets, local trigonometric transforms, classification, feature extraction, dimensionality reduction, linear discriminant analysis, classification and regression trees 1 I...

In this paper, we propose some new tools to allow machine learning classifiers to cope with time series data. We first argue that many time-series classification problems can be solved by detecting and combining local properties or patterns in time series. Then, a technique is proposed to find patterns which are useful for classification. These patterns are combined to build interpretable classification rules. Experiments, carried out on several artificial and real problems, highlight the interest of the approach both in terms of interpretability and accuracy of the induced classifiers.

Abstract. We describe an extension to the "best-basis " method to select an orthonormal basis suitable for sig-nal/image classification problems from a large collection of orthonormal bases consisting of wavelet packets or local trigonometric bases. The original best-basis algorithm selects a basis minimizing entropy from such a "library of orthonormal bases " whereas the proposed algorithm selects a basis maximizing a certain discriminant measure (e.g., relative entropy) among classes. Once such a basis is selected, a small number of most significant coordinates (features) are fed into a traditional classifier such as Linear Discriminant Analysis (LDA) or Classification and Regression Tree (CARTTM). The performance of these statistical methods is enhanced since the proposed methods reduce the dimensionality of the problem at hand without losing important information for that problem. Here, the basis functions which are well-localized in the time-frequency plane are used as feature extractors. We applied our method to two signal classification problems and an image texture classification problem. These experiments show the superiority of our method over the direct application of these classifiers on the input signals. As a further application, we also describe a method to extract signal component from data consisting of signal and textured background.

A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l 2 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.

We introduce a novel method of feature extraction for texture segmentation that relies on multi-channel wavelet frames and two-dimensional envelope detection. We describe and compare two algorithms for envelope detection based on (1) the Hilbert transform and (2) zero-crossings. We present criteria for filter selection and discuss quantitatively their effect on feature extraction. The performance of our method is demonstrated experimentally on samples of both natural and synthetic textures. Keywords--- Feature extraction, image segmentation, wavelet analysis. I. Introduction Features for texture representation are of crucial importance for accomplishing segmentation[1]. Previous multichannel approaches for texture feature extraction utilized the concept of spatial-frequency representation [2] [3], and have been supported by studies of the human visual system [4]. In these methods, both complex and real filters were used. Complex prolate spheroidal sequences were used as channel filter...

Time series are a ubiquitous form of data occurring in virtually every scientific discipline and business application. There has been much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time series [7]. Debregeas and Hebrail [8]

Wavelet packets are a useful extension of wavelets providing an adaptive timescale analysis. In using noisy observations of a signal of interest, the criteria for best bases representation are random variables. The search may thus be very sensitive to noise. In this paper, we characterize the asymptotic statistics of the criteria to gain insight which can in turn, be used to improve on the performance of the analysis. By way of a well-known information-theoretic principle, namely the Minimum Description Length, we provide an alternative approach to Minimax methods for deriving various attributes of nonlinear wavelet packet estimates. 1 Introduction Research interest in wavelets and their applications have tremendously grown over the last five years. Only, more recently, however, have their applications been considered in a stochastic setting [Fl1, Wo1, BB + , CH1]. A number of papers which have addressed the optimal representation of a signal in a wavelet/wavelet packet basis, have...

In this thesis, we generalize the classical discrete wavelet transform, and construct wavelet transforms that are shift-invariant, time-varying, undecimated, and signal dependent. The result is a set of powerful and efficient algorithms suitable for a wide variety of signal processing tasks, e.g., data compression, signal analysis, noise reduction, statistical estimation, and detection. These algorithms are comparable and often superior to traditional methods. In this sense, we put wavelets in action.