Many efforts have been made during the past decades to investigate the use of orthogonal basis functions in the field of least-squares approximation. Certain bases of orthogonal functions allow for a definition of fast update algorithms for approximations of time series in sliding or growing time windows. In fields such as technical data analytics, temporal data mining, or pattern recognition in time series, appropriate time series representations are needed to measure the similarity of time series or to segment them. This article bridges the gap between mathematical basic research and applications by making fast update techniques for standard polynomials and trigonometric polynomials accessible for time series classification or regression (e.g., forecasting), anomaly or motif detection in time series, etc. This is of utmost importance for online or big data applications. Time series or segments of time series will be represented by features derived from the orthogonal expansion coefficients of the approximating polynomials which capture the essential behavior in the time or spectral domain, i.e. trends and periodic behavior, using standard or trigonometric polynomials. Our experiments show that a reliable computation is possible at a very low runtime compared to a conventional least-squares approach. The algorithms are implemented in Java, C(++), Matlab, and Python and made publicly available.

Evolvable hardware (EHW) has shown itself to be a promising approach for prosthetic hand controllers. Besides competitive classification performance, EHW classifiers offer self-adaptation, fast training, and a compact implementation. However, EHW classifiers have not yet been sufficiently compared to state-of-the-art conventional classifiers. In this paper, we compare two EHW approaches to four conventional classification techniques:k-nearest-neighbor, decision trees, artificial neural networks, and support vector machines. We provide all classifiers with features extracted from electromyographic signals taken from forearm muscle contractions, and let the algorithms recognize eight to eleven different kinds of hand movements. We investigate classification accuracy on a fixed data set and stability of classification error rates when new data is introduced. For this purpose, we have recorded a short-term data set from three individuals over three consecutive days and a long-term data set from a single individual over three weeks. Experimental results demonstrate that EHW approaches are indeed able to compete with state-of-the-art classifiers in terms of classification performance.

The purpose of this paper is to evaluate and benchmark ensemble methods for time series prediction for daily currency exchange rates using ensemble feedforward neural networks and kernel partial least squares (K-PLS). Best-practice forecasting methods for the US Dollar (USD) per Indian Rupee (IR) are applied for training, validating, and testing the machine learning models. In order to perform the benchmarking evaluation study neural network forecasting methods are first compared on a benchmarked neural network time series prediction method for the Canadian Lynx time series. The K-PLS method is benchmarked in addition with support vector machines (SVM), a similar kernel-based method. Both one-step ahead and a roll-out methods for extended forecast horizons are applied for the currency exchange rates. The paper is novel in the sense that two new ensemble methods are introduced: weight seeding and multiple cross-validation averaging. The paper is also novel in the sense that several new validation indices are proposed that are especially applicable for time series: q2and Q2and the fraction of misses in the exchange rate return space, which is a more relevant metric for currency speculation. As a general conclusion it is found that the USD per IR is quite predictable, while other currencies such as the USD per Euro and the Australian Dollar (AUD) per Euro are not predictable.

In this article, we provide a new technique for temporal data mining which is based on classification rules that can easily be understood by human domain experts. Basically, time series are decomposed into short segments, and short-term trends of the time series within the segments (e.g., average, slope, and curvature) are described by means of polynomial models. Then, the classifiers assess short sequences of trends in subsequent segments with their rule premises. The conclusions gradually assign an input to a class. As the classifier is a generative model of the processes from which the time series are assumed to originate, anomalies can be detected, too. Segmentation and piecewise polynomial modeling are done extremely fast in only one pass over the time series. Thus, the approach is applicable to problems with harsh timing constraints. We lay the theoretical foundations for this classifier, including a new distance measure for time series and a new technique to construct a dynamic classifier from a static one, and demonstrate its properties by means of various benchmark time series, for example, Lorenz attractor time series, energy consumption in a building, or ECG data.

The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the orthogonal expansion of the approximating polynomial-obtained by means of the update steps-can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg-which is suitable for many data streaming applications-offers high accuracy at very low computational costs.

In this paper, a new technique for online signature verification or identification is proposed. The technique integrates a longest common subsequences (LCSS) detection algorithm which measures the similarity of signature time series into a kernel function for support vector machines (SVM). LCSS offers the possibility to consider the local variability of signals such as the time series of pen-tip coordinates on a graphic tablet, forces on a pen, or inclination angles of a pen measured during a signing process. Consequently, the similarity of two signature time series can be determined in a more reliable way than with other measures. A proprietary database with signatures of 153 test persons and the SVC 2004 benchmark database are used to show the properties of the new SVM-LCSS. We investigate its parameterization and compare it to SVM with other kernel functions such as dynamic time warping (DTW). Our experiments show that SVM with the LCSS kernel authenticate persons very reliably and with a performance which is significantly better than that of the best comparing technique, SVM with DTW kernel.