Tomasz Górecki

Using derivatives in time series classification

Over recent years the popularity of time series has soared. Given the widespread use of modern information technology, a large number of time series may be collected during business, medical or biological operations, for example. As a consequence there has been a dramatic increase in the amount of interest in querying and mining such data, which in turn has resulted in a large number of works introducing new methodologies for indexing, classification, clustering and approximation of time series. In particular, many new distance measures between time series have been introduced. In this paper, we propose a new distance function based on a derivative. In contrast to well-known measures from the literature, our approach considers the general shape of a time series rather than point-to-point function comparison. The new distance is used in classification with the nearest neighbor rule. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 20 time series datasets from a wide variety of application domains. Our experiments show that our method provides a higher quality of classification on most of the examined datasets.

Multivariate time series classification with parametric derivative dynamic time warping

We improve DTW distance measure in multivariate time series classification.We use derivatives to improve DTW in multivariate time series classification.We test effectiveness on 18 real time series.We present a detailed comparison of proposed methods. Multivariate time series (MTS) data are widely used in a very broad range of fields, including medicine, finance, multimedia and engineering. In this paper a new approach for MTS classification, using a parametric derivative dynamic time warping distance, is proposed. Our approach combines two distances: the DTW distance between MTS and the DTW distance between derivatives of MTS. The new distance is used in classification with the nearest neighbor rule. Experimental results performed on 18 data sets demonstrate the effectiveness of the proposed approach for MTS classification.

Non-isometric transforms in time series classification using DTW

Over recent years the popularity of time series has soared. As a consequence there has been a dramatic increase in the amount of interest in querying and mining such data. In particular, many new distance measures between time series have been introduced. In this paper we propose a new distance function based on derivatives and transforms of time series. In contrast to well-known measures from the literature, our approach combines three distances: DTW distance between time series, DTW distance between derivatives of time series, and DTW distance between transforms of time series. The new distance is used in classification with the nearest neighbor rule. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 47 time series data sets from a wide variety of application domains. Our experiments show that this new method provides a significantly more accurate classification on the examined data sets.

Using derivatives in a longest common subsequence dissimilarity measure for time series classification

Abstract Over recent years the popularity of time series has soared. Given the widespread use of modern information technology, a large number of time series may be collected. As a consequence there has been a dramatic increase in the amount of interest in querying and mining such data. A vital component in many types of time series analyses is the choice of an appropriate dissimilarity measure. Numerous measures have been proposed to date, with the most successful ones based on dynamic programming. One of such measures is longest common subsequence (LCSS). In this paper, we propose a parametrical extension of LCSS based on derivatives. In contrast to well-known measures from the literature, our approach considers the general shape of a time series rather than point-to-point function comparison. The new dissimilarity measure is used in classification with the nearest neighbor rule. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 47 real time series. Experiments show that our method provides a higher quality of classification compared with LCSS on examined data sets.

First and Second Derivatives in Time Series Classification Using DTW

In our previous work, we developed a new distance function based on a derivative and showed that our algorithm is effective. In contrast to well-known measures from the literature, our approach considers the general shape of a time series rather than standard distance of function (value) comparison. The new distance was used in classification with the nearest neighbor rule. Now we improve on our previous technique by adding the second derivative. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 47 time series datasets from a wide variety of application domains. Our experiments show that this new method provides a significantly more accurate classification on the examined datasets.

Functional Discriminant Coordinates

In this article we propose a new method of construction of discriminant coordinates and their kernel variant based on the regularization (ridge regression). Moreover, we compare the case of discriminant coordinates, functional discriminant coordinates and the kernel version of functional discriminant coordinates on 20 data sets from a wide variety of application domains using values of the criterion of goodness and statistical tests. Our experiments show that the kernel variant of discriminant coordinates provides significantly more accurate results on the examined data sets.

Linear discriminant analysis with a generalization of the Moore-Penrose pseudoinverse

The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore-Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.

Regression Methods for Combining Multiple Classifiers

As no single classification method outperforms other classification methods under all circumstances, decision-makers may solve a classification problem using several classification methods and examine their performance for classification purposes in the learning set. Based on this performance, better classification methods might be adopted and poor methods might be avoided. However, which single classification method is the best to predict the classification of new observations is still not clear, especially when some methods offer similar classification performance in the learning set. In this article we present various regression and classical methods, which combine several classification methods to predict the classification of new observations. The quality of the combined classifiers is examined on some real data. Nonparametric regression is the best method of combining classifiers.

Some Methods of Replacing the Nearest Neighbor Method

In this article, two classifiers, which generalize the nearest neighbor method, are introduced and studied. The first of them is based on calculating the distances to all objects from a learning sample. The second one additionally considers directions of the objects. Both of them have locally nonlinear classification borders. A number of real and artificial datasets and methods of error estimation are used.

Testing Normality of Functional Time Series: TESTING NORMALITY OF FUNCTIONAL TIME SERIES

We develop tests of normality for time series of functions. The tests are related to the commonly used Jarque–Bera test. The assumption of normality has played an important role in many methodological and theoretical developments in the field of functional data analysis. Yet, no inferential procedures to verify it have been proposed so far, even for i.i.d. functions. We propose several approaches which handle two paramount challenges: (i) the unknown temporal dependence structure and (ii) the estimation of the optimal finite†dimensional projection space. We evaluate the tests via simulations and establish their large sample validity under general conditions. We obtain useful insights by applying them to pollution and intraday price curves. While the pollution curves can be treated as normal, the normality of high†frequency price curves is rejected.