Maciej Łuczak

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.

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.

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.