A Measure of Similarity of Time Series Containing Missing Data Using the Mahalanobis Distance

The analysis of time series data is of interest to many application domains. But this analysis is challenging due to many reasons such as missing data in the series, unstructured nature of the data and errors in the data collection procedure, measuring equipment, etc. The problem of missing data while matching two time series is dealt with either by predicting a value for the missing data using the already collected data, or by completely ignoring the missing values. In this paper, we present an approach where we make use of the characteristics of the Mahalanobis Distance to inherently accommodate the missing values while finding the best match between two time series. Using this approach, we have designed two algorithms which can find the best match for a given query series in a candidate series, without imputing the missing values in the candidate. The initial algorithm finds the best nonwarped match between the candidate and the query time series, while the second algorithm is an extension of the initial algorithm to find the best match in the case of warped data using a Dynamic Time Warping (DTW) like algorithm. Thus, with experimental results we go on to conclude that the proposed warping algorithm is a good method for matching between two time series with warping and missing data.