On-Line Dynamic Time Warping for Streaming Time Series

Dynamic Time Warping is a well-known measure of dissimilarity between time series. Due to its flexibility to deal with non-linear distortions along the time axis, this measure has been widely utilized in machine learning models for this particular kind of data. Nowadays, the proliferation of streaming data sources has ignited the interest and attention of the scientific community around on-line learning models. In this work, we naturally adapt Dynamic Time Warping to the on-line learning setting. Specifically, we propose a novel on-line measure of dissimilarity for streaming time series which combines a warp constraint and a weighted memory mechanism to simplify the time series alignment and adapt to non-stationary data intervals along time. Computer simulations are analyzed and discussed so as to shed light on the performance and complexity of the proposed measure

On-line Elastic Similarity Measures for time series

The way similarity is measured among time series is of paramount importance in many data mining and machine learning tasks. For instance, Elastic Similarity Measures are widely used to determine whether two time series are similar to each other. Indeed, in off-line time series mining, these measures have been shown to be very effective due to their ability to handle time distortions and mitigate their effect on the resulting distance. In the on-line setting, where available data increase continuously over time and not necessary in a stationary manner, stream mining approaches are required to be fast with limited memory consumption and capable of adapting to different stationary intervals. In this sense, the computational complexity of Elastic Similarity Measures and their lack of flexibility to accommodate different stationary intervals, make these similarity measures incompatible with the requirements mentioned. To overcome these issues, this paper adapts the family of Elastic Similarity Measures – which includes Dynamic Time Warping, Edit Distance, Edit Distance for Real Sequences and Edit Distance with Real Penalty – to the on-line setting. The proposed adaptation is based on two main ideas: a forgetting mechanism and the incremental computation. The former makes the similarity consistent with streaming time series characteristics by giving more importance to recent observations, whereas the latter reduces the computational complexity by avoiding unnecessary computations. In order to assess the behavior of the proposed similarity measure in on-line settings, two different experiments have been carried out. The first aims at showing the efficiency of the proposed adaptation, to do so we calculate and compare the computation time for the elastic measures and their on-line adaptation. By analyzing the results drawn from a distance-based streaming machine learning model, the second experiment intends to show the effect of the forgetting mechanism on the resulting similarity value. The experimentation shows, for the aforementioned Elastic Similarity Measures, that the proposed adaptation meets the memory, computational complexity and flexibility constraints imposed by streaming data

Streaming Maximum-Minimum Filter Using No More than Three Comparisons per Element

The running maximum-minimum (max-min) filter computes the maxima and minima over running windows of size w. This filter has numerous applications in signal processing and time series analysis. We present an easy-to-implement online algorithm requiring no more than 3 comparisons per element, in the worst case. Comparatively, no algorithm is known to compute the running maximum (or minimum) filter in 1.5 comparisons per element, in the worst case. Our algorithm has reduced latency and memory usage.Comment: to appear in Nordic Journal of Computin

Time Series Data Mining Algorithms for Identifying Short RNA in Arabidopsis thaliana

The class of molecules called short RNAs (sRNAs) are known to play a key role in gene regulation. Th are typically sequences of nucleotides between 21-25 nucleotides in length. They are known to play a key role in gene regulation. The identification, clustering and classification of sRNA has recently become the focus of much research activity. The basic problem involves detecting regions of interest on the chromosome where the pattern of candidate matches is somehow unusual. Currently, there are no published algorithms for detecting regions of interest, and the unpublished methods that we are aware of involve bespoke rule based systems designed for a specific organism. Work in this very new field has understandably focused on the outcomes rather than the methods used to obtain the results. In this paper we propose two generic approaches that place the specific biological problem in the wider context of time series data mining problems. Both methods are based on treating the occurrences on a chromosome, or “hit count” data, as a time series, then running a sliding window along a chromosome and measuring unusualness. This formulation means we can treat finding unusual areas of candidate RNA activity as a variety of time series anomaly detection problem. The first set of approaches is model based. We specify a null hypothesis distribution for not being a sRNA, then estimate the p-values along the chromosome. The second approach is instance based. We identify some typical shapes from known sRNA, then use dynamic time warping and fourier trans-form based distance to measure how closely the candidate series matches. We demonstrate that these methods can find known sRNA on Arabidopsis thaliana chromosomes and illustrate the benefits of the added information provided by these algorithms