... mining time series data. Literally hundreds of papers have introduced new algorithms to index, classify, cluster and segment time series. In this work we make the following claim. Much of this work has very little utility because the contribution made (speed in the case of indexing, accuracy in the case of classification and clustering, model accuracy in the case of segmentation) offer an amount of "improvement" that would have been completely dwarfed by the variance that would have been observed by testing on many real world datasets, or the variance that would have been observed by changing minor (unstated) implementation details. To illustrate our point

We describe a method that aligns polyphonic audio recordings of music to symbolic score information in standard MIDI files without the difficult process of polyphonic transcription. By using this method, we can search through the MIDI database to find the MIDI file corresponding to a polyphonic audio recording. 1.

Existing trajectory clustering algorithms group similar trajectories as a whole, thus discovering common trajectories. Our key observation is that clustering trajectories as a whole could miss common sub-trajectories. Discovering common sub-trajectories is very useful in many applications, especially if we have regions of special interest for analysis. In this paper, we propose a new partition-and-group framework for clustering trajectories, which partitions a trajectory into a set of line segments, and then, groups similar line segments together into a cluster. The primary advantage of this framework is to discover common sub-trajectories from a trajectory database. Based on this partition-and-group framework, we develop a trajectory clustering algorithm TRA-CLUS. Our algorithm consists of two phases: partitioning and grouping. For the first phase, we present a formal trajectory partitioning algorithm using the minimum description length (MDL) principle. For the second phase, we present a density-based line-segment clustering algorithm. Experimental results demonstrate that TRACLUS correctly discovers common sub-trajectories from real trajectory data.

An important consideration in similarity-based retrieval of moving object trajectories is the definition of a distance function. The existing distance functions are usually sensitive to noise, shifts and scaling of data that commonly occur due to sensor failures, errors in detection techniques, disturbance signals, and different sampling rates. Cleaning data to eliminate these is not always possible. In this paper, we introduce a novel distance function, Edit Distance on Real sequence (EDR) which is robust against these data imperfections. Analysis and comparison of EDR with other popular distance

Time series data is perhaps the most frequently encountered type of data examined by the data mining community. Clustering is perhaps the most frequently used data mining algorithm, being useful in it’s own right as an exploratory technique, and also as a subroutine in more complex data mining algorithms such as rule discovery, indexing, summarization, anomaly detection, and classification. Given these two facts, it is hardly surprising that time series clustering has attracted much attention. The data to be clustered can be in one of two formats: many individual time series, or a single time series, from which individual time series are extracted with a sliding window. Given the recent explosion of interest in streaming data and online algorithms, the latter case has received much attention. In this work we make a surprising claim. Clustering of streaming time series is completely meaningless. More concretely, clusters extracted from streaming time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random. While this constraint can be intuitively demonstrated with a simple illustration and is simple to prove, it has never appeared in the literature. We can justify calling our claim surprising, since it invalidates the contribution of dozens of previously published papers. We will justify our claim with a theorem, illustrative examples, and a comprehensive set of experiments on reimplementations of previous work. Although the primary contribution of our work is to draw attention to the fact that an apparent solution to an important problem is incorrect and should no longer be used, we also introduce a novel method which, based on the concept of time series motifs, is able to meaningfully cluster some streaming time series datasets.

The last decade has witnessed a tremendous growths of interests in applications that deal with querying and mining of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been introduced. Each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive set of time series experiments re-implementing 8 different representation methods and 9 similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this paper, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. Our experiments have provided both a unified validation of some of the existing achievements, and in some cases, suggested that certain claims in the literature may be unduly optimistic. 1.

It has long been known that Dynamic Time Warping (DTW) is superior to Euclidean distance for classification and clustering of time series. However, until lately, most research has utilized Euclidean distance because it is more efficiently calculated. A recently introduced technique that greatly mitigates DTWs demanding CPU time has sparked a flurry of research activity. However, the technique and its many extensions still only allow DTW to be applied to moderately large datasets. In addition, almost all of the research on DTW has focused exclusively on speeding up its calculation; there has been little work done on improving its accuracy. In this work, we target the accuracy aspect of DTW performance and introduce a new framework that learns arbitrary constraints on the warping path of the DTW calculation. Apart from improving the accuracy of classification, our technique as a side effect speeds up DTW by a wide margin as well. We show the utility of our approach on datasets from diverse domains and demonstrate significant gains in accuracy and efficiency.

Existing studies on time series are based on two categories of distance functions. The first category consists of the Lp-norms. They are metric distance functions but cannot support local time shifting. The second category consists of distance functions which are capable of handling local time shifting but are nonmetric. The first

We present several methods for mining knowledge from the query logs of the MSN search engine. Using the query logs, we build a time series for each query word or phrase (e.g., ‘Thanksgiving ’ or ‘Christmas gifts’) where the elements of the time series are the number of times that a query is issued on a day. All of the methods we describe use sequences of this form and can be applied to time series data generally. Our primary goal is the discovery of semantically similar queries and we do so by identifying queries with similar demand patterns. Utilizing the best Fourier coefficients and the energy of the omitted components, we improve upon the state-of-the-art in time-series similarity matching. The extracted sequence features are then organized in an efficient metric tree index structure. We also demonstrate how to efficiently and accurately discover the important periods in a time-series. Finally we propose a simple but effective method for identification of bursts (long or short-term). Using the burst information extracted from a sequence, we are able to efficiently perform ’query-by-burst ’ on the database of timeseries. We conclude the presentation with the description of a tool that uses the described methods, and serves as an interactive exploratory data discovery tool for the MSN query database. 1.

The reuse of human motion capture data to create new, realistic motions by applying morphing and blending techniques has become an important issue in computer animation. This requires the identification and extraction of logically related motions scattered within some data set. Such content-based retrieval of motion capture data, which is the topic of this paper, constitutes a difficult and timeconsuming problem due to significant spatio-temporal variations between logically related motions. In our approach, we introduce various kinds of qualitative features describing geometric relations between specified body points of a pose and show how these features induce a time segmentation of motion capture data streams. By incorporating spatio-temporal invariance into the geometric features and adaptive segments, we are able to adopt efficient indexing methods allowing for flexible and efficient content-based retrieval and browsing in huge motion capture databases. Furthermore, we obtain an efficient preprocessing method substantially accelerating the cost-intensive classical dynamic time warping techniques for the time alignment of logically similar motion data streams. We present experimental results on a test data set of more than one million frames, corresponding to 180 minutes of motion. The linearity of our indexing algorithms guarantees the scalability of our results to much larger data sets.