Many algorithms have been proposed for the problem of time series classification. However, it is clear that one-nearest-neighbor with Dynamic Time Warping (DTW) distance is exceptionally difficult to beat. This approach has one weakness, however; it is computationally too demanding for many realtime applications. One way to mitigate this problem is to speed up the DTW calculations. Nonetheless, there is a limit to how much this can help. In this work, we propose an additional technique, numerosity reduction, to speed up one-nearestneighbor DTW. While the idea of numerosity reduction for nearest-neighbor classifiers has a long history, we show here that we can leverage off an original observation about the relationship between dataset size and DTW constraints to produce an extremely compact dataset with little or no loss in accuracy. We test our ideas with a comprehensive set of experiments, and show that it can efficiently produce extremely fast accurate classifiers.

For many real world problems we must perform classification under widely varying amounts of computational resources. For example, if asked to classify an instance taken from a bursty stream, we may have from milliseconds to minutes to return a class prediction. For such problems an anytime algorithm may be especially useful.In this work we show how we can convert the ubiquitous nearest neighbor classifier into an anytime algorithm that can produce an instant classification, or if given the luxury of additional time, can utilize the extra time to increase classification accuracy. We demonstrate the utility of our approach with a comprehensive set of experiments on data from diverse domains.

Shape matching and indexing is important topic in its own right, and is a fundamental subroutine in most shape data mining algorithms. Given the ubiquity of shape, shape matching is an important problem with applications in domains as diverse as biometrics, industry, medicine, zoology and anthropology. The distance/similarity measure for used for shape matching must be invariant to many distortions, including scale, offset, noise, articulation, partial occlusion, etc. Most of these distortions are relatively easy to handle, either in the representation of the data or in the similarity measure used. However, rotation invariance is noted in the literature as being an especially difficult challenge. Current approaches typically try to achieve rotation invariance in the representation of the data, at the expense of discrimination ability, or in the distance measure, at the expense of efficiency. In this work, we show that we can take the slow but accurate approaches and dramatically speed them up. On real world problems our technique can take current approaches and make them four orders of magnitude faster, without false

Among the visual features of multimedia content, shape is of particular interest because humans can often recognize objects solely on the basis of shape. Over the past three decades, there has been a great deal of research on shape analysis, focusing mostly on shape indexing, clustering, and classification. In this work, we introduce the new problem of finding shape discords, the most unusual shapes in a collection. We motivate the problem by considering the utility of shape discords in diverse domains including zoology, anthropology, and medicine. While the brute force search algorithm has quadratic time complexity, we avoid this by using locality-sensitive hashing to estimate similarity between shapes which enables us to reorder the search more efficiently. An extensive experimental evaluation demonstrates that our approach can speed up computation by three to four orders of magnitude.

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ABSTRACT

The problem of efficiently finding images that are similar to a target image has attracted much attention in the image processing community and is rightly considered an information retrieval task. However, the problem of finding structure and regularities in large image datasets is an area in which data mining is beginning to make fundamental contributions. In this work, we consider the new problem of discovering shape motifs, which are approximately repeated shapes within (or between) image collections. As we shall show, shape motifs can have applications in tasks as diverse as anthropology, law enforcement, and historical manuscript mining. Brute force discovery of shape motifs could be untenably slow, especially as many domains may require an expensive rotation invariant distance measure. We introduce an algorithm that is two to three orders of magnitude faster than brute force search, and demonstrate the utility of our approach with several real world datasets from diverse domains.

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