The problem of indexing time series has attracted much research interest in the database community. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However is has been forcefully shown that the Euclidean distance is a very brittle distance measure. Dynamic Time Warping (DTW) is a much more robust distance measure for time series, allowing similar shapes to match even if they are out of phase in the time axis.

1 Introduction Principled methods for estimating unobserved time-points,clustering, and aligning microarray gene expression timeseries are needed to make such data useful for detailed anal-ysis. Datasets measuring temporal behavior of thousands of genes offer rich opportunities for computational biologists. For example, Dynamic Bayesian Networks may be usedto build models and try to understand how genetic responses unfold. However, such modeling frameworks need a suf-ficient quantity of data in the appropriate format. Current gene expression time-series data often do not meet these re-quirements, since they may be missing data points, sampled non-uniformly, and measure biological processes that exhibittemporal variation.

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.

We present algorithms for time-series gene expression analysis that permit the principled estimation of unobserved time points, clustering, and dataset alignment. Each expression pro# le is modeled as a cubic spline (piecewise polynomial) that is estimated from the observed data and every time point in# uences the overall smooth expression curve. We constrain the spline coef# cients of genes in the same class to have similar expression patterns, while also allowing for gene speci# c parameters. We show that unobserved time points can be reconstructed using our method with 10--15% less error when compared to previous best methods. Our clustering algorithm operates directly on the continuous representations of gene expression pro# les, and we demonstrate that this is particularly effective when applied to nonuniformly sampled data. Our continuous alignment algorithm also avoids dif# culties encountered by discrete approaches. In particular, our method allows for control of the number of degrees of freedom of the warp through the speci# cation of parameterized functions, which helps to avoid over# tting. We demonstrate that our algorithm produces stable low-error alignments on real expression data and further show a speci# c application to yeast knock-out data that produces biologically meaningful results.

Vladimir Filkov Steven Skiena Jizu Zhi Dept. of Computer Science and Center for Biotechnology State University of New York Stony Brook, NY 11794-4400 fvl lkov|skiena|zjizug@cs.sunysb.edu September 27, 2000 1

Data-driven animation has become the industry standard for computer games and many animated movies and special effects. In particular, motion capture data recorded from live actors, is the most promising approach offered thus far for animating realistic human characters. However, the manipulation of such data for general use and re-use is not yet a solved problem. Many of the existing techniques dealing with editing motion rely on indexing for annotation, segmentation, and re-ordering of the data. Euclidean distance is inappropriate for solving these indexing problems because of the inherent variability found in human motion. The limitations of Euclidean distance stems from the fact that it is very sensitive to distortions in the time axis. A partial solution to this problem, Dynamic Time Warping (DTW), aligns the time axis

Time series are a ubiquitous form of data occurring in virtually every scientific discipline and business application. There has been much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time series [7]. Debregeas and Hebrail [8]

The Dynamic Time Warping (DTW) distance measure is a technique that has long been known in speech recognition community. It allows a non-linear mapping of one signal to another by minimizing the distance between the two. A decade ago, DTW was introduced into Data Mining community as a utility for various tasks for time series problems including classification, clustering, and anomaly detection. The technique has flourished, particularly in the last three years, and has been applied to a variety of problems in various disciplines. In spite of DTW’s great success, there are still several persistent “myths ” about it. These myths have caused confusion and led to much wasted research effort. In this work, we will dispel these myths with the most comprehensive set of time series experiments ever conducted.

Last year at OOPSLA we presented a methodology, vertical profiling, for understanding the performance of objectoriented programs. The key insight behind this methodology is that modern programs run on top of many layers (virtual machine, middleware, etc) and thus we need to collect and combine information from all layers in order to understand system performance. Although our methodology was able to explain previously unexplained performance phenomena, it was extremely labor intensive. In this paper we describe and evaluate techniques for automating two significant activities of vertical profiling: trace alignment and correlation. Trace alignment aligns traces obtained from separate runs so that one can reason across the traces. We are not aware of any prior approach that effectively and automatically aligns traces. Correlation sifts through hundreds of metrics to find ones that have a bearing on a performance anomaly of interest. In prior work we found that statistical correlation was only sometimes effective. We have identified highly-effective approaches for both activities. For aligning traces we explore dynamic time warping, and for correlation we explore eight correlators based on statistical correlation, distance measures, and piecewise linear segmentation. Although we explore these activities in the context of vertical profiling, both activities are widely applicable in the performance analysis area.

This paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we do not consider the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of geodesic paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and contour deformations.