KV-match: A Subsequence Matching Approach Supporting Normalization and Time Warping [Extended Version]

The volume of time series data has exploded due to the popularity of new applications, such as data center management and IoT. Subsequence matching is a fundamental task in mining time series data. All index-based approaches only consider raw subsequence matching (RSM) and do not support subsequence normalization. UCR Suite can deal with normalized subsequence match problem (NSM), but it needs to scan full time series. In this paper, we propose a novel problem, named constrained normalized subsequence matching problem (cNSM), which adds some constraints to NSM problem. The cNSM problem provides a knob to flexibly control the degree of offset shifting and amplitude scaling, which enables users to build the index to process the query. We propose a new index structure, KV-index, and the matching algorithm, KV-match. With a single index, our approach can support both RSM and cNSM problems under either ED or DTW distance. KV-index is a key-value structure, which can be easily implemented on local files or HBase tables. To support the query of arbitrary lengths, we extend KV-match to KV-match$_{DP}$, which utilizes multiple varied-length indexes to process the query. We conduct extensive experiments on synthetic and real-world datasets. The results verify the effectiveness and efficiency of our approach.Comment: 13 page

Approximating Dynamic Time Warping and Edit Distance for a Pair of Point Sequences

We give the first subquadratic-time approximation schemes for dynamic time warping (DTW) and edit distance (ED) of several natural families of point sequences in $\mathbb{R}^d$, for any fixed $d \ge 1$. In particular, our algorithms compute $(1+\varepsilon)$-approximations of DTW and ED in time near-linear for point sequences drawn from k-packed or k-bounded curves, and subquadratic for backbone sequences. Roughly speaking, a curve is $\kappa$-packed if the length of its intersection with any ball of radius $r$ is at most $\kappa \cdot r$, and a curve is $\kappa$-bounded if the sub-curve between two curve points does not go too far from the two points compared to the distance between the two points. In backbone sequences, consecutive points are spaced at approximately equal distances apart, and no two points lie very close together. Recent results suggest that a subquadratic algorithm for DTW or ED is unlikely for an arbitrary pair of point sequences even for $d=1$. Our algorithms work by constructing a small set of rectangular regions that cover the entries of the dynamic programming table commonly used for these distance measures. The weights of entries inside each rectangle are roughly the same, so we are able to use efficient procedures to approximately compute the cheapest paths through these rectangles

Real-time content-aware texturing for deformable surfaces

Animation of models often introduces distortions to their parameterisation, as these are typically optimised for a single frame. The net effect is that under deformation, the mapped features, i.e. UV texture maps, bump maps or displacement maps, may appear to stretch or scale in an undesirable way. Ideally, what we would like is for the appearance of such features to remain feasible given any underlying deformation. In this paper we introduce a real-time technique that reduces such distortions based on a distortion control (rigidity) map. In two versions of our proposed technique, the parameter space is warped in either an axis or a non-axis aligned manner based on the minimisation of a non-linear distortion metric. This in turn is solved using a highly optimised hybrid CPU-GPU strategy. The result is real-time dynamic content-aware texturing that reduces distortions in a controlled way. The technique can be applied to reduce distortions in a variety of scenarios, including reusing a low geometric complexity animated sequence with a multitude of detail maps, dynamic procedurally defined features mapped on deformable geometry and animation authoring previews on texture-mapped models. © 2013 ACM

A time series distance measure for efficient clustering of input output signals by their underlying dynamics

Starting from a dataset with input/output time series generated by multiple deterministic linear dynamical systems, this paper tackles the problem of automatically clustering these time series. We propose an extension to the so-called Martin cepstral distance, that allows to efficiently cluster these time series, and apply it to simulated electrical circuits data. Traditionally, two ways of handling the problem are used. The first class of methods employs a distance measure on time series (e.g. Euclidean, Dynamic Time Warping) and a clustering technique (e.g. k-means, k-medoids, hierarchical clustering) to find natural groups in the dataset. It is, however, often not clear whether these distance measures effectively take into account the specific temporal correlations in these time series. The second class of methods uses the input/output data to identify a dynamic system using an identification scheme, and then applies a model norm-based distance (e.g. H2, H-infinity) to find out which systems are similar. This, however, can be very time consuming for large amounts of long time series data. We show that the new distance measure presented in this paper performs as good as when every input/output pair is modelled explicitly, but remains computationally much less complex. The complexity of calculating this distance between two time series of length N is O(N logN).Comment: 6 pages, 4 figures, sent in for review to IEEE L-CSS (CDC 2017 option

Similarity searching in sequence databases under time warping.

Wong, Siu Fung.Thesis submitted in: December 2003.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 77-84).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgement --- p.viChapter 1 --- Introduction --- p.1Chapter 2 --- Preliminary --- p.6Chapter 2.1 --- Dynamic Time Warping (DTW) --- p.6Chapter 2.2 --- Spatial Indexing --- p.10Chapter 2.3 --- Relevance Feedback --- p.11Chapter 3 --- Literature Review --- p.13Chapter 3.1 --- Searching Sequences under Euclidean Metric --- p.13Chapter 3.2 --- Searching Sequences under Dynamic Time Warping Metric --- p.17Chapter 4 --- Subsequence Matching under Time Warping --- p.21Chapter 4.1 --- Subsequence Matching --- p.22Chapter 4.1.1 --- Sequential Search --- p.22Chapter 4.1.2 --- Indexing Scheme --- p.23Chapter 4.2 --- Lower Bound Technique --- p.25Chapter 4.2.1 --- Properties of Lower Bound Technique --- p.26Chapter 4.2.2 --- Existing Lower Bound Functions --- p.27Chapter 4.3 --- Point-Based indexing --- p.28Chapter 4.3.1 --- Lower Bound for subsequences matching --- p.28Chapter 4.3.2 --- Algorithm --- p.35Chapter 4.4 --- Rectangle-Based indexing --- p.37Chapter 4.4.1 --- Lower Bound for subsequences matching --- p.37Chapter 4.4.2 --- Algorithm --- p.41Chapter 4.5 --- Experimental Results --- p.43Chapter 4.5.1 --- Candidate ratio vs Width of warping window --- p.44Chapter 4.5.2 --- CPU time vs Number of subsequences --- p.45Chapter 4.5.3 --- CPU time vs Width of warping window --- p.46Chapter 4.5.4 --- CPU time vs Threshold --- p.46Chapter 4.6 --- Summary --- p.47Chapter 5 --- Relevance Feedback under Time Warping --- p.49Chapter 5.1 --- Integrating Relevance Feedback with DTW --- p.49Chapter 5.2 --- Query Reformulation --- p.53Chapter 5.2.1 --- Constraint Updating --- p.53Chapter 5.2.2 --- Weight Updating --- p.55Chapter 5.2.3 --- Overall Strategy --- p.58Chapter 5.3 --- Experiments and Evaluation --- p.59Chapter 5.3.1 --- Effectiveness of the strategy --- p.61Chapter 5.3.2 --- Efficiency of the strategy --- p.63Chapter 5.3.3 --- Usability --- p.64Chapter 5.4 --- Summary --- p.71Chapter 6 --- Conclusion --- p.72Chapter A --- Deduction of Data Bounding Hyper-rectangle --- p.74Chapter B --- Proof of Theorem2 --- p.76Bibliography --- p.77Publications --- p.8