The Variable Markov Oracle: Algorithms for Human Gesture Applications

This article introduces the Variable Markov Oracle (VMO) data structure for multivariate time series indexing. VMO can identify repetitive fragments and find sequential similarities between observations. VMO can also be viewed as a combination of online clustering algorithms with variable-order Markov constraints. The authors use VMO for gesture query-by-content and gesture following. A probabilistic interpretation of the VMO query-matching algorithm is proposed to find an analogy to the inference problem in a hidden Markov model (HMM). This probabilistic interpretation extends VMO to be not only a data structure but also a model for time series. Query-by-content experiments were conducted on a gesture database that was recorded using a Kinect 3D camera, showing state-of-the-art performance. The query-by-content experiments' results are compared to previous works using HMM and dynamic time warping. Gesture following is described in the context of an interactive dance environment that aims to integrate human movements with computer-generated graphics to create an augmented reality performance

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

Simultaneous Localization and Recognition of Dynamic Hand Gestures

A framework for the simultaneous localization and recognition of dynamic hand gestures is proposed. At the core of this framework is a dynamic space-time warping (DSTW) algorithm, that aligns a pair of query and model gestures in both space and time. For every frame of the query sequence, feature detectors generate multiple hand region candidates. Dynamic programming is then used to compute both a global matching cost, which is used to recognize the query gesture, and a warping path, which aligns the query and model sequences in time, and also finds the best hand candidate region in every query frame. The proposed framework includes translation invariant recognition of gestures, a desirable property for many HCI systems. The performance of the approach is evaluated on a dataset of hand signed digits gestured by people wearing short sleeve shirts, in front of a background containing other non-hand skin-colored objects. The algorithm simultaneously localizes the gesturing hand and recognizes the hand-signed digit. Although DSTW is illustrated in a gesture recognition setting, the proposed algorithm is a general method for matching time series, that allows for multiple candidate feature vectors to be extracted at each time step.National Science Foundation (CNS-0202067, IIS-0308213, IIS-0329009); Office of Naval Research (N00014-03-1-0108

Modeling Large Time Series for Efficient Approximate Query Processing

Evolving customer requirements and increasing competition force business organizations to store increasing amounts of data and query them for information at any given time. Due to the current growth of data volumes, timely extraction of relevant information becomes more and more difficult with traditional methods. In addition, contemporary Decision Support Systems (DSS) favor faster approximations over slower exact results. Generally speaking, processes that require exchange of data become inefficient when connection bandwidth does not increase as fast as the volume of data. In order to tackle these issues, compression techniques have been introduced in many areas of data processing. In this paper, we outline a new system that does not query complete datasets but instead utilizes models to extract the requested information. For time series data we use Fourier and Cosine transformations and piece-wise aggregation to derive the models. These models are initially created from the original data and are kept in the database along with it. Subsequent queries are answered using the stored models rather than scanning and processing the original datasets. In order to support model query processing, we maintain query statistics derived from experiments and when running the system. Our approach can also reduce communication load by exchanging models instead of data. To allow seamless integration of model-based querying into traditional data warehouses, we introduce a SQL compatible query terminology. Our experiments show that querying models is up to 80 % faster than querying over the raw data while retaining a high accuracy

Zoom-SVD: Fast and Memory Efficient Method for Extracting Key Patterns in an Arbitrary Time Range

Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many data mining applications including dimensionality reduction, principal component analysis, recommender systems, etc. Along with its static version, incremental SVD has been used to deal with multiple semi infinite time series data and to identify patterns of the data. However, existing SVD methods for the multiple time series data analysis do not provide functionality for detecting patterns of data in an arbitrary time range: standard SVD requires data for all intervals corresponding to a time range query, and incremental SVD does not consider an arbitrary time range. In this paper, we propose Zoom-SVD, a fast and memory efficient method for finding latent factors of time series data in an arbitrary time range. Zoom-SVD incrementally compresses multiple time series data block by block to reduce the space cost in storage phase, and efficiently computes singular value decomposition (SVD) for a given time range query in query phase by carefully stitching stored SVD results. Through extensive experiments, we demonstrate that Zoom-SVD is up to 15x faster, and requires 15x less space than existing methods. Our case study shows that Zoom-SVD is useful for capturing past time ranges whose patterns are similar to a query time range.Comment: 10 pages, 2018 ACM Conference on Information and Knowledge Management (CIKM 2018

Scalable Model-Based Management of Correlated Dimensional Time Series in ModelarDB+

To monitor critical infrastructure, high quality sensors sampled at a high frequency are increasingly used. However, as they produce huge amounts of data, only simple aggregates are stored. This removes outliers and fluctuations that could indicate problems. As a remedy, we present a model-based approach for managing time series with dimensions that exploits correlation in and among time series. Specifically, we propose compressing groups of correlated time series using an extensible set of model types within a user-defined error bound (possibly zero). We name this new category of model-based compression methods for time series Multi-Model Group Compression (MMGC). We present the first MMGC method GOLEMM and extend model types to compress time series groups. We propose primitives for users to effectively define groups for differently sized data sets, and based on these, an automated grouping method using only the time series dimensions. We propose algorithms for executing simple and multi-dimensional aggregate queries on models. Last, we implement our methods in the Time Series Management System (TSMS) ModelarDB (ModelarDB+). Our evaluation shows that compared to widely used formats, ModelarDB+ provides up to 13.7 times faster ingestion due to high compression, 113 times better compression due to the adaptivity of GOLEMM, 630 times faster aggregates by using models, and close to linear scalability. It is also extensible and supports online query processing.Comment: 12 Pages, 28 Figures, and 1 Tabl