Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Fast subsequence matching in time-series databases
SIGMOD '94 Proceedings of the 1994 ACM SIGMOD international conference on Management of data
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Efficiently supporting ad hoc queries in large datasets of time sequences
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
Dimensionality reduction for similarity searching in dynamic databases
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Multidimensional access methods
ACM Computing Surveys (CSUR)
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A comparison of DFT and DWT based similarity search in time-series databases
Proceedings of the ninth international conference on Information and knowledge management
Locally adaptive dimensionality reduction for indexing large time series databases
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Time series similarity measures and time series indexing (abstract only)
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Efficient Indexing of Spatiotemporal Objects
EDBT '02 Proceedings of the 8th International Conference on Extending Database Technology: Advances in Database Technology
Approximate Queries and Representations for Large Data Sequences
ICDE '96 Proceedings of the Twelfth International Conference on Data Engineering
Variable Length Queries for Time Series Data
Proceedings of the 17th International Conference on Data Engineering
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Fast Time Sequence Indexing for Arbitrary Lp Norms
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Local Dimensionality Reduction: A New Approach to Indexing High Dimensional Spaces
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Fast Similarity Search in the Presence of Noise, Scaling, and Translation in Time-Series Databases
VLDB '95 Proceedings of the 21th International Conference on Very Large Data Bases
Moving Objects Databases: Issues and Solutions
SSDBM '98 Proceedings of the 10th International Conference on Scientific and Statistical Database Management
Efficient Time Series Matching by Wavelets
ICDE '99 Proceedings of the 15th International Conference on Data Engineering
Landmarks: A New Model for Similarity-Based Pattern Querying in Time Series Databases
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
Similarity Search Over Time-Series Data Using Wavelets
ICDE '02 Proceedings of the 18th International Conference on Data Engineering
Indexing of Moving Objects for Location-Based Services
ICDE '02 Proceedings of the 18th International Conference on Data Engineering
Discovering Similar Multidimensional Trajectories
ICDE '02 Proceedings of the 18th International Conference on Data Engineering
Symbolic representation and retrieval of moving object trajectories
Proceedings of the 6th ACM SIGMM international workshop on Multimedia information retrieval
Robust and fast similarity search for moving object trajectories
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
Shapes based trajectory queries for moving objects
Proceedings of the 13th annual ACM international workshop on Geographic information systems
Event-based multimedia chronicling systems
CARPE '05 Proceedings of the 2nd ACM workshop on Continuous archival and retrieval of personal experiences
Proceedings of the third ACM international workshop on Video surveillance & sensor networks
Wavelet synopses for general error metrics
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2004
A Bit Level Representation for Time Series Data Mining with Shape Based Similarity
Data Mining and Knowledge Discovery
An efficient k nearest neighbor search for multivariate time series
Information and Computation
Indexing Spatio-Temporal Trajectories with Efficient Polynomial Approximations
IEEE Transactions on Knowledge and Data Engineering
Indexable PLA for efficient similarity search
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Efficient Similarity Search over Future Stream Time Series
IEEE Transactions on Knowledge and Data Engineering
iSAX: indexing and mining terabyte sized time series
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
On efficiently searching trajectories and archival data for historical similarities
Proceedings of the VLDB Endowment
Proceedings of the VLDB Endowment
Information Sciences: an International Journal
Periodic Pattern Analysis in Time Series Databases
DASFAA '09 Proceedings of the 14th International Conference on Database Systems for Advanced Applications
iSAX: disk-aware mining and indexing of massive time series datasets
Data Mining and Knowledge Discovery
Efficient processing of probabilistic reverse nearest neighbor queries over uncertain data
The VLDB Journal — The International Journal on Very Large Data Bases
Efficient anomaly monitoring over moving object trajectory streams
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
A time series representation model for accurate and fast similarity detection
Pattern Recognition
Time series analysis with multiple resolutions
Information Systems
Exploring movement-similarity analysis of moving objects
SIGSPATIAL Special
On-line discovery of flock patterns in spatio-temporal data
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Optimal distance bounds for fast search on compressed time-series query logs
ACM Transactions on the Web (TWEB)
Querying trajectories using flexible patterns
Proceedings of the 13th International Conference on Extending Database Technology
PAKDD'07 Proceedings of the 2007 international conference on Emerging technologies in knowledge discovery and data mining
Interval-focused similarity search in time series databases
DASFAA'07 Proceedings of the 12th international conference on Database systems for advanced applications
Approximate clustering of time series using compact model-based descriptions
DASFAA'08 Proceedings of the 13th international conference on Database systems for advanced applications
Searching trajectories by locations: an efficiency study
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Multi-resolution approach to time series retrieval
Proceedings of the Fourteenth International Database Engineering & Applications Symposium
Fast Discovery of Group Lag Correlations in Streams
ACM Transactions on Knowledge Discovery from Data (TKDD)
Top-k queries on temporal data
The VLDB Journal — The International Journal on Very Large Data Bases
Efficient algorithm for a novel pattern of time series
Expert Systems with Applications: An International Journal
An efficient approach for human motion data mining based on curves matching
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part I
TIDES--a new descriptor for time series oscillation behavior
Geoinformatica
Fast retrieval of time series using a multi-resolution filter with multiple reduced spaces
ADMA'10 Proceedings of the 6th international conference on Advanced data mining and applications: Part I
Synopses for probabilistic data over large domains
Proceedings of the 14th International Conference on Extending Database Technology
Voronoi-based range query for trajectory data in spatial networks
Proceedings of the 2011 ACM Symposium on Applied Computing
Scalable kNN search on vertically stored time series
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Quality of similarity rankings in time series
SSTD'11 Proceedings of the 12th international conference on Advances in spatial and temporal databases
Motion trajectory clustering for video retrieval using spatio-temporal approximations
VISUAL'05 Proceedings of the 8th international conference on Visual Information and Information Systems
Similarity search with implicit object features
WAIM'05 Proceedings of the 6th international conference on Advances in Web-Age Information Management
Similarity search on time series based on threshold queries
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
TQuEST: threshold query execution for large sets of time series
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
NNCluster: an efficient clustering algorithm for road network trajectories
DASFAA'10 Proceedings of the 15th international conference on Database Systems for Advanced Applications - Volume Part II
PA-tree: a parametric indexing scheme for spatio-temporal trajectories
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
Visually exploring movement data via similarity-based analysis
Journal of Intelligent Information Systems
Searching similar trajectories in real time: an effectiveness and efficiency study
WAIM'11 Proceedings of the 2011 international conference on Web-Age Information Management
User oriented trajectory search for trip recommendation
Proceedings of the 15th International Conference on Extending Database Technology
SFA: a symbolic fourier approximation and index for similarity search in high dimensional datasets
Proceedings of the 15th International Conference on Extending Database Technology
Parsimonious temporal aggregation
The VLDB Journal — The International Journal on Very Large Data Bases
Proceedings of the 16th International Database Engineering & Applications Sysmposium
ACM Computing Surveys (CSUR)
Genetic algorithms-based symbolic aggregate approximation
DaWaK'12 Proceedings of the 14th international conference on Data Warehousing and Knowledge Discovery
Experimental comparison of representation methods and distance measures for time series data
Data Mining and Knowledge Discovery
A representation of time series based on implicit polynomial curve
Pattern Recognition Letters
Calibrating trajectory data for similarity-based analysis
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Mobile Networks and Applications
A data-adaptive and dynamic segmentation index for whole matching on time series
Proceedings of the VLDB Endowment
Mining trajectories of moving dynamic spatio-temporal regions in sensor datasets
Data Mining and Knowledge Discovery
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In this paper, we attempt to approximate and index a d- dimensional (d ≥ 1) spatio-temporal trajectory with a low order continuous polynomial. There are many possible ways to choose the polynomial, including (continuous)Fourier transforms, splines, non-linear regressino, etc. Some of these possiblities have indeed been studied beofre. We hypothesize that one of the best possibilities is the polynomial that minimizes the maximum deviation from the true value, which is called the minimax polynomial. Minimax approximation is particularly meaningful for indexing because in a branch-and-bound search (i.e., for finding nearest neighbours), the smaller the maximum deviation, the more pruning opportunities there exist. However, in general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute. However, it has been shown thta the Chebyshev approximation is almost identical to the optimal minimax polynomial, and is easy to compute [16]. Thus, in this paper, we explore how to use the Chebyshev polynomials as a basis for approximating and indexing d-dimenstional trajectories.The key analytic result of this paper is the Lower Bounding Lemma. that is, we show that the Euclidean distance between two d-dimensional trajectories is lower bounded by the weighted Euclidean distance between the two vectors of Chebyshev coefficients. this lemma is not trivial to show, and it ensures that indexing with Chebyshev cofficients aedmits no false negatives. To complement that analystic result, we conducted comprehensive experimental evaluation with real and generated 1-dimensional to 4-dimensional data sets. We compared the proposed schem with the Adaptive Piecewise Constant Approximation (APCA) scheme. Our preliminary results indicate that in all situations we tested, Chebyshev indexing dominates APCA in pruning power, I/O and CPU costs.