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The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
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Locally adaptive dimensionality reduction for indexing large time series databases
ACM Transactions on Database Systems (TODS)
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hand Recognition Using Implicit Polynomials and Geometric Features
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Efficient Time Series Matching by Wavelets
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Boundary Estimation from Intensity/Color Images with Algebraic Curve Models
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 1
Discovering Similar Multidimensional Trajectories
ICDE '02 Proceedings of the 18th International Conference on Data Engineering
Indexing spatio-temporal trajectories with Chebyshev polynomials
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Technique for Finding the Symmetry Axes of Implicit Polynomial Curves under Perspective Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact indexing of dynamic time warping
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Robust and fast similarity search for moving object trajectories
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
An efficient and accurate method for evaluating time series similarity
Proceedings of the 2007 ACM SIGMOD international conference on Management of data
Experiencing SAX: a novel symbolic representation of time series
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VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Indexable PLA for efficient similarity search
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Implicit Invariants and Object Recognition
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Representing financial time series based on data point importance
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Rotations, translations and symmetry detection for complexified curves
Computer Aided Geometric Design
A time series representation model for accurate and fast similarity detection
Pattern Recognition
Image based visual servoing using algebraic curves applied to shape alignment
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
A review on time series data mining
Engineering Applications of Artificial Intelligence
Similarity search on time series based on threshold queries
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
Improving the stability of algebraic curves for applications
IEEE Transactions on Image Processing
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Implicit polynomial (IP) curve is applied to represent data set boundary in image processing and computer vision. In this work, we employed it to reduce dimensionality of time series and produce similarity measure for time series mining. To use IP curve, time series was transformed to star coordination series. Then the star coordination series was fitted by implicit polynomial curve. That is, IP curve approximated (IPA) time series. Lastly, similarity measure of the time series was produced from the fitting implicit polynomial curve. To guarantee no false negatives, the lower bounding lemma for the similarity measure based on IP curve (IPD) was proved. We extensively compared IPA with other similarity measure and dimension reduction techniques in classification frameworks. Experimental results from the tests on various datasets indicate that IPA is more efficient than other methods.