Ten lectures on wavelets
Fast multiresolution image querying
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Wavelet-based histograms for selectivity estimation
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Locally adaptive dimensionality reduction for indexing large time series databases
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Locally adaptive dimensionality reduction for indexing large time series databases
ACM Transactions on Database Systems (TODS)
Approximate Query Processing Using Wavelets
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Dynamic Maintenance of Wavelet-Based Histograms
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Surfing Wavelets on Streams: One-Pass Summaries for Approximate Aggregate Queries
Proceedings of the 27th International Conference on Very Large Data Bases
Histogramming Data Streams with Fast Per-Item Processing
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Extended wavelets for multiple measures
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
Probabilistic wavelet synopses
ACM Transactions on Database Systems (TODS)
Deterministic wavelet thresholding for maximum-error metrics
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Space efficiency in synopsis construction algorithms
VLDB '05 Proceedings of the 31st international conference on Very large data bases
One-pass wavelet synopses for maximum-error metrics
VLDB '05 Proceedings of the 31st international conference on Very large data bases
XWAVE: optimal and approximate extended wavelets
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Optimal workload-based weighted wavelet synopses
ICDT'05 Proceedings of the 10th international conference on Database Theory
Space efficiency in synopsis construction algorithms
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Approximation algorithms for wavelet transform coding of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Suppressing model overfitting in mining concept-drifting data streams
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Efficient range-constrained similarity search on wavelet synopses over multiple streams
CIKM '06 Proceedings of the 15th ACM international conference on Information and knowledge management
Exploiting duality in summarization with deterministic guarantees
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Efficient Process of Top-k Range-Sum Queries over Multiple Streams with Minimized Global Error
IEEE Transactions on Knowledge and Data Engineering
The VLDB Journal — The International Journal on Very Large Data Bases
Proceedings of the VLDB Endowment
PROUD: a probabilistic approach to processing similarity queries over uncertain data streams
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Unrestricted wavelet synopses under maximum error bound
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
On Multidimensional Wavelet Synopses for Maximum Error Bounds
DASFAA '09 Proceedings of the 14th International Conference on Database Systems for Advanced Applications
Hierarchically compressed wavelet synopses
The VLDB Journal — The International Journal on Very Large Data Bases
AMID: Approximation of MultI-measured Data using SVD
Information Sciences: an International Journal
Learning from Data Streams: Synopsis and Change Detection
Proceedings of the 2008 conference on STAIRS 2008: Proceedings of the Fourth Starting AI Researchers' Symposium
Building data synopses within a known maximum error bound
APWeb/WAIM'07 Proceedings of the joint 9th Asia-Pacific web and 8th international conference on web-age information management conference on Advances in data and web management
Synopses for probabilistic data over large domains
Proceedings of the 14th International Conference on Extending Database Technology
Building wavelet histograms on large data in MapReduce
Proceedings of the VLDB Endowment
Fast approximate wavelet tracking on streams
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
Subquadratic algorithms for workload-aware haar wavelet synopses
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Constructing optimal wavelet synopses
EDBT'06 Proceedings of the 2006 international conference on Current Trends in Database Technology
Monitoring incremental histogram distribution for change detection in data streams
Sensor-KDD'08 Proceedings of the Second international conference on Knowledge Discovery from Sensor Data
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches
Foundations and Trends in Databases
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We consider the wavelet synopsis construction problem for data streams where given n numbers we wish to estimate the data by constructing a synopsis, whose size, say B is much smaller than n. The B numbers are chosen to minimize a suitable error between the original data and the estimate derived from the synopsis.Several good one-pass wavelet construction streaming algorithms minimizing the l2 error exist. For other error measures, the problem is less understood. We provide the first one-pass small space streaming algorithms with provable error guarantees (additive approximation) for minimizing a variety of non-Euclidean error measures including all weighted lp (including l∞) and relative error lp metrics.In several previous works solutions (for weighted l2, l∞ and maximum relative error) where the B synopsis coefficients are restricted to be wavelet coefficients of the data were proposed. This restriction yields suboptimal solutions on even fairly simple examples. Other lines of research, such as probabilistic synopsis, imposed restrictions on how the synopsis was arrived at. To the best of our knowledge this paper is the first paper to address the general problem, without any restriction on how the synopsis is arrived at, as well as provide the first streaming algorithms with guaranteed performance for these classes of error measures.