Wavelet decomposition of data streams. by Dragana Veljkovic
|
|
- Jocelyn Gordon
- 6 years ago
- Views:
Transcription
1 Wavelet decomposition of data streams by Dragana Veljkovic
2 Motivation Continuous data streams arise naturally in: telecommunication and internet traffic retail and banking transactions web server log records etc. Many applications need this data to be processed on a 24*7 basis in only one pass
3 Motivation cont. Usually this data is accumulated and archived for later use, but not always (e.g. network security) The ability to make decisions and interpret interesting patterns online can be crucial and has real dollar value for large corporations (e.g. fraud detection)
4 Our motivation Currently working on data collected from 100 electrodes receiving electrical potential of monkey brain over long periods of time We want to look at this data in real time and seek patterns, trends and surprises
5 Outline Background streams wavelets sketches error analysis Results Implementation details Strengths and weaknesses of this approach
6 Data streams Sequence of unbounded, real time data with high rate that can only be read once by an application Problems: Unbounded memory requirements High data rate
7 Underlying signal Signal is one dimensional function a: [0,, N-1]? Z + Data item that arrives in time is an ordered pair: <domain, value> Example: voting results <Texas, 60> Example: phone call records < , 12>
8 Data model Two different data models used for rendering the underlying signal: Cash register Aggregate Example: cash register model < ,10>, < ,13>, < , 20>, < , 5>, < , 2>, < , 30> where the underlying signal is < , 32>, < , 13>, < , 35>
9 Stream format Two distinct formats for the stream Ordered Unordered Example: Aggregate ordered stream any time series Example: Unordered cash-register stream phone call records Ordered cash-register is trivial to convert to order aggregate
10 Wavelets Basis functions of limited duration and average value of zero Basis functions are shifted and scaled versions of the original wavelet
11 Discrete wavelet transform Uses only fixed values for wavelet scales based on powers of two Wavelet positions are also fixed and non overlapping Wavelets form a set of wavelet basis vectors of length N Haar wavelets for signal of size 8 Example: Haar wavelets on signal of length N = 8 j = 1,, logn levels k = 0,, 2 j -1 spaces for each level
12 Wavelet decomposition Wavelet decomposition can be regarded as projection of the signal on the set of wavelet basis vectors Each wavelet coefficient can be computed as the dot product of the signal with the corresponding basis vector Example: Table 1. from Gilbert et al
13 Best B-term decomposition The signal can be fully recovered from the wavelet decomposition Best B-term decomposition uses only a small number of coefficients, B, that carry the highest energy The signal reconstructed using the B-term coefficients and the corresponding vectors is called the best B-term approximation Most signals that occur in nature can be well approximated using only a small number of coefficients (5-10).
14 Computing best B-term decomposition in runtime For the ordered aggregate model Maintain two sets of items Highest B wavelet basis coefficients for the signal seen so far logn straddling coefficients, one for each level When the data item is read the affected straddling coefficients get updated. If a coefficient is no longer straddling it is compared to existing highest B coefficient and the set is updated if necessary. New straddling coefficient is initialized. Takes O(B + logn) storage and time for the ordered aggregate model
15 Sketches Sketch is made by projecting a signal onto several different low dimensional spaces which are chosen at random Many properties of the signal, such as histograms, can be accurately estimated by looking at the sketch
16 Definition of a sketch Atomic sketch of signal a is the dot product <a, r> where r is a random vector of ±1 valued random variables A sketch of a signal is k independent atomic sketches, each with a different random vector r j Sketch size is small compared to the signal size
17 Sketches Maintaining the sketch is easy as we are receiving the data If element <i, a(i)> arrives, add a(i)*r ij to the sketch corresponding to random vector r j Example: In cash-register receive <5, 10>, need to add 10* r 5j to each atomic sketch corresponding to the random vector r j
18 Error metrics SSE (sum squared error) if R is a representation of the signal a then SSE is defined as Pseudoenergy of the representation R is computed as
19 Query processing Batched queries are posed at certain periodic intervals Ad hoc a query may be posed at any time
20 Batch query using best B-term approximation for day 0 of call records Figure 2. from Gilbert et al
21 Batch query using best B-term approximation for all 7 days of call records Figure 3. from Gilbert et al
22 Estimating a point query Answer to point query i is a(i) Direct point estimate directly estimating a(i) using the sketch Direct wavelet estimate use the sketch to estimate the wavelet coefficients whose support intersects i and reconstruct a(i) using these coefficients Another way is to compute a(i) using only the high wavelet coefficients (like the known B-term approximation) whose support intersects a(i)
23 Using sketches to estimate dot product Following parameters characterize how well the sketch does e distortion parameter d failure probability? failure threshold Sketch of a signal is independent atomic sketches, each with a different random vector If the cosine between vectors a and b is greater than? we estimate the dot product within (1±e) with probability at least 1- d
24 Sketches and random vectors If element <i, a(i)> arrives, add a(i)*r ij to the sketch corresponding to random vector r j In order to use the sketches we need to get the elements r j quickly. r j is of size N, it can not be stored explicitly
25 Generating random vectors The paper shows that r ij can be generated by a pseudorandom number generator using a seed s j of size log O(1) N Generator G is based on second order Reed-Muller codes The generator G takes s j and i and outputs r j i = G(s j, i) quickly
26 Estimation of dot products using sketches Lemma: Let X be a O(logN/ d)-wise median of e 2 )-wise means of independent copies of O(1/ then we have with probability of 1-1 d Note: : use b=a to estimate energy of a using this lemma
27 Example: Want to estimate dot product of vectors a and b with no more than 30% error with probability of 80%, assuming the cosine between these two vectors is greater then 0.25 That is e = 0.3,? = 0.25 and d = 0.2 and for a signal of size N=1024 we would need about 30 atomic sketches
28 Theorem There is a streaming algorithm, A, such that, given a signal a[1,, N] with energy a 22 if there is a B-term representation with energy at least?* a 22, then, with probability at least (1-d) A finds a representation of at most B terms with pseudoenergy at least (1-e)?* a 22. If there is no such B-term representation with energy?* a 22, A reports no good representation. In any case A uses space and per item time while processing the stream. This holds with both aggregate and cash-register models Example: take?=0.3, d=0.2, e=0.3 and B=10. Then if there exists a 10 terms representation of the signal that captures at least 30% of the signal s energy the algorithm will output a 10 term representation with energy at least 21% of the signal with 80% probability
29 Strengths and weaknesses Good example how to work with cashregister models Shows several ways to estimate the signal using a sketch Time requirements seem higher than the paper claims On-line algorithms do not seem as promising as batch algorithms
30 References 1. A. C. Gilbert, Y. Kotidis, S. Muthukrishnan and M. J. Strauss, "Onepass wavelet decomposition of data streams," IEEE transactions on knowledge and data engineering, Vol. 15, No. 3, May/June A. C. Gilbert, Y. Kotidis, S. Muthukrishnan and M. J. Strauss, "Surfing wavelets on streams: one-pass summaries for approximate aggregate queries," Proceedings of the 27th VLDB Conference, Roma, Italy A. C. Gilbert, S. Guha, P. Indyk, Y. Kotidis, S. Muthukrishnan and M. J. Strauss, "Fast, small-space algorithms for approximate histogram maintenance," STOC 02, May 19-21, 2002, Montreal, Quebec, Canada.
31 Answering queries on-line Comparison of sse/energy of top B wavelets against direct estimates Table 1. from Gilbert et al Table 2. from Gilbert et al
32 Direct estimates for the top 10 heavy hitters Figure 6. from Gilbert et al
33 Direct estimates for the top 10 heavy hitters using the greedy algorithm Figure 7. from Gilbert et al
34 Adaptive greedy pursuit for heavy hitters Obtain a very accurate estimate for the first heavy hitter Get a new sketch by subtracting this value from the original sketch. This can be done because sketches are linear New sketch is a good estimation of the residual distribution in which the second heavy hitter is the peak value Use the new sketch to estimate the second heavy hitter Repeat procedure for more heavy hitters Each estimate introduces an error and after many iterations the errors tend to overwhelm the benefits
B669 Sublinear Algorithms for Big Data
B669 Sublinear Algorithms for Big Data Qin Zhang 1-1 2-1 Part 1: Sublinear in Space The model and challenge The data stream model (Alon, Matias and Szegedy 1996) a n a 2 a 1 RAM CPU Why hard? Cannot store
More informationLinear Sketches A Useful Tool in Streaming and Compressive Sensing
Linear Sketches A Useful Tool in Streaming and Compressive Sensing Qin Zhang 1-1 Linear sketch Random linear projection M : R n R k that preserves properties of any v R n with high prob. where k n. M =
More informationSparse analysis Lecture VII: Combining geometry and combinatorics, sparse matrices for sparse signal recovery
Sparse analysis Lecture VII: Combining geometry and combinatorics, sparse matrices for sparse signal recovery Anna C. Gilbert Department of Mathematics University of Michigan Sparse signal recovery measurements:
More informationCombining geometry and combinatorics
Combining geometry and combinatorics A unified approach to sparse signal recovery Anna C. Gilbert University of Michigan joint work with R. Berinde (MIT), P. Indyk (MIT), H. Karloff (AT&T), M. Strauss
More informationExplicit Constructions for Compressed Sensing of Sparse Signals
Explicit Constructions for Compressed Sensing of Sparse Signals Piotr Indyk MIT July 12, 2007 1 Introduction Over the recent years, a new approach for obtaining a succinct approximate representation of
More informationSparse analysis Lecture V: From Sparse Approximation to Sparse Signal Recovery
Sparse analysis Lecture V: From Sparse Approximation to Sparse Signal Recovery Anna C. Gilbert Department of Mathematics University of Michigan Connection between... Sparse Approximation and Compressed
More informationA Pass-Efficient Algorithm for Clustering Census Data
A Pass-Efficient Algorithm for Clustering Census Data Kevin Chang Yale University Ravi Kannan Yale University Abstract We present a number of streaming algorithms for a basic clustering problem for massive
More informationSample Optimal Fourier Sampling in Any Constant Dimension
1 / 26 Sample Optimal Fourier Sampling in Any Constant Dimension Piotr Indyk Michael Kapralov MIT IBM Watson October 21, 2014 Fourier Transform and Sparsity Discrete Fourier Transform Given x C n, compute
More informationMaintaining Significant Stream Statistics over Sliding Windows
Maintaining Significant Stream Statistics over Sliding Windows L.K. Lee H.F. Ting Abstract In this paper, we introduce the Significant One Counting problem. Let ε and θ be respectively some user-specified
More informationHeavy Hitters. Piotr Indyk MIT. Lecture 4
Heavy Hitters Piotr Indyk MIT Last Few Lectures Recap (last few lectures) Update a vector x Maintain a linear sketch Can compute L p norm of x (in zillion different ways) Questions: Can we do anything
More informationEstimating Dominance Norms of Multiple Data Streams Graham Cormode Joint work with S. Muthukrishnan
Estimating Dominance Norms of Multiple Data Streams Graham Cormode graham@dimacs.rutgers.edu Joint work with S. Muthukrishnan Data Stream Phenomenon Data is being produced faster than our ability to process
More informationWhat s New: Finding Significant Differences in Network Data Streams
What s New: Finding Significant Differences in Network Data Streams Graham Cormode S. Muthukrishnan Abstract Monitoring and analyzing network traffic usage patterns is vital for managing IP Networks. An
More informationEstimating Dominance Norms of Multiple Data Streams
Estimating Dominance Norms of Multiple Data Streams Graham Cormode and S. Muthukrishnan Abstract. There is much focus in the algorithms and database communities on designing tools to manage and mine data
More informationA Deterministic Algorithm for Summarizing Asynchronous Streams over a Sliding Window
A Deterministic Algorithm for Summarizing Asynchronous Streams over a Sliding Window Costas Busch 1 and Srikanta Tirthapura 2 1 Department of Computer Science Rensselaer Polytechnic Institute, Troy, NY
More informationA Simpler and More Efficient Deterministic Scheme for Finding Frequent Items over Sliding Windows
A Simpler and More Efficient Deterministic Scheme for Finding Frequent Items over Sliding Windows ABSTRACT L.K. Lee Department of Computer Science The University of Hong Kong Pokfulam, Hong Kong lklee@cs.hku.hk
More informationThe Count-Min-Sketch and its Applications
The Count-Min-Sketch and its Applications Jannik Sundermeier Abstract In this thesis, we want to reveal how to get rid of a huge amount of data which is at least dicult or even impossible to store in local
More informationData Stream Methods. Graham Cormode S. Muthukrishnan
Data Stream Methods Graham Cormode graham@dimacs.rutgers.edu S. Muthukrishnan muthu@cs.rutgers.edu Plan of attack Frequent Items / Heavy Hitters Counting Distinct Elements Clustering items in Streams Motivating
More informationBlock Heavy Hitters Alexandr Andoni, Khanh Do Ba, and Piotr Indyk
Computer Science and Artificial Intelligence Laboratory Technical Report -CSAIL-TR-2008-024 May 2, 2008 Block Heavy Hitters Alexandr Andoni, Khanh Do Ba, and Piotr Indyk massachusetts institute of technology,
More informationData Streams & Communication Complexity
Data Streams & Communication Complexity Lecture 1: Simple Stream Statistics in Small Space Andrew McGregor, UMass Amherst 1/25 Data Stream Model Stream: m elements from universe of size n, e.g., x 1, x
More informationAn Optimal Algorithm for l 1 -Heavy Hitters in Insertion Streams and Related Problems
An Optimal Algorithm for l 1 -Heavy Hitters in Insertion Streams and Related Problems Arnab Bhattacharyya, Palash Dey, and David P. Woodruff Indian Institute of Science, Bangalore {arnabb,palash}@csa.iisc.ernet.in
More informationAn Introduction to Sparse Approximation
An Introduction to Sparse Approximation Anna C. Gilbert Department of Mathematics University of Michigan Basic image/signal/data compression: transform coding Approximate signals sparsely Compress images,
More informationSparse analysis Lecture III: Dictionary geometry and greedy algorithms
Sparse analysis Lecture III: Dictionary geometry and greedy algorithms Anna C. Gilbert Department of Mathematics University of Michigan Intuition from ONB Key step in algorithm: r, ϕ j = x c i ϕ i, ϕ j
More informationEfficient Sketches for Earth-Mover Distance, with Applications
Efficient Sketches for Earth-Mover Distance, with Applications Alexandr Andoni MIT andoni@mit.edu Khanh Do Ba MIT doba@mit.edu Piotr Indyk MIT indyk@mit.edu David Woodruff IBM Almaden dpwoodru@us.ibm.com
More informationTwo applications of max stable distributions: Random sketches and Heavy tail exponent estimation
Two applications of max stable distributions: Random sketches and Heavy tail exponent estimation Stilian Stoev (sstoev@umich.edu) Department of Statistics University of Michigan Boston University Probability
More information15-451/651: Design & Analysis of Algorithms September 13, 2018 Lecture #6: Streaming Algorithms last changed: August 30, 2018
15-451/651: Design & Analysis of Algorithms September 13, 2018 Lecture #6: Streaming Algorithms last changed: August 30, 2018 Today we ll talk about a topic that is both very old (as far as computer science
More informationSparse Fourier Transform (lecture 1)
1 / 73 Sparse Fourier Transform (lecture 1) Michael Kapralov 1 1 IBM Watson EPFL St. Petersburg CS Club November 2015 2 / 73 Given x C n, compute the Discrete Fourier Transform (DFT) of x: x i = 1 x n
More informationSparse Fourier Transform (lecture 4)
1 / 5 Sparse Fourier Transform (lecture 4) Michael Kapralov 1 1 IBM Watson EPFL St. Petersburg CS Club November 215 2 / 5 Given x C n, compute the Discrete Fourier Transform of x: x i = 1 n x j ω ij, j
More informationLecture 1: Introduction to Sublinear Algorithms
CSE 522: Sublinear (and Streaming) Algorithms Spring 2014 Lecture 1: Introduction to Sublinear Algorithms March 31, 2014 Lecturer: Paul Beame Scribe: Paul Beame Too much data, too little time, space for
More informationEstimating Frequencies and Finding Heavy Hitters Jonas Nicolai Hovmand, Morten Houmøller Nygaard,
Estimating Frequencies and Finding Heavy Hitters Jonas Nicolai Hovmand, 2011 3884 Morten Houmøller Nygaard, 2011 4582 Master s Thesis, Computer Science June 2016 Main Supervisor: Gerth Stølting Brodal
More informationAlgorithms for Streaming Data
Algorithms for Piotr Indyk Problems defined over elements P={p 1,,p n } The algorithm sees p 1, then p 2, then p 3, Key fact: it has limited storage Can store only s
More informationApproximate Query Processing Using Wavelets
Approximate Query Processing Using Wavelets Kaushik Chakrabarti Minos Garofalakis Rajeev Rastogi Kyuseok Shim Presented by Guanghua Yan Outline Approximate query processing: Problem and Prior solutions
More informationSketching and Streaming for Distributions
Sketching and Streaming for Distributions Piotr Indyk Andrew McGregor Massachusetts Institute of Technology University of California, San Diego Main Material: Stable distributions, pseudo-random generators,
More informationProbabilistic Near-Duplicate. Detection Using Simhash
Probabilistic Near-Duplicate Detection Using Simhash Sadhan Sood, Dmitri Loguinov Presented by Matt Smith Internet Research Lab Department of Computer Science and Engineering Texas A&M University 27 October
More informationDATA STREAMS. Elena Ikonomovska Jožef Stefan Institute Department of Knowledge Technologies
QUERYING AND MINING DATA STREAMS Elena Ikonomovska Jožef Stefan Institute Department of Knowledge Technologies Outline Definitions Datastream models Similarity measures Historical background Foundations
More informationStreaming Algorithms for Set Cover. Piotr Indyk With: Sepideh Mahabadi, Ali Vakilian
Streaming Algorithms for Set Cover Piotr Indyk With: Sepideh Mahabadi, Ali Vakilian Set Cover Input: a collection S of sets S 1...S m that covers U={1...n} I.e., S 1 S 2. S m = U Output: a subset I of
More informationCambridge University Press The Mathematics of Signal Processing Steven B. Damelin and Willard Miller Excerpt More information
Introduction Consider a linear system y = Φx where Φ can be taken as an m n matrix acting on Euclidean space or more generally, a linear operator on a Hilbert space. We call the vector x a signal or input,
More informationAn Adaptive Sublinear Time Block Sparse Fourier Transform
An Adaptive Sublinear Time Block Sparse Fourier Transform Volkan Cevher Michael Kapralov Jonathan Scarlett Amir Zandieh EPFL February 8th 217 Given x C N, compute the Discrete Fourier Transform (DFT) of
More informationA Non-sparse Tutorial on Sparse FFTs
A Non-sparse Tutorial on Sparse FFTs Mark Iwen Michigan State University April 8, 214 M.A. Iwen (MSU) Fast Sparse FFTs April 8, 214 1 / 34 Problem Setup Recover f : [, 2π] C consisting of k trigonometric
More information12 Count-Min Sketch and Apriori Algorithm (and Bloom Filters)
12 Count-Min Sketch and Apriori Algorithm (and Bloom Filters) Many streaming algorithms use random hashing functions to compress data. They basically randomly map some data items on top of each other.
More informationImproved Range-Summable Random Variable Construction Algorithms
Improved Range-Summable Random Variable Construction Algorithms A. R. Calderbank A. Gilbert K. Levchenko S. Muthukrishnan M. Strauss January 19, 2005 Abstract Range-summable universal hash functions, also
More informationECEN 689 Special Topics in Data Science for Communications Networks
ECEN 689 Special Topics in Data Science for Communications Networks Nick Duffield Department of Electrical & Computer Engineering Texas A&M University Lecture 5 Optimizing Fixed Size Samples Sampling as
More informationLecture 01 August 31, 2017
Sketching Algorithms for Big Data Fall 2017 Prof. Jelani Nelson Lecture 01 August 31, 2017 Scribe: Vinh-Kha Le 1 Overview In this lecture, we overviewed the six main topics covered in the course, reviewed
More informationWavelet Synopsis for Data Streams: Minimizing Non-Euclidean Error
Wavelet Synopsis for Data Streams: Minimizing Non-Euclidean Error Sudipto Guha Department of Computer Science University of Pennsylvania Philadelphia, PA 904. sudipto@cis.upenn.edu Boulos Harb Department
More informationProcessing Count Queries over Event Streams at Multiple Time Granularities
Processing Count Queries over Event Streams at Multiple Time Granularities Aykut Ünal, Yücel Saygın, Özgür Ulusoy Department of Computer Engineering, Bilkent University, Ankara, Turkey. Faculty of Engineering
More informationFinding Frequent Items in Probabilistic Data
Finding Frequent Items in Probabilistic Data Qin Zhang, Hong Kong University of Science & Technology Feifei Li, Florida State University Ke Yi, Hong Kong University of Science & Technology SIGMOD 2008
More informationSPARSE signal representations have gained popularity in recent
6958 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 10, OCTOBER 2011 Blind Compressed Sensing Sivan Gleichman and Yonina C. Eldar, Senior Member, IEEE Abstract The fundamental principle underlying
More informationImage Compression. 1. Introduction. Greg Ames Dec 07, 2002
Image Compression Greg Ames Dec 07, 2002 Abstract Digital images require large amounts of memory to store and, when retrieved from the internet, can take a considerable amount of time to download. The
More informationMulti-Dimensional Online Tracking
Multi-Dimensional Online Tracking Ke Yi and Qin Zhang Hong Kong University of Science & Technology SODA 2009 January 4-6, 2009 1-1 A natural problem Bob: tracker f(t) g(t) Alice: observer (t, g(t)) t 2-1
More informationImage Compression Using the Haar Wavelet Transform
College of the Redwoods http://online.redwoods.cc.ca.us/instruct/darnold/laproj/fall2002/ames/ 1/33 Image Compression Using the Haar Wavelet Transform Greg Ames College of the Redwoods Math 45 Linear Algebra
More informationLecture 2. Frequency problems
1 / 43 Lecture 2. Frequency problems Ricard Gavaldà MIRI Seminar on Data Streams, Spring 2015 Contents 2 / 43 1 Frequency problems in data streams 2 Approximating inner product 3 Computing frequency moments
More informationAn Improved Frequent Items Algorithm with Applications to Web Caching
An Improved Frequent Items Algorithm with Applications to Web Caching Kevin Chen and Satish Rao UC Berkeley Abstract. We present a simple, intuitive algorithm for the problem of finding an approximate
More information13 Searching the Web with the SVD
13 Searching the Web with the SVD 13.1 Information retrieval Over the last 20 years the number of internet users has grown exponentially with time; see Figure 1. Trying to extract information from this
More information9 Searching the Internet with the SVD
9 Searching the Internet with the SVD 9.1 Information retrieval Over the last 20 years the number of internet users has grown exponentially with time; see Figure 1. Trying to extract information from this
More informationLeveraging Big Data: Lecture 13
Leveraging Big Data: Lecture 13 http://www.cohenwang.com/edith/bigdataclass2013 Instructors: Edith Cohen Amos Fiat Haim Kaplan Tova Milo What are Linear Sketches? Linear Transformations of the input vector
More informationOnline Forest Density Estimation
Online Forest Density Estimation Frédéric Koriche CRIL - CNRS UMR 8188, Univ. Artois koriche@cril.fr UAI 16 1 Outline 1 Probabilistic Graphical Models 2 Online Density Estimation 3 Online Forest Density
More informationSparse Recovery Using Sparse (Random) Matrices
Sparse Recovery Using Sparse (Random) Matrices Piotr Indyk MIT Joint work with: Radu Berinde, Anna Gilbert, Howard Karloff, Martin Strauss and Milan Ruzic Linear Compression (learning Fourier coeffs, linear
More informationLecture 16 Oct. 26, 2017
Sketching Algorithms for Big Data Fall 2017 Prof. Piotr Indyk Lecture 16 Oct. 26, 2017 Scribe: Chi-Ning Chou 1 Overview In the last lecture we constructed sparse RIP 1 matrix via expander and showed that
More informationSuccinct Data Structures for Approximating Convex Functions with Applications
Succinct Data Structures for Approximating Convex Functions with Applications Prosenjit Bose, 1 Luc Devroye and Pat Morin 1 1 School of Computer Science, Carleton University, Ottawa, Canada, K1S 5B6, {jit,morin}@cs.carleton.ca
More informationSensing systems limited by constraints: physical size, time, cost, energy
Rebecca Willett Sensing systems limited by constraints: physical size, time, cost, energy Reduce the number of measurements needed for reconstruction Higher accuracy data subject to constraints Original
More informationComputing the Entropy of a Stream
Computing the Entropy of a Stream To appear in SODA 2007 Graham Cormode graham@research.att.com Amit Chakrabarti Dartmouth College Andrew McGregor U. Penn / UCSD Outline Introduction Entropy Upper Bound
More informationFinding Frequent Items in Data Streams
Finding Frequent Items in Data Streams Moses Charikar 1, Kevin Chen 2, and Martin Farach-Colton 3 1 Princeton University moses@cs.princeton.edu 2 UC Berkeley kevinc@cs.berkeley.edu 3 Rutgers University
More informationBoutsidis, Garber, Karnin, Liberty. PRESENTED BY Firstname Lastname August 25, 2013 PRESENTED BY Zohar Karnin November 23, 2014
A Online PowerPoint Principal Presentation Component Analysis Boutsidis, Garber, Karnin, Liberty PRESENTED BY Firstname Lastname August 5, 013 PRESENTED BY Zohar Karnin November 3, 014 Data Matrix Often,
More informationApproximate counting: count-min data structure. Problem definition
Approximate counting: count-min data structure G. Cormode and S. Muthukrishhan: An improved data stream summary: the count-min sketch and its applications. Journal of Algorithms 55 (2005) 58-75. Problem
More informationMining Data Streams. The Stream Model. The Stream Model Sliding Windows Counting 1 s
Mining Data Streams The Stream Model Sliding Windows Counting 1 s 1 The Stream Model Data enters at a rapid rate from one or more input ports. The system cannot store the entire stream. How do you make
More informationClassic Network Measurements meets Software Defined Networking
Classic Network s meets Software Defined Networking Ran Ben Basat, Technion, Israel Joint work with Gil Einziger and Erez Waisbard (Nokia Bell Labs) Roy Friedman (Technion) and Marcello Luzieli (UFGRS)
More informationTime-Decayed Correlated Aggregates over Data Streams
Time-Decayed Correlated Aggregates over Data Streams Graham Cormode AT&T Labs Research graham@research.att.com Srikanta Tirthapura Bojian Xu ECE Dept., Iowa State University {snt,bojianxu}@iastate.edu
More informationCausality & Concurrency. Time-Stamping Systems. Plausibility. Example TSS: Lamport Clocks. Example TSS: Vector Clocks
Plausible Clocks with Bounded Inaccuracy Causality & Concurrency a b exists a path from a to b Brad Moore, Paul Sivilotti Computer Science & Engineering The Ohio State University paolo@cse.ohio-state.edu
More information14.1 Finding frequent elements in stream
Chapter 14 Streaming Data Model 14.1 Finding frequent elements in stream A very useful statistics for many applications is to keep track of elements that occur more frequently. It can come in many flavours
More informationLecture 6 September 13, 2016
CS 395T: Sublinear Algorithms Fall 206 Prof. Eric Price Lecture 6 September 3, 206 Scribe: Shanshan Wu, Yitao Chen Overview Recap of last lecture. We talked about Johnson-Lindenstrauss (JL) lemma [JL84]
More informationStream Computation and Arthur- Merlin Communication
Stream Computation and Arthur- Merlin Communication Justin Thaler, Yahoo! Labs Joint Work with: Amit Chakrabarti, Dartmouth Graham Cormode, University of Warwick Andrew McGregor, Umass Amherst Suresh Venkatasubramanian,
More informationZero-One Laws for Sliding Windows and Universal Sketches
Zero-One Laws for Sliding Windows and Universal Sketches Vladimir Braverman 1, Rafail Ostrovsky 2, and Alan Roytman 3 1 Department of Computer Science, Johns Hopkins University, USA vova@cs.jhu.edu 2 Department
More informationHash-based Indexing: Application, Impact, and Realization Alternatives
: Application, Impact, and Realization Alternatives Benno Stein and Martin Potthast Bauhaus University Weimar Web-Technology and Information Systems Text-based Information Retrieval (TIR) Motivation Consider
More informationTitle: Count-Min Sketch Name: Graham Cormode 1 Affil./Addr. Department of Computer Science, University of Warwick,
Title: Count-Min Sketch Name: Graham Cormode 1 Affil./Addr. Department of Computer Science, University of Warwick, Coventry, UK Keywords: streaming algorithms; frequent items; approximate counting, sketch
More informationOutline. Approximation: Theory and Algorithms. Application Scenario. 3 The q-gram Distance. Nikolaus Augsten. Definition and Properties
Outline Approximation: Theory and Algorithms Nikolaus Augsten Free University of Bozen-Bolzano Faculty of Computer Science DIS Unit 3 March 13, 2009 2 3 Nikolaus Augsten (DIS) Approximation: Theory and
More informationLecture 5: Web Searching using the SVD
Lecture 5: Web Searching using the SVD Information Retrieval Over the last 2 years the number of internet users has grown exponentially with time; see Figure. Trying to extract information from this exponentially
More informationIs Quantum Search Practical?
DARPA Is Quantum Search Practical? George F. Viamontes Igor L. Markov John P. Hayes University of Michigan, EECS Outline Motivation Background Quantum search Practical Requirements Quantum search versus
More informationSome notes on streaming algorithms continued
U.C. Berkeley CS170: Algorithms Handout LN-11-9 Christos Papadimitriou & Luca Trevisan November 9, 016 Some notes on streaming algorithms continued Today we complete our quick review of streaming algorithms.
More informationMATCHING-PURSUIT DICTIONARY PRUNING FOR MPEG-4 VIDEO OBJECT CODING
MATCHING-PURSUIT DICTIONARY PRUNING FOR MPEG-4 VIDEO OBJECT CODING Yannick Morvan, Dirk Farin University of Technology Eindhoven 5600 MB Eindhoven, The Netherlands email: {y.morvan;d.s.farin}@tue.nl Peter
More informationSketching in Adversarial Environments
Sketching in Adversarial Environments Ilya Mironov Moni Naor Gil Segev Abstract We formalize a realistic model for computations over massive data sets. The model, referred to as the adversarial sketch
More informationResource Allocation for Video Streaming in Wireless Environment
Resource Allocation for Video Streaming in Wireless Environment Shahrokh Valaee and Jean-Charles Gregoire Abstract This paper focuses on the development of a new resource allocation scheme for video streaming
More informationWavelets for Efficient Querying of Large Multidimensional Datasets
Wavelets for Efficient Querying of Large Multidimensional Datasets Cyrus Shahabi University of Southern California Integrated Media Systems Center (IMSC) and Dept. of Computer Science Los Angeles, CA 90089-0781
More informationA Mergeable Summaries
A Mergeable Summaries Pankaj K. Agarwal, Graham Cormode, Zengfeng Huang, Jeff M. Phillips, Zhewei Wei, and Ke Yi We study the mergeability of data summaries. Informally speaking, mergeability requires
More informationRange-efficient computation of F 0 over massive data streams
Range-efficient computation of F 0 over massive data streams A. Pavan Dept. of Computer Science Iowa State University pavan@cs.iastate.edu Srikanta Tirthapura Dept. of Elec. and Computer Engg. Iowa State
More informationMining Data Streams. The Stream Model Sliding Windows Counting 1 s
Mining Data Streams The Stream Model Sliding Windows Counting 1 s 1 The Stream Model Data enters at a rapid rate from one or more input ports. The system cannot store the entire stream. How do you make
More informationTwo heads better than one: Pattern Discovery in Time-evolving Multi-Aspect Data
Two heads better than one: Pattern Discovery in Time-evolving Multi-Aspect Data Jimeng Sun 1, Charalampos E. Tsourakakis 2, Evan Hoke 4, Christos Faloutsos 2, and Tina Eliassi-Rad 3 1 IBM T.J. Watson Research
More informationAd Placement Strategies
Case Study 1: Estimating Click Probabilities Tackling an Unknown Number of Features with Sketching Machine Learning for Big Data CSE547/STAT548, University of Washington Emily Fox 2014 Emily Fox January
More informationLecture 10. Sublinear Time Algorithms (contd) CSC2420 Allan Borodin & Nisarg Shah 1
Lecture 10 Sublinear Time Algorithms (contd) CSC2420 Allan Borodin & Nisarg Shah 1 Recap Sublinear time algorithms Deterministic + exact: binary search Deterministic + inexact: estimating diameter in a
More informationRandom Sampling on Big Data: Techniques and Applications Ke Yi
: Techniques and Applications Ke Yi Hong Kong University of Science and Technology yike@ust.hk Big Data in one slide The 3 V s: Volume Velocity Variety Integers, real numbers Points in a multi-dimensional
More informationNonconvex penalties: Signal-to-noise ratio and algorithms
Nonconvex penalties: Signal-to-noise ratio and algorithms Patrick Breheny March 21 Patrick Breheny High-Dimensional Data Analysis (BIOS 7600) 1/22 Introduction In today s lecture, we will return to nonconvex
More informationOnline Learning, Mistake Bounds, Perceptron Algorithm
Online Learning, Mistake Bounds, Perceptron Algorithm 1 Online Learning So far the focus of the course has been on batch learning, where algorithms are presented with a sample of training data, from which
More informationAlgorithms for Nearest Neighbors
Algorithms for Nearest Neighbors Background and Two Challenges Yury Lifshits Steklov Institute of Mathematics at St.Petersburg http://logic.pdmi.ras.ru/~yura McGill University, July 2007 1 / 29 Outline
More information6. Iterative Methods for Linear Systems. The stepwise approach to the solution...
6 Iterative Methods for Linear Systems The stepwise approach to the solution Miriam Mehl: 6 Iterative Methods for Linear Systems The stepwise approach to the solution, January 18, 2013 1 61 Large Sparse
More informationQuicksort. Where Average and Worst Case Differ. S.V. N. (vishy) Vishwanathan. University of California, Santa Cruz
Quicksort Where Average and Worst Case Differ S.V. N. (vishy) Vishwanathan University of California, Santa Cruz vishy@ucsc.edu February 1, 2016 S.V. N. Vishwanathan (UCSC) CMPS101 1 / 28 Basic Idea Outline
More informationBeyond Distinct Counting: LogLog Composable Sketches of frequency statistics
Beyond Distinct Counting: LogLog Composable Sketches of frequency statistics Edith Cohen Google Research Tel Aviv University TOCA-SV 5/12/2017 8 Un-aggregated data 3 Data element e D has key and value
More informationWavelet Footprints: Theory, Algorithms, and Applications
1306 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 51, NO. 5, MAY 2003 Wavelet Footprints: Theory, Algorithms, and Applications Pier Luigi Dragotti, Member, IEEE, and Martin Vetterli, Fellow, IEEE Abstract
More informationCS 598CSC: Algorithms for Big Data Lecture date: Sept 11, 2014
CS 598CSC: Algorithms for Big Data Lecture date: Sept 11, 2014 Instructor: Chandra Cheuri Scribe: Chandra Cheuri The Misra-Greis deterministic counting guarantees that all items with frequency > F 1 /
More informationGreedy Signal Recovery and Uniform Uncertainty Principles
Greedy Signal Recovery and Uniform Uncertainty Principles SPIE - IE 2008 Deanna Needell Joint work with Roman Vershynin UC Davis, January 2008 Greedy Signal Recovery and Uniform Uncertainty Principles
More informationAn Algorithmist s Toolkit Nov. 10, Lecture 17
8.409 An Algorithmist s Toolkit Nov. 0, 009 Lecturer: Jonathan Kelner Lecture 7 Johnson-Lindenstrauss Theorem. Recap We first recap a theorem (isoperimetric inequality) and a lemma (concentration) from
More informationSieving for Shortest Vectors in Ideal Lattices:
Sieving for Shortest Vectors in Ideal Lattices: a Practical Perspective Joppe W. Bos Microsoft Research LACAL@RISC Seminar on Cryptologic Algorithms CWI, Amsterdam, Netherlands Joint work with Michael
More informationReducing Computation Time for the Analysis of Large Social Science Datasets
Reducing Computation Time for the Analysis of Large Social Science Datasets Douglas G. Bonett Center for Statistical Analysis in the Social Sciences University of California, Santa Cruz Jan 28, 2014 Overview
More information