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Stream Data Introduction

Stream Data Introduction. Outline. Streaming Data description Uses/Applications Problems/Challenges Main Concepts variance & k-means aging & sliding windows algorithms References. Sizing the challenge. WalMart Records 20 Million Transactions Google Handles 100 Million Searches

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Stream Data Introduction

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  1. Stream Data Introduction

  2. Outline • Streaming Data description • Uses/Applications • Problems/Challenges • Main Concepts • variance & k-means • aging & sliding windows • algorithms • References

  3. Sizing the challenge • WalMart Records 20 Million Transactions • Google Handles 100 Million Searches • AT&T produces 275 million call records • Earth sensing satellite produces GBs of data This just in a day!

  4. Characteristics/Description • Stream data sets are… • Continuous • Massive • Unbounded • Possibly infinite • Fast changing and requires fast, real-time response

  5. Example: Network Management Application • Network Management involves monitoring and configuring network hardware and software to ensure smooth operation • Monitor link bandwidth usage, estimate traffic demands • Quickly detect faults, congestion and isolate root cause • Load balancing, improve utilization of network resources AT&T collects 100 GBs of NetFlow data each day!

  6. Network Management Application (cont.) Network Operations Center Measurements Alarms Network

  7. Uses/Applications • Banking/Stocks/Financials • credit card fraud detection • stock trends monitoring • Sensors • power grid balancing • engine controls • collision avoidance • driver sleep monitor

  8. Problems/Challenges • ‘Zillions of data • Continuous/Unbounded • Examples arrive faster than they can be mined • Application may require fast, real-time response • Examples: life threatening: collision avoidance lost revenue/transactions: hung-up networks

  9. Problems/Challenges • Time/Space constrained • Not enough memory • Can’t afford storing/revisiting the data • Single pass computation • External memory algorithms for handling data sets larger than main memory cannot be used. • Do not support continuous queries • Too slow real-time response

  10. Problems/Challenges • In summary… • Can’t stop to smell the roses… • Only one chance/single pass/look at the data

  11. Problems/Challenges • Other Considerations • Classical algorithms (i.e. CART, C4.5) do not scale up to data stream [DH00] • Most need entire data set for analysis • Random access (or multiple passes) to the data • Difficult to compute answers accurately with limited memory • With probability at least 1 - , algorithms compute an approximate answer within a factor  of the actual answer • Noise (bad sensors, outliers) • Aging/Old/Stale data

  12. Computation Model Synopsis in Memory Data Streams Stream Processing Engine (Approximate) Answer Decision Making

  13. Model Components • Synopsis • Summary of the data • Samples, Histograms • Processing Engine • Implementation/Management System • STREAM (Stanford): general-purpose • Aurora (Brown/MIT): sensor monitoring, dataflow • Telegraph (Berkeley): adaptive engine for sensors • Decision Making • Apply Data Mining techniques • Decision Trees, Clusters, Association Rules

  14. Synopsis: Dealing with Time/Space Constraints • Since data can’t be contained, or revisited, the best alternative is to summarize what has been seen. • Basic stream synopsis computation • Random Sampling: Generate statistics using a representative sample of the data • Histograms: Distribution/Grouping data representation • Wavelets: Mathematical tool for hierarchical decomposition of functions/signals

  15. Reservoir Sampling • Sample first m items • Choose to sample the i’th item (i>m) with probability m/i • If sampled, randomly replace a previously sampled item • Optimization: when i gets large, compute which item will be sampled next, skip over intervening items

  16. Reservoir Sampling - Analysis 1 i i+1n-2n-1  …  i i+1 i+2 n-1 n • Analyze simple case: sample size m = 1 • Probability i’th item is the sample from stream length n: • Prob. i is sampled on arrival  prob. i survives to end = 1/n • Case for m > 1 is similar, easy to show uniform probability • Drawbacks of reservoir sampling: hard to parallelize

  17. Min-wise Sampling • For each item, pick a random fraction between 0 and 1 • Store item(s) with the smallest random tag [Nath et al.’04] 0.391 0.908 0.291 0.555 0.619 0.273 • Each item has same chance of least tag, so uniform • Can run on multiple streams separately, then merge

  18. Histograms • Histograms approximate the frequency distribution of element values in a stream • A histogram (typically) consists of • A partitioning of element domain values into buckets • A count per bucket B (of the number of elements in B) • Long history of use for selectivity estimation within a query optimizer

  19. Histogram Sampling • Equi-Depth • Element counts per bucket are kept constant • V-Optimal • Minimize frequency variance within buckets • Exponential Histograms (EH) • Bucket sizes are non-decreasing powers of 2 • Size: Total number of 1’s in the bucket. • For every bucket other than the last bucket, there are at least k/2 and at most k/2+1 buckets of that size • Example: k=4: (1,1,2,2,2,4,4,4,8,8,..) • Essential component of “sliding windows” technique addressing “aging” data.

  20. Equi-Depth • V-Optimal • Exponential Histograms

  21. Exponential Histogram Assume k/2 = 2 32,16,8,8,4,4,2,1,1

  22. Exponential Histogram Assume k/2 = 2 32,16,8,8,4,4,2,1,1 1

  23. Exponential Histogram Assume k/2 = 2 32,16,8,8,4,4,2,1,1,1 32,16,8,8,4,4,2,2,1 Merged! Merge!

  24. Exponential Histogram Assume k/2 = 2 32,16,8,8,4,4,2,1,1 32,16,8,8,4,4,2,2,1 32,16,8,8,4,4,2,2,1,1 32,16,16,8,4,2,1

  25. Exponential Histogram Assume k/2 = 2 32,16,8,8,4,4,2,1,1 32,16,8,8,4,4,2,2,1 32,16,8,8,4,4,2,2,1,1 32,16,16,8,4,2,1

  26. Answering Queries using Histograms answer: 3.5 * • (Implicitly) map the histogram back to an approximate relation, & apply the query to the approximate relation • Example: select count(*) from R where 4<=R.e<=15 • For equi-depth histograms, maximum error: Count spread evenly among bucket values 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4  R.e  15

  27. Sliding Windows Technique • Background: • Some applications rely on ALL historical data • But for most applications, OLD data is considered less relevant and could skew results from NEW trends or conditions • new processes/procedures • new hardware/sensors • new fashion trends

  28. Sliding Windows (cont.) • Common approaches addressing Old data: • Aging Model • elements are associated with “weights” that decrease over time • may use some exponential decay formulas • Sliding Windows Model • Only last “N” elements are considered • Incorporate examples as they arrive • The record “expires” at time t+N (N is the window length) • Count only the “1’s” in bit-stream data

  29. Sliding Window (SW) Model Time Increases ….1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1… Window Size N = 7 Current Time

  30. Sliding Windows Plus Exponential Histograms • Sliding Windows Approach (pseudo-pseudo code) • Consider only the last N elements. • Define k=1/ε, and approximate k/2 to nearest integer. • Time Stamp each “1” that arrives in the stream and insert into a first bucket, shifting any initial ones. • First bucket value is “1” since there is only one “1” • If the number of buckets with same value exceeds k/2 +1, merge the oldest buckets, but keeping at least k/2 buckets of the same value • Merging creates a new bucket with size equal to the sum • Eliminate last bucket if its last 1 time stamp exceeds N

  31. Benefits of Sliding Windows • Incorporates new elements as they appear. • Easy to calculate statistics over data streams with respect to the last N elements based on the histogram. • Can estimate the number of 1’s within a factor of (1 + ε) using only θ((1/ε)(log2N)) bits of memory.

  32. Expansion of Sliding Windows • The original Sliding Window Method was not fully applicable to two important statistics during the “merging” of the buckets: • k-median and variance • A solution was devised by Babcock, Datar, Motwani and O’Callaghan • Their work derived a methodology for Variance, that was also applied for k-medians.

  33. Variance and k-Medians • Variance: Σ(xi – μ)2, μ = Σ xi/N • k-median clustering: • Given: N points (x1… xN) in a metric space • Find k points C = {c1, c2, …, ck} that minimize Σ d(xi, C) (the assignment distance) • Clustering to be covered in detail future presentation

  34. Notation Current window, size = N ……………… Bm-1 Bm B2 B1 Vi = Variance of the ith bucket ni = number of elements in ith bucket μi = mean of the ith bucket

  35. Variance – composition • Bi,j = concatenation of buckets i and j

  36. Decision Making • The problem of addressing time changing data had also significant influence on decision algorithms. • Pedro Domingos, who had originally developed a successful decision table algorithm (VFDT), also conceptualized the need to work with recent data, resulting in a new algorithm known as CVFDT. • VFDT - Very Fast Decision Tree • CVFDT - Concept Drift Very Fast Decision Tree • Implemented a window approach

  37. Decision Making • Both VFDT and CVFDT make use of a statistical result known as Hoeffding* bound • Used to estimate the minimum number of necessary examples needed to make a decision for a node in a decision tree. • This is the key concept for these algorithms to work. * W.Hoefding, Probability Inequalities sums bounded Variables, Journal American Statistics Association, 1963

  38. Hoeffding Bound • random variable a whose range is R • n independent observations of a; Mean: ā • Hoeffding bound states: With probability 1- , the true mean of a is at least ā - , where

  39. Hoeffding Bound • Significance… • This estimate/bound is incorporated into an ID3 type decision tree, hence VFDT/CVFDT • The information gain is evaluated against 

  40. VFDT Algorithm

  41. VFDT Algorithm Results

  42. CVFDT vs. VFDT • CVFDT is an extension to VFDT that incorporated “windowing” • CFVDT concept: • Generate tree as regular but using a window of “w” elements. • Monitor changes in gain for attributes. • If changes, generate alternate subtree with new “best” attribute, but keep on background. • Replace if new subtree becomes more accurate.

  43. References • [BDMO03] B. Babcock, M. Datar, R. Motwani, and J. L. O’Callaghan. “Maintaining Variance and k-Medians over Data Stream Windows”. ACM PODS, 2003. http://citeseer.nj.nec.com/591910.html http://www.stanford.edu/~babcock/papers/pods03.ppt • [DH00] P. Domingos and G. Hulten. “Mining High-Speed Data Streams”. ACM KDD, 2000. http://citeseer.nj.nec.com/domingos00mining.html • [HSD01] G. Hulten, L. Spencer and P. Domingos. “Mining Time-Changing Data Streams”. ACM KDD, 2001. http://citeseer.nj.nec.com/hulten01mining.html • [DGIM02] Mayur Datar, Aristides Gionis, Piotr Indyk and Rajeev Motwani. “Maintaining Stream Statistics over Sliding Windows” ACM-SIAM SODA 2002. http://www.stanford.edu/~babcock/papers/pods03.ppt • [GGR02] Minos Garofalakis, Johannes Gehrke and Rajeev Rastogi. “Querying and Mining Data Streams: You Only Get One Look”. SIGMOD 2002 (tutorial). http://www.bell-labs.com/user/minos/Talks/streams-tutorial02.ppt

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