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A lecture describing several ways to make Hadoop programs go faster.

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- 1. Hadoop Performance©MapR Technologies - Confidential 1
- 2. Agenda What is performance? Optimization? Case 1: Aggregation Case 2: Recommendations Case 3: Clustering Case 4: Matrix decomposition©MapR Technologies - Confidential 2
- 3. What is Performance? Is doing something faster better? Is it the right task? Do you have a wide enough view? What is the right performance metric?©MapR Technologies - Confidential 3
- 4. Aggregation Word-count and friends – How many times did X occur? – How many unique X’s occurred? Associative metrics permit decomposition – Partial sums and grand totals for example – Use combiners – Use high resolution aggregates to compute low resolution aggregates Rank-based statistics do not permit decomposition – Avoid them – Use approximations©MapR Technologies - Confidential 4
- 5. Inside Map-Reduce the, 1 "The time has come," the Walrus said, time, 1 "To talk of many things: come, [3,2,1] has, 1 Of shoes—and ships—and sealing-wax [1,5,2] has, come, 6 come, 1 the, [1,2,1] has, 8 … time, [10,1,3 the, 4 ] time, 14 Input Map Combine Shuffle … Reduce … Output and sort Reduce©MapR Technologies - Confidential 5 5
- 6. Don’t Do This Daily Raw Weekly Monthly©MapR Technologies - Confidential 6
- 7. Do This Instead Daily Weekly Raw Monthly©MapR Technologies - Confidential 7
- 8. Aggregation First rule: – Don’t read the big input multiple times – Compute longer term aggregates from short term aggregates Second rule: – Don’t read the big input multiple times – Compute multiple windowed aggregates at the same time©MapR Technologies - Confidential 8
- 9. Rank Statistics Can Be Tamed Approximate quartiles are easily computed – (but sorted data is evil) Approximate unique counts are easily computed – use Bloom filter and extrapolate from number of set bits – use multiple filters at different down-sample rates Approximate high or low approximate quantiles are easily computed – keep largest 1000 elements – keep largest 1000 elements from 10x down-sampled data – and so on Approximate top-40 also possible©MapR Technologies - Confidential 9
- 10. Recommendations Common patterns in the past may predict common patterns in the future People who bought item x also bought item y But also, people who bought Chinese food in the past, … Or people in SoMa really liked this restaurant in the past©MapR Technologies - Confidential 10
- 11. People who bought … Key operation is counting number of people who bought x and y – for all x’s and all y’s The raw problem appears to be O(N^3) At the least, O(k_max^2) – for most prolific user, there are k^2 pairs to count – k_max can be near N Scalable problems must be O(N)©MapR Technologies - Confidential 11
- 12. But … What do we learn from users who buy everything – they have no discrimination – they are often the QA team – they tell us nothing What do we learn from items bought by everybody – the dual of omnivorous buyers – these are often teaser items – they tell us nothing©MapR Technologies - Confidential 12
- 13. Also … What would you learn about a user from purchases – 1 … 20? – 21 … 100? – 101 … 1000? – 1001 … ∞? What about learning about an item? – how many people do we need to see before we understand the item?©MapR Technologies - Confidential 13
- 14. So … Cheat! Downsample every user to at most 1000 interactions – most recent – most rare – random selection – whatever is easiest Now k_max ≤ 1000©MapR Technologies - Confidential 14
- 15. The Fundamental Things Apply Don’t read the raw data repeatedly Sessionize and denormalize per hour/day/week – that is, group by user – expand items with categories and content descriptors if feasible Feed all down-stream processing in one pass – baby join to item characteristics – downsample – count grand totals – compute cooccurrences©MapR Technologies - Confidential 15
- 16. Deployment Matters, Too For restaurant case, basic recommendation info includes: – user x merchant histories – user x cuisine histories – top local restaurant by anomalous repeat visits – restaurant x indicator merchant cooccurrence matrix – restaurant x indicator cuisine cooccurrence matrix These can all be stored and accessed using text retrieval techniques Fast deployment using mirrors and NFS (not standard Hadoop)©MapR Technologies - Confidential 16
- 17. Non-Traditional Deployment Demo DEMO©MapR Technologies - Confidential 17
- 18. EM Algorithms Start with random model estimates Use model estimates to classify examples Use classified examples to find probability maximum estimates Use model estimates to classify examples Use classified examples to find probability maximum estimates … And so on …©MapR Technologies - Confidential 18
- 19. K-means as EM Algorithm Assign a random seed to each cluster Assign points to nearest cluster Move cluster to average of contained points Assign points to nearest cluster … and so on …©MapR Technologies - Confidential 19
- 20. K-means as Map-Reduce Assignment of points to cluster is trivially parallel Computation of new clusters is also parallel Moving points to averages is ideal for map-reduce©MapR Technologies - Confidential 20
- 21. But … With map-reduce, iteration is evil Starting a program can take 10-30s Saving data to disk and then immediately reading from disk is silly Input might even fit in cluster memory©MapR Technologies - Confidential 21
- 22. Fix #1 Don’t do that! Use Spark – in memory interactive map-reduce – 100x to 1000x faster – must fit in memory Use Giraph – BSP programming model rather than map-reduce – essentially map-reduce-reduce-reduce… Use GraphLab – Like BSP without the speed brakes – 100x faster©MapR Technologies - Confidential 22
- 23. Fix #2 Use a sketch-based algorithm Do one pass over the data to compute sketch of the data Cluster the sketch Done. With good theoretic bounds on accuracy Speedup of 3000x or more©MapR Technologies - Confidential 23
- 24. An Example©MapR Technologies - Confidential 24
- 25. The Problem Spirals are a classic “counter” example for k-means Classic low dimensional manifold with added noise But clustering still makes modeling work well©MapR Technologies - Confidential 25
- 26. An Example©MapR Technologies - Confidential 26
- 27. An Example©MapR Technologies - Confidential 27
- 28. The Cluster Proximity Features Every point can be described by the nearest cluster – 4.3 bits per point in this case – Significant error that can be decreased (to a point) by increasing number of clusters Or by the proximity to the 2 nearest clusters (2 x 4.3 bits + 1 sign bit + 2 proximities) – Error is negligible – Unwinds the data into a simple representation©MapR Technologies - Confidential 28
- 29. Lots of Clusters Are Fine©MapR Technologies - Confidential 29
- 30. Surrogate Method Start with sloppy clustering into κ = k log n clusters Use this sketch as a weighted surrogate for the data Cluster surrogate data using ball k-means Results are provably good for highly clusterable data Sloppy clustering is on-line Surrogate can be kept in memory Ball k-means pass can be done at any time©MapR Technologies - Confidential 30
- 31. Algorithm Costs O(k d log n) per point per iteration for Lloyd’s algorithm Number of iterations not well known Iteration > log n reasonable assumption©MapR Technologies - Confidential 31
- 32. Algorithm Costs Surrogate methods – fast, sloppy single pass clustering with κ = k log n – fast sloppy search for nearest cluster, O(d log κ) = O(d (log k + log log n)) per point – fast, in-memory, high-quality clustering of κ weighted centroids O(κ k d + k3 d) = O(k2 d log n + k3 d) for small k, high quality O(κ d log k) or O(d log κ log k) for larger k, looser quality – result is k high-quality centroids • Even the sloppy clusters may suffice©MapR Technologies - Confidential 32
- 33. Algorithm Costs How much faster for the sketch phase? – take k = 2000, d = 10, n = 100,000 – k d log n = 2000 x 10 x 26 = 500,000 – log k + log log n = 11 + 5 = 17 – 30,000 times faster is a bona fide big deal©MapR Technologies - Confidential 33
- 34. Pragmatics But this requires a fast search internally Have to cluster on the fly for sketch Have to guarantee sketch quality Previous methods had very high complexity©MapR Technologies - Confidential 34
- 35. How It Works For each point – Find approximately nearest centroid (distance = d) – If (d > threshold) new centroid – Else if (u > d/threshold) new cluster – Else add to nearest centroid If centroids > κ ≈ C log N – Recursively cluster centroids with higher threshold Result is large set of centroids – these provide approximation of original distribution – we can cluster centroids to get a close approximation of clustering original – or we can just use the result directly©MapR Technologies - Confidential 35
- 36. Matrix Decomposition Many big matrices can often be compressed = Often used in recommendations©MapR Technologies - Confidential 36
- 37. Neighest Neighbor Very high dimensional vectors can be compressed to 10-100 dimensions with little loss of accuracy Fast search algorithms work up to dimension 50-100, don’t work above that©MapR Technologies - Confidential 37
- 38. Random Projections Many problems in high dimension can be reduce to low dimension Reductions with good distance approximation are available Surprisingly, these methods can be done using random vectors©MapR Technologies - Confidential 38
- 39. Fundamental Trick Random orthogonal projection preserves action of A Ax - Ay » Q Ax - Q Ay T T©MapR Technologies - Confidential 39
- 40. Projection Search total ordering!©MapR Technologies - Confidential 40
- 41. LSH Bit-match Versus Cosine 1 0.8 0.6 0.4 0.2 Y Ax is 0 0 8 16 24 32 40 48 56 64 - 0.2 - 0.4 - 0.6 - 0.8 -1 X Ax is©MapR Technologies - Confidential 41
- 42. But How? Y = AW Q1 R = Y B = Q1T A LQ2 = B USV = L T (Q1U) S (Q2V ) » A T©MapR Technologies - Confidential 42
- 43. Summary Don’t repeat big scans – Cascade aggregations – Compute several aggregates at once Use approximate measures for rank statistics Downsample where appropriate Use non-traditional deployment Use sketches Use random projections©MapR Technologies - Confidential 43
- 44. Contact Me! We’re hiring at MapR in US and Europe Come get the slides at http://www.mapr.com/company/events/cmu-hadoop-performance-11-1- 12 Get the code at https://github.com/tdunning Contact me at tdunning@maprtech.com or @ted_dunning©MapR Technologies - Confidential 44

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