CMU Lecture on Hadoop Performance

1©MapR Technologies - Confidential
Hadoop Performance

Agenda
 What is performance? Optimization?
 Case 1: Aggregation
 Case 2: Recommendations
 Case 3: Clustering
 Case 4: Matrix decomposition

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?

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

Inside Map-Reduce
5
Input Map CombineShuffle
and sort
Reduce Output
Reduce
"The time has come," the Walrus said,
"To talk of many things:
Of shoes—and ships—and sealing-wax
the, 1
time, 1
has, 1
come, 1
…
come, [3,2,1]
has, [1,5,2]
the, [1,2,1]
time,
[10,1,3]
…
come, 6
has, 8
the, 4
time, 14
…

Don’t Do This
Raw
Daily
Weekly
Monthly

Do This Instead
Raw
Daily Weekly
Monthly

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

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

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

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)

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

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?

So …
 Cheat!
 Downsample every user to at most 1000 interactions
– most recent
– most rare
– random selection
– whatever is easiest
 Now k_max ≤ 1000

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

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)

Non-Traditional Deployment Demo
DEMO

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 …

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 …

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

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

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

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

An Example

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

An Example

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

Lots of Clusters Are Fine

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

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

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

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

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

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

Matrix Decomposition
 Many big matrices can often be compressed
 Often used in recommendations
=

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

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

Fundamental Trick
 Random orthogonal projection preserves action of A
Ax - Ay » QT
Ax -QT
Ay

Projection Search
total ordering!

LSH Bit-match Versus Cosine
0 8 16 24 32 40 48 56 64
1
- 1
- 0.8
- 0.6
- 0.4
- 0.2
0
0.2
0.4
0.6
0.8
X Axis
YAxis

But How?
Y = AW
Q1R = Y
B = Q1
T
A
LQ2 = B
USVT
= L
(Q1U) S (Q2V)T
» A

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

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

CMU Lecture on Hadoop Performance

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