Transcript slides - salsahpc - Indiana University

Analysis Tools for
Data Enabled Science
Judy Qiu
[email protected]
http://SALSAhpc.indiana.edu
School of Informatics and Computing
Indiana University
Summer Workshop on Algorithms and Cyberinfrastructure
for large scale optimization/AI, August 9, 2013
Big Data Challenge
(Source: Helen Sun, Oracle Big Data)
Learning from Big Data
Converting raw data to knowledge discovery
Exponential data growth
Continuous analysis of streaming data
A variety of algorithms and data structures
Multi/Manycore and GPU architectures
Thousands of cores in clusters and millions in data centers
Cost and time trade-off
Parallelism is a must to process data in a meaningful
length of time
SALSA
Programming Runtimes
Pig Latin, Hive
Hadoop
MapReduce
Workflows, Swift, Falkon
PaaS:
Worker
Roles
Classic Cloud:
Queues,
Workers
Achieve Higher Throughput
MPI, PVM, HPF
DAGMan,
BOINC
Chapel,
X10
Perform Computations Efficiently
High-level programming models such as MapReduce adopt a data-centered design
Computation starts from data
Support moving computation to data
Shows promising results for data-intensive computing
( Google, Yahoo, Amazon, Microsoft …)
Challenges: traditional MapReduce and classical parallel runtimes cannot solve iterative
algorithms efficiently
Hadoop: repeated data access to HDFS, no optimization to (in memory) data caching
and (collective) intermediate data transfers
MPI: no natural support of fault tolerance; programming interface is complicated
SALSA
Applications & Different Interconnection Patterns
(a) Map Only
(Pleasingly Parallel)
Input
map
Output
- CAP3 Gene Analysis
- Smith-Waterman
Distances
- Document conversion
(PDF -> HTML)
- Brute force searches in
cryptography
- Parametric sweeps
- PolarGrid MATLAB data
analysis
No Communication
(b) Classic
MapReduce
(c) Iterative
MapReduce
(d) Loosely
Synchronous
Input iterations
map
Input
map
Pij
reduce
- High Energy Physics
(HEP) Histograms
- Distributed search
- Distributed sorting
- Information retrieval
- Calculation of Pairwise
Distances for
sequences (BLAST)
reduce
- Expectation
maximization
algorithms
- Linear Algebra
- Data mining, includes
K-means clustering
- Deterministic
Annealing Clustering
- Multidimensional
Scaling (MDS)
- PageRank
Collective Communication
Domain of MapReduce and Iterative Extensions
Many MPI scientific
applications utilizing
wide variety of
communication
constructs, including
local interactions
- Solving Differential
Equations and particle
dynamics with short
range forces
MPI
SALSA
Data Analysis Tools
MapReduce optimized for iterative computations
Twister: the speedy elephant
Abstractions
In-Memory
Data Flow
Thread
• Cacheable
map/reduce tasks
• Iterative
• Loop Invariant
• Variable data
• Lightweight
• Local aggregation
Map-Collective Portability
• HPC (Java)
• Communication
patterns optimized for • Azure Cloud (C#)
large intermediate data
transfer
SALSA
Programming Model for Iterative MapReduce
Loop Invariant Data
Loaded only once
Variable data
Configure()
Main Program
while(..)
{
runMapReduce(..)
}
Cacheable
map/reduce tasks
(in memory)
Map(Key, Value)
Reduce (Key, List<Value>)
Combine(Map<Key,Value>)
Faster intermediate
data transfer
mechanism
Combiner operation
to collect all reduce
outputs
Distinction on loop invariant data and variable data (data flow vs. δ flow)
Cacheable map/reduce tasks (in-memory)
Combine operation
SALSA
Map-Collective Communication Model
Patterns
MapReduce
MapReduceMap-AllGather
• Wordcount, Grep MergeBroadcast • MDS-BCCalc
• KMeansClustering,
PageRank
Map-AllReduce
Map-ReduceScatter
• KMeansClustering, • PageRank, Belief
Propagation
MDS-StressCalc
We generalize the Map-Reduce concept to Map-Collective, noting that large collectives are a
distinguishing feature of data intensive and data mining applications.
Collectives generalize Reduce to include all large scale linked communication-compute patterns.
MapReduce already includes a step in the collective direction with sort, shuffle, merge as well as basic
reduction.
SALSA
Case Studies: Data Analysis Algorithms
Support a suite of parallel data-analysis capabilities
Clustering using image data
Parallel Inverted Indexing used for HBase
Matrix algebra as needed
Matrix Multiplication
Equation Solving
Eigenvector/value Calculation
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Iterative Computations
K-means
Performance of K-Means
Matrix
Multiplication
Parallel Overhead Matrix Multiplication
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PageRank
Partial
Adjacency
Matrix
Current
Page ranks
(Compressed)
Iterations
C
M
Partial
Updates
R
Partially merged
Updates
Well-known page rank algorithm [1]
Used ClueWeb09 [2] (1TB in size) from CMU
Hadoop loads the web graph in every iteration
Twister keeps the graph in memory
Pregel approach seems natural to graph-based problems
[1] Pagerank Algorithm, http://en.wikipedia.org/wiki/PageRank
[2] ClueWeb09 Data Set, http://boston.lti.cs.cmu.edu/Data/clueweb09/
SALSA
Data Intensive Kmeans Clustering
Collaboration with Prof. David Crandall
Image
s
9900007
Patches
99000070-0
HOG Features
𝑓1 , 𝑓2 … 𝑓𝑑𝑖𝑚
99000070
0
9900007
6
99000076
9900043
99000432
2
Clusters
I
99000070-4
𝑓1 , 𝑓2 … 𝑓𝑑𝑖𝑚
II
99000432-0
𝑓1 , 𝑓2 … 𝑓𝑑𝑖𝑚
III
99000432-4
Feature Extraction
𝑓1 , 𝑓2 … 𝑓𝑑𝑖𝑚
Clustering
Image Classification: 7 million images; 512 features per image; 1 million clusters; 10K
Map tasks; 64G broadcasting data (1GB data transfer per Map task node); 20 TB
intermediate data in shuffling.
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High Dimensional Image Data
K-means Clustering algorithm is used to cluster the images with similar
features.
Each image is characterized as a data point (vector) with dimensions in
the range of 512 ~ 2048. Each value (feature) ranges from 0 to 255.
A full execution of the image clustering application
We successfully cluster 7.42 million vectors into 1 million cluster
centers. 10000 map tasks are created on 125 nodes. Each node has
80 tasks, each task caches 742 vectors.
For 1 million centroids, broadcasting data size is about 512 MB.
Shuffling data is 20 TB, while the data size after local aggregation is
about 250 GB.
Since the total memory size on 125 nodes is 2 TB, we cannot even
execute the program unless local aggregation is performed.
SALSA
Image Clustering Control Flow in Twister
with new local aggregation feature in Map-Collective to drastically reduce intermediate data size
Broadcast from Driver
Worker 1
Worker 2
Worker 3
Map
Map
Map
Local Aggregation
Local Aggregation
Local Aggregation
Shuffle
Reduce
Reduce
Reduce
Combine to Driver
We explore operations such as high performance broadcasting and shuffling, then add
them to Twister iterative MapReduce framework. There are different algorithms for
broadcasting.
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Pipeline (works well for Cloud)
minimum-spanning tree
bidirectional exchange
bucket algorithm
SALSA
Broadcast Comparison: Twister vs. MPI
Performance comparison of Twister
chain method and Open MPI MPI_Bcast
Performance comparison of Twister chain
method and MPJ broadcasting method
(MPJ 2GB is prediction only)
Chain method with/without topologyawareness
The new topology-aware chain broadcasting algorithm gives 20% better performance than
best C/C++ MPI methods (four times faster than Java MPJ)
A factor of 5 improvement over non-optimized (for topology) pipeline-based method over
150 nodes.
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SALSA
Broadcast Comparison: Local Aggregation
Comparison between shuffling with and
without local aggregation
Communication cost per iteration of the
image clustering application
Left figure shows the time cost on shuffling is only 10% of the original time
Right figure presents the collective communication cost per iteration, which is 169
seconds (less than 3 minutes).
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SALSA
Triangle Inequality and Kmeans
Dominant part of Kmeans algorithm is finding nearest center to each point
O(#Points * #Clusters * Vector Dimension)
Simple algorithms find
min over centers c: d(x, c) = distance(point x, center c)
But most of d(x, c) calculations are wasted, as they are much larger than
minimum value
Elkan [1] showed how to use triangle inequality to speed up
relations like:
d(x, c) >= d(x, c-last) – d(c, c-last)
c-last position of center at last iteration
So compare d(x,c-last) – d(c, c-last) with d(x, c-best) where c-best is nearest
cluster at last iteration
Complexity reduced by a factor = Vector Dimension, and so this is important in
clustering high dimension spaces such as social imagery with 512 or more
features per image
[1] Charles Elkan, Using the triangle inequality to accelerate k-means, in TWENTIETH INTERNATIONAL CONFERENCE ON
MACHINE LEARNING, Tom Fawcett and Nina Mishra, Editors. August 21-24, 2003. Washington DC. pages. 147-153.
SALSA
Fast Kmeans Algorithm
d(x(P), m(now, c1)) ≥ d(x(P), m(last, c1)) – d(m(now, c1), m(last, c1))
(1)
lower_bound = d(x(P), m(last, c)) – d(m(now, c), m(last, c)) ≥
d(x(P), m(last, c - current_best))
(2)
Graph shows fraction of distances d(x, c) calculated in each iteration
for a test data set
200K points, 124 centers, Vector Dimension 74
SALSA
Results on Fast Kmeans Algorithm
Histograms of distance distributions for 3200 clusters for 76800 points in a 2048 dimensional space.
The distances of points to their nearest center is shown as triangles; the distance to other centers
(further away) as crosses; the distances between centers are the filled circles
SALSA
Data Analysis Architecture
Applications/
Algorithms
Support Scientific Simulations (Data Mining and Data Analysis)
Kernels, Genomics, Proteomics, Information Retrieval, Polar Science,
Scientific Simulation Data Analysis and Management, Dissimilarity
Computation, Clustering, Multidimensional Scaling, Generative Topological
Mapping
Security, Provenance, Portal
Services and Workflow
Programming
Model
Runtime
Storage
Infrastructure
Hardware
High Level Language
Cross Platform Iterative MapReduce (Collectives, Fault Tolerance, Scheduling)
Distributed File Systems
Object Store
Windows Server
Linux HPC Amazon Cloud
HPC
Bare-system
Bare-system
Virtualization
CPU Nodes
Data Parallel File System
Azure Cloud
Virtualization
Grid
Appliance
GPU Nodes
SALSA