Transcript High Performance Data mining on Multicore Systems

Service Aggregated Linked Sequential Activities
SALSA Team
Geoffrey Fox
Xiaohong Qiu
Seung-Hee Bae
Huapeng Yuan
Indiana University
Technology Collaboration
George Chrysanthakopoulos
Henrik Frystyk Nielsen
Microsoft
Application Collaboration
Cheminformatics
Rajarshi Guha
David Wild
Bioinformatics
Haiku Tang
Demographics (GIS)
Neil Devadasan
IU Bloomington and IUPUI
GOALS: Increasing number of cores
accompanied by continued data deluge
Develop scalable parallel data mining
algorithms with good multicore and
cluster performance; understand
software runtime and parallelization
method. Use managed code (C#) and
package algorithms as services to
encourage broad use assuming
experts parallelize core algorithms.
CURRENT RESUTS: Microsoft CCR supports MPI,
dynamic threading and via DSS a Service model of
computing; detailed performance measurements
Speedups of 7.5 or above on 8-core systems for
“large problems” with deterministic annealed (avoid
local minima) algorithms for clustering, Gaussian
Mixtures, GTM and MDS (dimensional reduction) etc.
SALSA
General Problem Classes
N data points X(x) in D dimensional space OR
points with dissimilarity ij defined between them
Unsupervised Modeling
• Find clusters without prejudice
• Model distribution as clusters formed from
Gaussian distributions with general shape
• Both can use multi-resolution annealing
Dimensional Reduction/Embedding
• Given vectors, map into lower dimension space
“preserving topology” for visualization: SOM and GTM
• Given ij associate data points with vectors in a
Euclidean space with Euclidean distance approximately
ij : MDS (can anneal) and Random Projection
Data Parallel over N data points X(x)
SALSA


Minimize Free Energy F = E-TS where E objective function
(energy) and S entropy.
Reduce temperature T logarithmically; T=  is dominated by
Entropy, T small by objective function





S regularizes E in a natural fashion
In simulated annealing, use Monte Carlo but in deterministic
annealing, use mean field averages
<F> =  exp(-E0/T) F over the Gibbs distribution
P0 = exp(-E0/T) using an energy function E0 similar to E but for
which integrals can be calculated
E0 = E for clustering and related problems
General simple choice is E0 =  (xi - i)2 where xi parameters to be
annealed

E.g. MDS has quartic E and replace this by quadratic E0
N data points E(x) in D dim. space and Minimize F by EM
N
N
x 1
x 1
2 2
F  F
T
 aT( x
) ln{
p(
x) ln{
g
(
k
)
exp[
exp[


0.5(
(
X
(
X
x
(
)
x

)
Y

(
Y
k
(
))
k
))/ T/](Ts (k ))]
k 1  k 1
K
K
Deterministic Annealing Clustering (DAC)
• a(x) = 1/N or generally p(x) with  p(x) =1
• g(k)=1 and s(k)=0.5
• T is annealing temperature varied down from 
with final value of 1
• Vary cluster centerY(k)
• K starts at 1 and is incremented by algorithm;
pick resolution NOT number of clusters
• My 4th most cited article but little used; probably
as no good software compared to simple K-means
• Avoid local minima
SALSA
Deterministic Annealing Clustering of Indiana Census Data
Decrease temperature (distance scale) to discover more clusters
Distance Scale
Temperature0.5
Deterministic
Annealing
F({Y}, T)
Solve Linear
Equations for
each
temperature
Nonlinearity
removed by
approximating
with solution
at previous
higher
temperature
Configuration {Y}

Minimum evolving as temperature decreases

Movement at fixed temperature going to local
minima if not initialized “correctly”
N data points E(x) in D dim. space and Minimize F by EM
N
F  T  a ( x) ln{ k 1 g (k ) exp[0.5( X ( x)  Y (k )) 2 / (Ts (k ))]
K
x 1
Generative
Topographic
Mapping
(GTM)
Deterministic
Traditional
Annealing
Gaussian
Clustering
(DAC)
Deterministic
Annealing
Gaussian
models
GM
D/2 with
= 1/N
or
generally
p(x)
 p(x) =1
Mixture
models
(DAGM)
• a(x) •=a(x)
1 and
g(k)
=mixture
(1/K)(/2)
• As
DAGM
but set T=1 and fix K
g(k)=1
and
s(k)=0.5
• s(k)••=a(x)
1/ =and
T
=
1
1
M
•
T
is
annealing
temperature
varied down from 
•Y(k)• =g(k)={P
m=1
W

(X(k))
2
D/2
1/T
m
m
) }
DAGTM:
Deterministic
Annealed
k/(2(k)
2/2 )
with
final
value
of
1
• Choose
fixed

2
(X)
=
exp(
0.5
(X-
)
m
• s(k)=
(k) m(takingTopographic
case of spherical
Gaussian)
Generative
Mapping
• Varyand
cluster
but
can
weight
• Vary
 butcenterY(k)
fix values of
Mvaried
andcalculate
Kdown
a priori
mannealing
• TW
is
temperature
from

2
•
GTM
has
several
natural
annealing
PE(x)
correlation
matrix
s(k) =high
(k) D(even
for space
•Y(k)with
Wm
are
vectors
in original
dimension
k and
final
value
of
1
2)based
versions
on
either DAC
or DAGM:
matrix
(k)
using
IDENTICAL
formulae
for space
• X(k)• and

are
vectors
in
2
dimensional
mapped
m
Vary
Y(k)investigation
Pk and (k)
under
Gaussian
mixtures
• K starts at 1 and is incremented by algorithm
•K starts at 1 and is incremented by algorithm
• DAMDS different form as different
Gibbs distribution (different E0)
SALSA
Multicore Matrix Multiplication
(dominant linear algebra in GTM)
Speedup = Number of cores/(1+f)
f = (Sum of Overheads)/(Computation per core)
10,000.00
Execution Time
Seconds 4096X4096 matrices
Computation  Grain Size n . # Clusters K
Overheads are
Synchronization: small with CCR
Load Balance: good
Memory Bandwidth Limit:  0 as K  
Cache Use/Interference: Important
Runtime Fluctuations: Dominant large n, K
All our “real” problems have f ≤ 0.05 and
speedups on 8 core systems greater than 7.6
1 Core
1,000.00
Parallel Overhead
 1%
8 Cores
100.00
Block Size
10.00
1
0.14
10
100
1000
10000
Parallel GTM Performance
0.12
Fractional
Overhead
f
0.1
0.08
0.06
4096 Interpolating Clusters
0.04
0.02
1/(Grain Size n)
0
0
0.002
n = 500
0.004
0.006
0.008
0.01
100
0.012
0.014
0.016
0.018
0.02
50 SALSA

We implement micro-parallelism using Microsoft CCR
(Concurrency and Coordination Runtime) as it supports both MPI rendezvous
and dynamic (spawned) threading style of parallelism
http://msdn.microsoft.com/robotics/

CCR Supports exchange of messages between threads using named ports
and has primitives like:
 FromHandler: Spawn threads without reading ports
 Receive: Each handler reads one item from a single port
 MultipleItemReceive: Each handler reads a prescribed number of items of
a given type from a given port. Note items in a port can be general
structures but all must have same type.
 MultiplePortReceive: Each handler reads a one item of a given type from
multiple ports.

CCR has fewer primitives than MPI but can implement MPI collectives
efficiently

Use DSS (Decentralized System Services) built in terms of CCR for service
model

DSS has ~35 µs and CCR a few µs overhead
SALSA
MPI Exchange Latency in µs (20-30 µs computation between messaging)
Machine
Intel8c:gf12
(8 core
2.33 Ghz)
(in 2 chips)
Intel8c:gf20
(8 core
2.33 Ghz)
Intel8b
(8 core
2.66 Ghz)
AMD4
(4 core
2.19 Ghz)
Intel(4 core)
OS
Runtime
Grains
Parallelism
MPI Latency
Redhat
MPJE(Java)
Process
8
181
MPICH2 (C)
Process
8
40.0
MPICH2:Fast
Process
8
39.3
Nemesis
Process
8
4.21
MPJE
Process
8
157
mpiJava
Process
8
111
MPICH2
Process
8
64.2
Vista
MPJE
Process
8
170
Fedora
MPJE
Process
8
142
Fedora
mpiJava
Process
8
100
Vista
CCR (C#)
Thread
8
20.2
XP
MPJE
Process
4
185
Redhat
MPJE
Process
4
152
mpiJava
Process
4
99.4
MPICH2
Process
4
39.3
XP
CCR
Thread
4
16.3
XP
CCR
Thread
4
25.8
Fedora
Messaging CCR versus MPI
C# v. C v. Java
SALSA
Parallel Generative Topographic Mapping GTM
Reduce dimensionality preserving
topology and perhaps distances
Here project to 2D
GTM Projection of PubChem:
10,926,94 compounds in 166
dimension binary property space takes
4 days on 8 cores. 64X64 mesh of GTM
clusters interpolates PubChem. Could
usefully use 1024 cores! David Wild will
use for GIS style 2D browsing interface
to chemistry
PCA
GTM
Linear PCA v. nonlinear GTM on 6 Gaussians in 3D
PCA is Principal Component Analysis
GTM Projection of 2 clusters
of 335 compounds in 155
SALSA
dimensions




Minimize Stress
(X) = i<j=1n weight(i,j) (ij - d(Xi , Xj))2
ij are input dissimilarities and d(Xi , Xj) the Euclidean distance
squared in embedding space (2D here)
SMACOF or Scaling by minimizing a complicated function is clever
steepest descent algorithm
Use GTM to initialize SMACOF
SMACOF
GTM




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

Use deterministically annealed version of GTM
Do not use GTM at all but rather find clusters by DAC
algorithm and then use MDS iteratively with one point
(cluster center) added each iteration
and/or use Newton’s method for MDS as only thousands
of parameters (# clusters times dimension l)
and/or use deterministically annealed MDS (DAMDS)
(X,T) = i<j=1n weight(i,j) (d(Xi , Xj) + 2T(l+2)- ij )2
Where T annealing temperature and l dimension of
embedding space (2 in example)
d(Xi , Xj) = (Xi – Xi)2 in l dimensional latent space
ij is dissimilarity in original space






(X,T) = i<j=1n weight(i,j) (d(Xi , Xj) + 2T(l+2)- ij )2
Note that that at T=, 2T(l+2)- ij is positive and all
points Xi are at origin. As T decreases, the terms with
large ij become negative and associated points gradually
expand from origin
“Physical Optimization”: Think of points Xi as “particles”
moving under influence of forces with other points.
Forces are in direction of vector between particles
Attractive: d(Xi , Xj) > ij - 2T(l+2)
Repulsive: d(Xi , Xj) < ij - 2T(l+2)
Can use iterative method based on this particle dynamics
analogy and this makes (deterministic) annealing quite
natural






Developed (partially) by Hofmann and Buhmann in 1997 but little
or no application
Applicable in cases where no (clean) vectors associated with points
HPC = 0.5 i=1N j=1N d(i, j) k=1K Mi(k) Mj(k) / C(k)
Mi(k) is probability that point I belongs to cluster k
C(k) = i=1N Mi(k) is number of points in k’th cluster
Mi(k)  exp( -i(k)/T ) with Hamiltonian i=1N k=1K Mi(k) i(k)
3D MDS
3 Clusters in sequences of length  300
PCA
2D MDS
“Main Thread” and Memory M
MPI/CCR/DSS
From other nodes
MPI/CCR/DSS
From other nodes
0
m0
1
m1
2
m2
3
m3
4
m4
5
m5
6
m6
7
m7
Subsidiary threads t with memory mt

Use Data Decomposition as in classic distributed memory
but use shared memory for read variables. Each thread
uses a “local” array for written variables to get good cache
performance

Multicore and Cluster use same parallel algorithms but
different runtime implementations; algorithms are
 Accumulate matrix and vector elements in each process/thread
 At iteration barrier, combine contributions (MPI_Reduce)
 Linear Algebra (multiplication, equation solving, SVD)
SALSA


All parallel algorithms packaged as services and not traditional
libraries
MPI-Style Micro-parallelism uses low latency CCR threads or MPI
processes


CCR microseconds; local services 10’s microseconds; distributed services
milliseconds
Services can be used where loose coupling natural


Input data
Algorithms
 PCA
 DAC GTM GM DAGM DAGTM – both for complete algorithm and for each
iteration
 Linear Algebra used inside or outside above
 Metric embedding MDS, Bourgain, Quadratic Programming ….
 HMM, SVM ….

User interface: GIS (Web map Service) or equivalent
SALSA






This class of data mining does/will parallelize well on current/future
multicore nodes
Several engineering issues for use in large applications
 How to take CCR in multicore node to cluster (MPI or crosscluster CCR?)
 Use Google MapReduce on Cloud/Grid
 Need high performance linear algebra for C# (PLASMA from
UTenn)
 Access linear algebra services in a different language?
 Need equivalent of Intel C Math Libraries for C# (vector
arithmetic – level 1 BLAS)
 Service model to integrate modules
Although work used C#, similar results in C, C++, Java, Fortran
Future work is more applications; any suggestions?
Refine current algorithms such as DAGTM, SMACOF, DAMDS
New parallel algorithms
 Bourgain Random Projection for metric embedding
 Support use of Newton’s Method (Marquardt’s method) as EM
alternative
 Later HMM and SVM
SALSA