1. 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 1

2. 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 2

3. Deterministic Annealing
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

4. Deterministic Annealing Clustering (DAC)
N data points E(x) in D dim. space and Minimize F by EM
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 center Y(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 4

5. Deterministic Annealing Clustering of Indiana Census Data
Decrease temperature (distance scale) to discover more clusters
Distance Scale Temperature0.5

6. 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”

7. Generative Topographic Mapping (GTM)
N data points E(x) in D dim. space and Minimize F by EM
a(x) = 1 and g(k) = (1/K)(/2)D/2
s(k) = 1/  and T = 1
Y(k) = m=1M Wmm(X(k))
Choose fixed m(X) = exp( (X-m)2/2 )
Vary Wm and  but fix values of M and K a priori
Y(k) E(x) Wm are vectors in original high D dimension space
X(k) and m are vectors in 2 dimensional mapped space
Generative Topographic Mapping (GTM)
Deterministic Annealing Gaussian Mixture models (DAGM)
a(x) = 1
g(k)={Pk/(2(k)2)D/2}1/T
s(k)= (k)2 (taking case of spherical Gaussian)
T is annealing temperature varied down from  with final value of 1
Vary Y(k) Pk and (k)
K starts at 1 and is incremented by algorithm
As DAGM but set T=1 and fix K
Traditional Gaussian
mixture models GM
GTM has several natural annealing versions based on either DAC or DAGM: under investigation
DAMDS different form as different Gibbs distribution (different E0)
DAGTM: Deterministic Annealed Generative Topographic Mapping
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 center Y(k) but can calculate weight Pk and correlation matrix s(k) = (k)2 (even for matrix (k)2) using IDENTICAL formulae for Gaussian mixtures
K starts at 1 and is incremented by algorithm
SALSA 7

8. SALSA Speedup = Number of cores/(1+f)
f = (Sum of Overheads)/(Computation per core)
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
SALSA 8

9. Runtime System Used
We implement micro-parallelism using Microsoft CCR (Concurrency and Coordination Runtime) as it supports both MPI rendezvous and dynamic (spawned) threading style of parallelism
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

10. MPI Exchange Latency in µs (20-30 µs computation between messaging)
Machine OS
Runtime
Grains
Parallelism
MPI Latency
Intel8c:gf12
(8 core
2.33 Ghz)
(in 2 chips)
Redhat
MPJE(Java)
Process 8
181
MPICH2 (C)
40.0
MPICH2:Fast
39.3
Nemesis
4.21
Intel8c:gf20
Fedora
MPJE
157
mpiJava
111
MPICH2
64.2
Intel8b
2.66 Ghz)
Vista
170
142
100
CCR (C#)
Thread
20.2
AMD4
(4 core
2.19 Ghz) XP 4
185
152
99.4
CCR
16.3
Intel(4 core)
25.8
Messaging CCR versus MPI C# v. C v. Java
SALSA 10

11. 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
GTM Projection of 2 clusters of 335 compounds in 155 dimensions
Linear PCA v. nonlinear GTM on 6 Gaussians in 3D
PCA is Principal Component Analysis
SALSA 11

12. Multidimensional Scaling MDS
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

13. Better ways to do this ? 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

14. Deterministically Annealed MDS (DAMDS)
(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

15. Deterministic Annealing for Pairwise Clustering
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

16. Parallel Programming Strategy
“Main Thread” and Memory M 1 m1 m0 2 m2 3 m3 4 m4 5 m5 6 m6 7 m7
Subsidiary threads t with memory mt
MPI/CCR/DSS
From other nodes
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

18. Services can be used where loose coupling natural
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

19. Several engineering issues for use in large applications
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 cross-cluster 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