1. 1 High Performance Robust Datamining for Cheminformatics Division of Chemical Information Session: Cheminformatics: From Teaching to Research ACS Spring Meeting New Orleans April 8 2008 Geoffrey Fox Community Grids Laboratory, School of informatics Indiana University http://www.chembiogrid.org http://www.infomall.org/multicore gcf@indiana.edugcf@indiana.edu, http://www.infomall.orghttp://www.infomall.org

2. Too much Computing? Historically both grids and parallel computing have tried to increase computing capabilities by Optimizing performance of codes at cost of re-usability Exploiting all possible CPU’s such as Graphics co- processors and “idle cycles” (across administrative domains) Linking central computers together such as NSF/DoE/DoD supercomputer networks without clear user requirements Next Crisis in technology area will be the opposite problem – commodity chips will be 32-128way parallel in 5 years time and we currently have no idea how to use them on commodity systems – especially on clients Only 2 releases of standard software (e.g. Office) in this time span so need solutions that can be implemented in next 3-5 years Intel RMS analysis: Gaming and Generalized decision support (data mining) are ways of using these cycles

3. Intel’s Projection

4. Too much Data to the Rescue? Multicore servers have clear “universal parallelism” as many users can access and use machines simultaneously Maybe also need application parallelism (e.g. datamining) as needed on client machines Over next years, we will be submerged of course in data deluge Scientific observations for e-Science including cheminformatics (high throughput screening) Local (video, environmental) sensors Data fetched from Internet defining users interests Maybe data-mining of this “too much data” will use up the “too much computing” both for science and commodity PC’s PC will use this data(-mining) to be intelligent user assistant? Must have highly parallel algorithms and new algorithms for large datasets

5. CICC Chemical Informatics and Cyberinfrastructure Collaboratory Web Service Infrastructure Portal Services RSS Feeds User Profiles Collaboration as in Sakai Core Grid Services Service Registry Job Submission and Management Local Clusters IU Big Red, TeraGrid, Open Science Grid Varuna.net Quantum Chemistry OSCAR Document Analysis InChI Generation/Search Computational Chemistry (Gamess, Jaguar etc.) Need to make all this parallel Hide parallelism in service Dimension Reduction Embedding

6. Service Aggregated Linked Sequential Activities 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 Team (funded by Geoffrey Fox Microsoft) Xiaohong Qiu Seung-Hee Bae Huapeng Yuan Indiana University Technology Collaboration George Chrysanthakopoulos Henrik Frystyk Nielsen Microsoft Application Collaboration Cheminformatics (funded by NIH Rajarshi Guha ECCR) David Wild Bioinformatics Haiku Tang Demographics (GIS) Neil Devadasan IU Bloomington and IUPUI SALSASALSA

7. Unsupervised Modeling Find clusters without prejudice Model distribution as clusters formed from Gaussian distributions with general shape Both can use multi-resolution annealing SALSASALSA N data points X(x) in D dimensional space OR points with dissimilarity  ij defined between them General Problem Classes 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)

8.  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  =  exp(-E 0 /T) F over the Gibbs distribution P 0 = exp(-E 0 /T) using an energy function E 0 similar to E but for which integrals can be calculated  E 0 = E for clustering and related problems  General simple choice is E 0 =  (x i -  i ) 2 where x i parameters to be annealed  E.g. MDS has quartic E and replace this by quadratic E 0

9. 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 4 th most cited article but little used; probably as no good software compared to simple K-means Avoid local minima SALSASALSA N data points E(x) in D dim. space and Minimize F by EM

10. Deterministic Annealing Clustering of Indiana Census Data Decrease temperature (distance scale) to discover more clusters Distance Scale Temperature 0.5

11.  Minimum evolving as temperature decreases  Movement at fixed temperature going to local minima if not initialized “correctly” Solve Linear Equations for each temperature Nonlinearity removed by approximating with solution at previous higher temperature Deterministic Annealing F({Y}, T) Configuration {Y}

12. 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 P k 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 Deterministic Annealing Gaussian Mixture models (DAGM ) a(x) = 1 g(k)={P k /(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) P k and  (k) K starts at 1 and is incremented by algorithm SALSASALSA 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=1 M W m  m (X(k)) Choose fixed  m (X) = exp( - 0.5 (X-  m ) 2 /  2 ) Vary W m and  but fix values of M and K a priori Y(k) E(x) W m are vectors in original high D dimension space X(k) and  m are vectors in 2 dimensional mapped space Generative Topographic Mapping (GTM) 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 E 0 ) DAGTM: Deterministic Annealed Generative Topographic Mapping

13. 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 SALSASALSA

14.  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/ 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 SALSASALSA

15. MPI Exchange Latency in µs (20-30 µs computation between messaging) MachineOSRuntimeGrainsParallelismMPI Latency Intel8c:gf12 (8 core 2.33 Ghz) (in 2 chips) RedhatMPJE(Java)Process8181 MPICH2 (C)Process840.0 MPICH2:FastProcess839.3 NemesisProcess84.21 Intel8c:gf20 (8 core 2.33 Ghz) FedoraMPJEProcess8157 mpiJavaProcess8111 MPICH2Process864.2 Intel8b (8 core 2.66 Ghz) VistaMPJEProcess8170 FedoraMPJEProcess8142 FedorampiJavaProcess8100 VistaCCR (C#)Thread820.2 AMD4 (4 core 2.19 Ghz) XPMPJEProcess4185 RedhatMPJEProcess4152 mpiJavaProcess499.4 MPICH2Process439.3 XPCCRThread416.3 Intel(4 core)XPCCRThread425.8 SALSASALSA Messaging CCR versus MPI C# v. C v. Java

16. GTM Projection of 2 clusters of 335 compounds in 155 dimensions 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 PCAGTM Linear PCA v. nonlinear GTM on 6 Gaussians in 3D PCA is Principal Component Analysis Parallel Generative Topographic Mapping GTM Reduce dimensionality preserving topology and perhaps distances Here project to 2D SALSASALSA

17.  Minimize Stress  (X) =  i<j =1 n weight(i,j) (  ij - d(X i, X j )) 2   ij are input dissimilarities and d(X i, X j ) 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

18.  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 =1 n weight(i,j) (d(X i, X j ) + 2T(l+2)-  ij ) 2  Where T annealing temperature and l dimension of embedding space (2 in example)  d(X i, X j ) = (X i – X i ) 2 in l dimensional latent space   ij is dissimilarity in original space

19.   (X,T) =  i<j =1 n weight(i,j) (d(X i, X j ) + 2T(l+2)-  ij ) 2  Note that that at T= , 2T(l+2)-  ij is positive and all points X i 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 X i as “particles” moving under influence of forces with other points. Forces are in direction of vector between particles  Attractive: d(X i, X j ) >  ij - 2T(l+2)  Repulsive: d(X i, X j ) <  ij - 2T(l+2)  Can use iterative method based on this particle dynamics analogy and this makes (deterministic) annealing quite natural

20.  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) “Main Thread” and Memory M 1m11m1 0m00m0 2m22m2 3m33m3 4m44m4 5m55m5 6m66m6 7m77m7 Subsidiary threads t with memory m t MPI/CCR/DSS From other nodes MPI/CCR/DSS From other nodes SALSASALSA

22.  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 SALSASALSA

23.  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  Clustering with pairwise distances but no vector spaces. Deterministic annealing here well understood but even less used  Bourgain Random Projection for metric embedding  Support use of Newton’s Method (Marquardt’s method) as EM alternative  Later HMM and SVM SALSASALSA