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.edu, http://www.infomall.org 1 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 coprocessors 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 Intel’s Projection 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 CICC Chemical Informatics and Cyberinfrastructure Collaboratory Web Service Infrastructure Cheminformatics Services Statistics Services Database Services Core functionality Fingerprints Similarity Descriptors 2D diagrams File format conversion Computation functionality Regression Classification Clustering Sampling distributions Dimension Reduction Embedding 3D structures by CID SMARTS 3D Similarity Docking scores/poses by CID SMARTS Protein Docking scores Applications Applications Docking Predictive models Filtering Feature selection Druglikeness 2D plots Toxicity predictions Arbitrary R code (PkCell) Mutagenecity predictions Need to make PubChem related data by Anti-cancer activity predictions all this parallel Pharmacokinetic parameters CID, SMARTS Hide parallelism OSCAR Document Analysis in service InChI Generation/Search Computational Chemistry (Gamess, Jaguar etc.) Core Grid Services Service Registry Job Submission and Management Local Clusters IU Big Red, TeraGrid, Open Science Grid Varuna.net Quantum Chemistry Portal Services RSS Feeds User Profiles Collaboration as in Sakai Service Aggregated Linked Sequential Activities 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 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 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 “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 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 SALSA