visualizing and clustering life science applications in parallel
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Visualizing and Clustering Life Science Applications in Parallel
HiCOMB 2015 14th IEEE International Workshop onHigh Performance Computational Biology at IPDPS 2015
Hyderabad, India
May 25 2015Geoffrey Fox
[email protected] http://www.infomall.org
School of Informatics and ComputingDigital Science Center
Indiana University Bloomington5/25/2015
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Deterministic AnnealingAlgorithms
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Some Motivation• Big Data requires high performance – achieve with parallel computing• Big Data sometimes requires robust algorithms as more opportunity
to make mistakes• Deterministic annealing (DA) is one of better approaches to robust
optimization and broadly applicable– Started as “Elastic Net” by Durbin for Travelling Salesman Problem
TSP– Tends to remove local optima– Addresses overfitting– Much Faster than simulated annealing
• Physics systems find true lowest energy state if you anneal i.e. you equilibrate at each temperature as you cool
• Uses mean field approximation, which is also used in “Variational Bayes” and “Variational inference”5/25/2015 3
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(Deterministic) Annealing• Find minimum at high temperature when trivial• Small change avoiding local minima as lower temperature• Typically gets better answers than standard libraries- R and Mahout• And can be parallelized and put on GPU’s etc.
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General Features of DA• In many problems, decreasing temperature is classic
multiscale – finer resolution (√T is “just” distance scale)• In clustering √T is distance in space of points (and
centroids), for MDS scale in mapped Euclidean space• T = ∞, all points are in same place – the center of universe• For MDS all Euclidean points are at center and distances
are zero. For clustering, there is one cluster• As Temperature lowered there are phase transitions in
clustering cases where clusters split– Algorithm determines whether split needed as second derivative
matrix singular• Note DA has similar features to hierarchical methods and
you do not have to specify a number of clusters; you need to specify a final distance scale 55/25/2015
Math of Deterministic Annealing• H() is objective function to be minimized as a function of
parameters (as in Stress formula given earlier for MDS)• Gibbs Distribution at Temperature T
P() = exp( - H()/T) / d exp( - H()/T)• Or P() = exp( - H()/T + F/T ) • Use the Free Energy combining Objective Function and Entropy
F = < H - T S(P) > = d {P()H + T P() lnP()}• Simulated annealing performs these integrals by Monte Carlo• Deterministic annealing corresponds to doing integrals analytically
(by mean field approximation) and is much much faster • Need to introduce a modified Hamiltonian for some cases so that
integrals are tractable. Introduce extra parameters to be varied so that modified Hamiltonian matches original
• In each case temperature is lowered slowly – say by a factor 0.95 to 0.9999 at each iteration5/25/2015 6
Some Uses of Deterministic Annealing DA• Clustering improved K-means
– Vectors: Rose (Gurewitz and Fox 1990 – 486 citations encouraged me to revisit) – Clusters with fixed sizes and no tails (Proteomics team at Broad)
– No Vectors: Hofmann and Buhmann (Just use pairwise distances)
• Dimension Reduction for visualization and analysis
– Vectors: GTM Generative Topographic Mapping
– No vectors SMACOF: Multidimensional Scaling) MDS (Just use pairwise distances)
• Can apply to HMM & general mixture models (less study)
– Gaussian Mixture Models
– Probabilistic Latent Semantic Analysis with Deterministic Annealing DA-PLSA as alternative to Latent Dirichlet Allocation for finding “hidden factors”
• Have scalable parallel versions of much of above – mainly Java
• Many clustering methods – not clear what is best although DA pretty good and improves K-means at increased computing cost which is not always useful
• DA clearly improves MDS which is ~only reliable” dimension reduction?5/25/2015 7
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Clusters v. Regions
• In Lymphocytes clusters are distinct; DA useful• In Pathology, clusters divide space into regions and
sophisticated methods like deterministic annealing are probably unnecessary
Pathology 54D
Lymphocytes 4D
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Some Problems we are working on• Analysis of Mass Spectrometry data to find peptides by
clustering peaks (Broad Institute/Hyderabad)– ~0.5 million points in 2 dimensions (one collection) -- ~ 50,000
clusters summed over charges
• Metagenomics – 0.5 million (increasing rapidly) points NOT in a vector space – hundreds of clusters per sample– Apply MDS to Phylogenetic trees
• Pathology Images >50 Dimensions• Social image analysis is in a highish dimension vector space
– 10-50 million images; 1000 features per image; million clusters
• Finding communities from network graphs coming from Social media contacts etc.5/25/2015
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MDS and Clustering on ~60K EMR
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Colored by Sample – not clustered.Distances from vectors in word space. This 128 4mers for ~200K sequences
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Examples of current DA algorithms: LCMS
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Background on LC-MS• Remarks of collaborators – Broad Institute/Hyderabad• Abundance of peaks in “label-free” LC-MS enables large-scale comparison of
peptides among groups of samples. • In fact when a group of samples in a cohort is analyzed together, not only is it
possible to “align” robustly or cluster the corresponding peaks across samples, but it is also possible to search for patterns or fingerprints of disease states which may not be detectable in individual samples.
• This property of the data lends itself naturally to big data analytics for biomarker discovery and is especially useful for population-level studies with large cohorts, as in the case of infectious diseases and epidemics.
• With increasingly large-scale studies, the need for fast yet precise cohort-wide clustering of large numbers of peaks assumes technical importance.
• In particular, a scalable parallel implementation of a cohort-wide peak clustering algorithm for LC-MS-based proteomic data can prove to be a critically important tool in clinical pipelines for responding to global epidemics of infectious diseases like tuberculosis, influenza, etc.
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Proteomics 2D DA Clustering T= 25000 with 60 Clusters (will be 30,000 at T=0.025)
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The brownish triangles are “sponge” (soaks up trash) peaks outside any cluster. The colored hexagons are peaks inside clusters with the white hexagons being determined cluster center
Fragment of 30,000 Clusters241605 Points
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Continuous Clustering• This is a very useful subtlety introduced by Ken Rose but not widely known
although it greatly improves algorithm• Take a cluster k to be split into 2 with centers Y(k)A and Y(k)B with initial
values Y(k)A = Y(k)B at original center Y(k)• Then typically if you make this change
and perturb the Y(k)A and Y(k)B, they will return to starting position as F at stable minimum (positive eigenvalue)
• But instability (the negative eigenvalue) can develop and one finds
• Implement by adding arbitrary number p(k) of centers for each cluster Zi = k=1
K p(k) exp(-i(k)/T) and M step gives p(k) = C(k)/N• Halve p(k) at splits; can’t split easily in standard case p(k) = 1• Show weighting in sums like Zi now equipoint not equicluster as p(k)
proportional to points C(k) in cluster
Free Energy F
Y(k)A and Y(k)B
Y(k)A + Y(k)B
Free Energy F Free Energy F
Y(k)A - Y(k)B
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Trimmed Clustering• Clustering with position-specific constraints on variance: Applying
redescending M-estimators to label-free LC-MS data analysis (Rudolf Frühwirth , D R Mani and Saumyadipta Pyne) BMC Bioinformatics 2011, 12:358
• HTCC = k=0K i=1
N Mi(k) f(i,k)– f(i,k) = (X(i) - Y(k))2/2(k)2 k > 0– f(i,0) = c2 / 2 k = 0
• The 0’th cluster captures (at zero temperature) all points outside clusters (background)
• Clusters are trimmed (X(i) - Y(k))2/2(k)2 < c2 / 2
• Relevant when well defined errors
T ~ 0T = 1
T = 5
Distance from cluster center
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1.00E-031.00E-021.00E-011.00E+001.00E+011.00E+021.00E+031.00E+041.00E+051.00E+060
10000
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DAVS(2) DA2D
Temperature
Clus
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ount
Start Sponge DAVS(2)
Add Close Cluster Check
Sponge Reaches final value
Cluster Count v. Temperature for 2 Runs
• All start with one cluster at far left• T=1 special as measurement errors divided out• DA2D counts clusters with 1 member as clusters. DAVS(2) does not5/25/2015 18
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Simple Parallelism as in k-means• Decompose points i over processors• Equations either pleasingly parallel “maps” over i• Or “All-Reductions” summing over i for each cluster• Parallel Algorithm:
– Each process holds all clusters and calculates contributions to clusters from points in node
– e.g. Y(k) = i=1N <Mi(k)> Xi / C(k)
• Runs well in MPI or MapReduce– See all the MapReduce k-means papers
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Better Parallelism• The previous model is correct at start but each point does
not really contribute to each cluster as damped exponentially by exp( - (Xi- Y(k))2 /T )
• For Proteomics problem, on average only 6.45 clusters needed per point if require (Xi- Y(k))2 /T ≤ ~40 (as exp(-40) small)
• So only need to keep nearby clusters for each point• As average number of Clusters ~ 20,000, this gives a factor
of ~3000 improvement• Further communication is no longer all global; it has
nearest neighbor components and calculated by parallelism over clusters which can be done in parallel if separated5/25/2015
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Speedups for several runs on Tempest from 8-way through 384 way MPI parallelism with one thread per process. We look at different choices for MPI processes which are either inside nodes or on separate nodes
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Parallelism within a Single Node of Madrid Cluster. A set of runs on 241605 peak data with a single node with 16 cores with either threads or MPI giving parallelism. Parallelism is either number of threads or number of MPI processes.
Parallelism (#threads or #processes)5/25/2015
METAGENOMICS -- SEQUENCE CLUSTERING
Non-metric SpacesO(N2) Algorithms – Illustrate Phase Transitions
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• Start at T= “” with 1 Cluster
• Decrease T, Clusters emerge at instabilities
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446K sequences~100 clusters
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METAGENOMICS -- SEQUENCE CLUSTERING
Non-metric SpacesO(N2) Algorithms – Compare Other Methods
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“Divergent” Data Sample23 True Clusters
CDhitUClust
Divergent Data Set UClust (Cuts 0.65 to 0.95) DAPWC 0.65 0.75 0.85 0.95Total # of clusters 23 4 10 36 91Total # of clusters uniquely identified 23 0 0 13 16(i.e. one original cluster goes to 1 uclust cluster )Total # of shared clusters with significant sharing 0 4 10 5 0(one uclust cluster goes to > 1 real cluster) Total # of uclust clusters that are just part of a real cluster 0 4 10 17(11) 72(62)(numbers in brackets only have one member) Total # of real clusters that are 1 uclust cluster 0 14 9 5 0but uclust cluster is spread over multiple real clusters Total # of real clusters that have 0 9 14 5 7significant contribution from > 1 uclust cluster
DA-PWC
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PROTEOMICS
No clear clusters
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Protein Universe Browser for COG Sequences with a few illustrative biologically identified clusters
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Heatmap of biology distance (Needleman-Wunsch) vs 3D Euclidean Distances
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If d a distance, so is f(d) for any monotonic f. Optimize choice of f5/25/2015
O(N2) ALGORITHMS?
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Algorithm Challenges• See NRC Massive Data Analysis report• O(N) algorithms for O(N2) problems • Parallelizing Stochastic Gradient Descent• Streaming data algorithms – balance and interplay between batch
methods (most time consuming) and interpolative streaming methods• Graph algorithms – need shared memory?• Machine Learning Community uses parameter servers; Parallel
Computing (MPI) would not recommend this?– Is classic distributed model for “parameter service” better?
• Apply best of parallel computing – communication and load balancing – to Giraph/Hadoop/Spark
• Are data analytics sparse?; many cases are full matrices• BTW Need Java Grande – Some C++ but Java most popular in ABDS,
with Python, Erlang, Go, Scala (compiles to JVM) …..5/25/2015 34
O(N2) interactions between green and purple clusters should be able to represent by centroids as in Barnes-Hut.
Hard as no Gauss theorem; no multipole expansion and points really in 1000 dimension space as clustered before 3D projection
O(N2) green-green and purple-purple interactions have value but green-purple are “wasted”
“clean” sample of 446K
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Use Barnes Hut OctTree, originally developed to make O(N2) astrophysics O(NlogN), to give similar speedups in machine learning
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OctTree for 100K sample of Fungi
We use OctTree for logarithmic interpolation (streaming data)
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Fungi Analysis
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Fungi Analysis• Multiple Species from multiple places• Several sources of sequences starting with 446K and eventually
boiled down to ~10K curated sequences with 61 species• Original sample – clustering and MDS• Final sample – MDS and other clustering methods• Note MSA and SWG gives similar results• Some species are clearly split• Some species are diffuse; others compact making a fixed distance
cut unreliable– Easy for humans!
• MDS very clear on structure and clustering artifacts• Why not do “high-value” clustering as interactive iteration driven
by MDS?5/25/2015 39
Fungi -- 4 Classic Clustering Methods
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Same Species
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Same Species Different Locations
Parallel Data Mining
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Parallel Data Analytics• Streaming algorithms have interesting differences but• “Batch” Data analytics is “just classic parallel computing” with usual
features such as SPMD and BSP • Expect similar systematics to simulations where• Static Regular problems are straightforward but• Dynamic Irregular Problems are technically hard and high level
approaches fail (see High Performance Fortran HPF)– Regular meshes worked well but– Adaptive dynamic meshes did not although “real people with MPI” could
parallelize• However using libraries is successful at either
– Lowest: communication level– Higher: “core analytics” level
• Data analytics does not yet have “good regular parallel libraries”– Graph analytics has most attention5/25/2015 46
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Remarks on Parallelism I• Maximum Likelihood or 2 both lead to objective functions like• Minimize sum items=1
N (Positive nonlinear function of unknown
parameters for item i)
• Typically decompose items i and parallelize over both i and parameters to be determined
• Solve iteratively with (clever) first or second order approximation to shift in objective function– Sometimes steepest descent direction; sometimes Newton– Have classic Expectation Maximization structure– Steepest descent shift is sum over shift calculated from each point
• Classic method – take all (millions) of items in data set and move full distance– Stochastic Gradient Descent SGD – take randomly a few hundred of
items in data set and calculate shifts over these and move a tiny distance
– SGD cannot parallelize over items
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Remarks on Parallelism II• Need to cover non vector semimetric and vector spaces for
clustering and dimension reduction (N points in space)• Semimetric spaces just have pairwise distances defined between
points in space (i, j) • MDS Minimizes Stress and illustrates this
(X) = i<j=1N weight(i,j) ((i, j) - d(Xi , Xj))2
• Vector spaces have Euclidean distance and scalar products– Algorithms can be O(N) and these are best for clustering but for MDS O(N)
methods may not be best as obvious objective function O(N2)– Important new algorithms needed to define O(N) versions of current O(N2) –
“must” work intuitively and shown in principle
• Note matrix solvers often use conjugate gradient – converges in 5-100 iterations – a big gain for matrix with a million rows. This removes factor of N in time complexity
• Ratio of #clusters to #points important; new clustering ideas if ratio >~ 0.1 5/25/2015
Problem Structure• Note learning networks have huge number of parameters (11 billion
in Stanford work) so that inconceivable to look at second derivative• Clustering and MDS have lots of parameters but can be practical to
look at second derivative and use Newton’s method to minimize• Parameters are determined in distributed fashion but are typically
needed globally – MPI use broadcast and “AllCollectives” implying Map-Collective is a useful
programming model– AI community: use parameter server and access as needed. Non-optimal?
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(1) Map Only(4) Point to Point or
Map-Communication
(3) Iterative Map Reduce or Map-Collective
(2) Classic MapReduce
Input
map
reduce
Input
map
reduce
IterationsInput
Output
map
Local
Graph
(5) Map-Streaming
maps brokers
Events
(6) Shared memory Map Communicates
Map & Communicate
Shared Memory
MDS in more detail
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WDA-SMACOF “Best” MDS• Semimetric spaces just have pairwise distances defined between
points in space (i, j) • MDS Minimizes Stress with pairwise distances (i, j)
(X) = i<j=1N weight(i,j) ((i, j) - d(Xi , Xj))2
• SMACOF clever Expectation Maximization method choses good steepest descent
• Improved by Deterministic Annealing reducing distance scale; DA does not impact compute time much and gives DA-SMACOF
• Classic SMACOF is O(N2) for uniform weight and O(N3) for non trivial weights but get nonuniform weight from– The preferred Sammon method weight(i,j) = 1/(i, j) or– Missing distances put in as weight(i,j) = 0
• Use conjugate gradient – converges in 5-100 iterations – a big gain for matrix with a million rows. This removes factor of N in time complexity and gives WDA-SMACOF5/25/2015
Timing of WDA SMACOF• 20k to 100k AM Fungal sequences on 600 cores
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Time Cost Comparison between WDA-SMA-COF with Equal Weights and Sammon's
MappingEqual Weights Sammon's Mapping
Data Size
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WDA-SMACOF Timing• Input Data: 100k to 400k AM Fungal sequences• Environment: 32 nodes (1024 cores) to 128 nodes (4096 cores) on
BigRed2.• Using Harp plug in for Hadoop (MPI Performance)
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Time Cost of WDA-SMACOF over Increas-ing Data Size
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Parallel Efficiency of WDA-SMACOF over Increasing Number of Processors
WDA-SMACOF (Harp)
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Spherical Phylogram• Take a set of sequences mapped to nD with MDS (WDA-SMACOF)
(n=3 or ~20)– N=20 captures ~all features of dataset?
• Consider a phylogenetic tree and use neighbor joining formulae to calculate distances of nodes to sequences (or later other nodes) starting at bottom of tree
• Do a new MDS fixing mapping of sequences noting that sequences + nodes have defined distances
• Use RAxML or Neighbor Joining (N=20?) to find tree• Random note: do not need Multiple Sequence Alignment;
pairwise tools are easier to use and give reliably good results
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RAxML result visualized in FigTree. Spherical Phylogram visualized in PlotViz for MSA or SWG distances
Spherical Phylograms
MSA
SWG
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Quality of 3D Phylogenetic Tree• EM-SMACOF is basic SMACOF• LMA was previous best method using Levenberg-Marquardt nonlinear 2
solver• WDA-SMACOF finds best result• 3 different distance measures
Sum of branch lengths of the Spherical Phylogram generated in 3D space on two datasets
MSA SWG NW0
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30Sum of Branches on 599nts Data
WDA-SMACOF LMA EM-SMACOF
Sum
of B
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MSA SWG NW0
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WDA-SMACOF LMA EM-SMACOF
Sum
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Summary• Always run MDS. Gives insight into data and performance
of machine learning– Leads to a data browser as GIS gives for spatial data– 3D better than 2D– ~20D better than MSA?
• Clustering Observations– Do you care about quality or are you just cutting up space into parts
– Deterministic Clustering always makes more robust– Continuous clustering enables hierarchy– Trimmed Clustering cuts off tails– Distinct O(N) and O(N2) algorithms
• Use Conjugate Gradient 575/25/2015
Java Grande
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Java Grande• We once tried to encourage use of Java in HPC with Java Grande
Forum but Fortran, C and C++ remain central HPC languages. – Not helped by .com and Sun collapse in 2000-2005
• The pure Java CartaBlanca, a 2005 R&D100 award-winning project, was an early successful example of HPC use of Java in a simulation tool for non-linear physics on unstructured grids.
• Of course Java is a major language in ABDS and as data analysis and simulation are naturally linked, should consider broader use of Java
• Using Habanero Java (from Rice University) for Threads and mpiJava or FastMPJ for MPI, gathering collection of high performance parallel Java analytics– Converted from C# and sequential Java faster than sequential C#
• So will have either Hadoop+Harp or classic Threads/MPI versions in Java Grande version of Mahout5/25/2015 59
Performance of MPI Kernel Operations
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Performance of MPI send and receive operations
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Performance of MPI allreduce operation
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Performance of MPI send and receive on Infiniband and Ethernet
Performance of MPI allreduce on Infinibandand Ethernet
Pure Java as in FastMPJ slower than Java interfacing to C version of MPI
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Java Grande and C# on 40K point DAPWC ClusteringVery sensitive to threads v MPI
64 Way parallel128 Way parallel 256 Way
parallel
TXPNodesTotal
C#Java
C# Hardware 0.7 performance Java Hardware
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Java and C# on 12.6K point DAPWC ClusteringJava
C##Threads x #Processes per node# NodesTotal Parallelism
Time hours
1x1 2x21x2 1x42x1 1x84x1 2x4 4x2 8x1#Threads x #Processes per node
C# Hardware 0.7 performance Java Hardware
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Data Analytics in SPIDAL
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Analytics and the DIKW Pipeline• Data goes through a pipeline
Raw data Data Information Knowledge Wisdom Decisions
• Each link enabled by a filter which is “business logic” or “analytics”• We are interested in filters that involve “sophisticated analytics”
which require non trivial parallel algorithms– Improve state of art in both algorithm quality and (parallel) performance
• Design and Build SPIDAL (Scalable Parallel Interoperable Data Analytics Library)
More Analytics KnowledgeInformation
AnalyticsInformationData
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Strategy to Build SPIDAL• Analyze Big Data applications to identify analytics needed
and generate benchmark applications• Analyze existing analytics libraries (in practice limit to some
application domains) – catalog library members available and performance– Mahout low performance, R largely sequential and missing key algorithms, MLlib just starting
• Identify big data computer architectures• Identify software model to allow interoperability and
performance• Design or identify new or existing algorithm including parallel
implementation• Collaborate application scientists, computer systems and
statistics/algorithms communities5/25/2015 65
Machine Learning in Network Science, Imaging in Computer Vision, Pathology, Polar Science, Biomolecular Simulations
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Algorithm Applications Features Status Parallelism
Graph Analytics
Community detection Social networks, webgraph
Graph .
P-DM GML-GrC
Subgraph/motif finding Webgraph, biological/social networks P-DM GML-GrB
Finding diameter Social networks, webgraph P-DM GML-GrB
Clustering coefficient Social networks P-DM GML-GrC
Page rank Webgraph P-DM GML-GrC
Maximal cliques Social networks, webgraph P-DM GML-GrB
Connected component Social networks, webgraph P-DM GML-GrB
Betweenness centrality Social networks Graph, Non-metric, static
P-ShmGML-GRA
Shortest path Social networks, webgraph P-Shm
Spatial Queries and Analytics
Spatial relationship based queries
GIS/social networks/pathology informatics
Geometric
P-DM PP
Distance based queries P-DM PP
Spatial clustering Seq GML
Spatial modeling Seq PP
GML Global (parallel) MLGrA Static GrB Runtime partitioning
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Some specialized data analytics in SPIDAL
• aa
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Algorithm Applications Features Status Parallelism
Core Image Processing
Image preprocessing
Computer vision/pathology informatics
Metric Space Point Sets, Neighborhood sets & Image features
P-DM PP
Object detection & segmentation P-DM PP
Image/object feature computation P-DM PP
3D image registration Seq PP
Object matchingGeometric
Todo PP
3D feature extraction Todo PP
Deep Learning
Learning Network, Stochastic Gradient Descent
Image Understanding, Language Translation, Voice Recognition, Car driving
Connections in artificial neural net P-DM GML
PP Pleasingly Parallel (Local ML)Seq Sequential AvailableGRA Good distributed algorithm needed
Todo No prototype AvailableP-DM Distributed memory AvailableP-Shm Shared memory Available5/25/2015
Some Core Machine Learning Building Blocks
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Algorithm Applications Features Status //ism
DA Vector Clustering Accurate Clusters Vectors P-DM GMLDA Non metric Clustering Accurate Clusters, Biology, Web Non metric, O(N2) P-DM GMLKmeans; Basic, Fuzzy and Elkan Fast Clustering Vectors P-DM GMLLevenberg-Marquardt Optimization
Non-linear Gauss-Newton, use in MDS Least Squares P-DM GML
SMACOF Dimension Reduction DA- MDS with general weights Least Squares, O(N2) P-DM GML
Vector Dimension Reduction DA-GTM and Others Vectors P-DM GML
TFIDF Search Find nearest neighbors in document corpus
Bag of “words” (image features)
P-DM PP
All-pairs similarity searchFind pairs of documents with TFIDF distance below a threshold Todo GML
Support Vector Machine SVM Learn and Classify Vectors Seq GML
Random Forest Learn and Classify Vectors P-DM PPGibbs sampling (MCMC) Solve global inference problems Graph Todo GML
Latent Dirichlet Allocation LDA with Gibbs sampling or Var. Bayes Topic models (Latent factors) Bag of “words” P-DM GML
Singular Value Decomposition SVD Dimension Reduction and PCA Vectors Seq GML
Hidden Markov Models (HMM) Global inference on sequence models Vectors Seq PP &
GML5/25/2015
Some Futures• Always run MDS. Gives insight into data
– Leads to a data browser as GIS gives for spatial data
• Claim is algorithm change gave as much performance increase as hardware change in simulations. Will this happen in analytics?– Today is like parallel computing 30 years ago with regular meshs.
We will learn how to adapt methods automatically to give “multigrid” and “fast multipole” like algorithms
• Need to start developing the libraries that support Big Data – Understand architectures issues– Have coupled batch and streaming versions– Develop much better algorithms
• Please join SPIDAL (Scalable Parallel Interoperable Data Analytics Library) community 695/25/2015