Scalable Clustering on the Data Grid

Scalable Clustering on the Data Grid

Patrick Wendel ([email protected])Moustafa GhanemYike Guo

Discovery NetDepartment of ComputingImperial College, London

20/09/2005All Hands Meeting, Nottingham

Outline

Discovery Net Data Clustering Mining Distributed Data Description of the strategy Deployment Evaluation Conclusions – Future Works


Discovery Net Multidisciplinary project funded by the EPSRC under the UK e-Science programme

(started Oct 2002, ended March 05)

Developed an infrastructure for Knowledge Discovery Services for integrating and analysing data collected from high throughput devices and sensors

Applications to: Life Sciences

• High throughput genomics and proteomics Real-time Environmental Monitoring

• High throughput dispersed air sensing technology Geo-Hazard modelling

• Earthquake modelling through satellite imagery

The project covered many areas including infrastructure, applications and algorithms (text mining)

Produced the Discovery Net platform which aims to integrate, compose, coordinate and deploy knowledge discovery services using a workflow technology.


Discovery Net

Using Distributed Computing Resources

ScientificInformationScientific

InformationScientific Discovery

LiteratureLiterature

DatabasesDatabases

OperationalData

OperationalData

ImagesImages

InstrumentData

InstrumentData

e-Sciencelarge scale science that will increasingly be carried out through distributed global collaborations enabled by the Internet.


Data Clustering We concentrate on a particular class of data mining

algorithms: Clustering

A class of explorative data mining techniques, used to find out groups of points that are similar/close to each other.

Popular analysis technique. Useful for exploring, understanding, modelling large data sets

Two main types of clustering: Hierarchical: Reorganises the data set into a hierarchy of

clusters based on their similarity. Partition/Model based: Tries to partition the data set into a

number of clusters or try to fit a statistical model (e.g. mixture of Gaussians) to a data set

Successfully applied to sociological data, image processing and genomic data.


Mining Data on the Grid

Changing environment for data analysis: From analysing data files held locally (or

close to the algorithm), to using remote data source, using remote services through portals, now towards distributed data executions.

Distributed data sources: Data mining processes can now require data

spread across multiple organisations Service-oriented approach:

High-level functionalities are now available through well-defined services, instead of providing low-level (terminal etc..) access to resources


Goal

Design a service-oriented distributed data clustering strategy:

that can be deployed on a Grid environment (i.e. a standard-based, service oriented, secure distributed environment)

that would allow the end-user/data analysts to deploy easily against its own data sets


Requirements 1/2

Performance issues: The analysis process using data grids directly and

analysis services must be more efficient than gathering all the data on my desktop!

Accuracy: The strategy should at least provide a model more

representative of the overall data set Security

The deployed strategy should ensure consistent handling of authentication and authorization aspects throughout

Privacy: Restricted access to the data source


Requirements 2/2

Heterogeneity of the resources used and/or connectivity It’s very unlikely the set of resources involved in the

distributed analysis process will be similar or work over networks of similar bandwidth

Loose-coupling between resources participating in the distributed analysis The analyst has less control on what is available/provided

by each data grid or each analysis service. Therefore the framework should, as much as possible, be unaffected by minor differences between functionalities provided by each site.

Service-oriented approach: The deployment of the analysis process should be based on the co-ordination of high-level services (instead of a dedicated distributed algorithm, e.g. MPI implementation)


Current strategy

We restrict the current framework to the case where instances are distributed but have the same attributes on each different fragments (~ horizontal fragments)

Based on the EM-Clustering algorithm (mixture of Gaussian model fitting algorithm). Hierarchical clustering inherently complex to

distribute Statistical approach of EM provides a sound basis to

define a model combination strategy


Approach

Generate clustering models at each data source location (compute near the data)

Transfer partial models in standard format (PMML) to a combiner site

Normalise the relative weights of each model

Perform an EM-based method on partial models to generate a global model.


Combining Cluster Models

Derived from the EM-Clustering algorithm itself

Adapted to take as input the models generated at each site

Each partial model is treated like a (very) compressed representation of the fragment (similar to the two step approaches of some scalable clustering algorithms).

More detailed algorithm and formulae in proceedings


Deployment: Discovery Net

The Discovery Net platform is used to build and deploy this framework.

Implementation based on an open architecture re-using common protocols and common infrastructure elements (such as the Globus Toolkits).

It also defines its own protocol for workflows, Discovery Process Markup Language (DPML) which allows the definition of data analysis workflows to be executed on distributed resources.

The platform comprises a server that stores, schedules the workflows and manage the data, and a thick client to help the workflow construction process.

Thus giving the end user the ability to define application-specific workflows performing such tasks as distributed data mining.

The model combiner is implemented as a workflow activity in Discovery Net


DeploymentData sources Discovery Net servers

Partial clustering

Partial clustering

Partial clustering

PMML

PMML

PMML

Partial models

Global model

Combiner site

Source A

Source B

Source C


Deployment: Workflow

The Discovery Net client enables the composition and the execution of the distributed process as a workflow constructed visually.

The execution engine will coordinate the distributed execution


Accuracy Evaluation: Data Distribution Comparison of the accuracy of the combined model with the

average accuracy of partial models against the entire data sets (i.e. have we gained some accuracy by considering the fragments together)

Accuracy will strongly depend on how the data is distributed among different sites. In the evaluation we introduce a randomness ratio to determine how similar the data distribution is among fragments. 0 meaning that each site would have data drawn from

different distributions 1 meaning that the data from all fragments are drawn from

the same distribution Measured by log-likelihood function of the test data set:

The likelihood function of a data set represents how much that data is likely to be following the distribution function defined by the model


Accuracy Evaluation: Data distribution

Randomness ratio effect

-120000

-100000

-80000

-60000

-40000

-20000

0

0 0.2 0.4 0.6 0.8 1 1.2

Ratio

LL

ikel

iho

od

Average log-Likelihood

Combined log-Likelihood

As expected, the ratio has a huge effect on gained accuracy. For low levels, each fragment becomes less and less representative of the complete data set, therefore the combined

model will outperform partial ones.


Accuracy Evaluation: Number of fragments

-80000

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

2 3 4 5 6 7 8 9 10

Avg Likelihood

Combined Likelihood

(r= 0.2, 10,000 points, 5 clusters) The accuracy does degrade with increasing number of fragments, but so does the average accuracy of models generated from individual fragments.


Accuracy Evaluation: Increasing data size

(r=0.2,d=5,5 fragments). Consistent behaviour of the combined model’s accuracy over partial ones.

Increasing data size

-5000000

-4000000

-3000000

-2000000

-1000000

0

0 200000 400000 600000 800000 1000000

1200000

# instances

LL

ikel

iho

od

Average log-Likelihood

Combined log-Likelihood


Performance Evaluation Performance evaluation is only partially relevant, as the process does not

feed back combined models and partial models are generated near the data.

The heterogeneity of real deployments is difficult to take into account.

Time in seconds, for an increasing number of fragments


Performance Evaluation

Execution time with lower dimensionality and larger data sets


Conclusions

Encouraging results in terms of accuracy vs. performance, given the constraints.

But is the trade-off between accuracy and flexibility (generally the case in distributed data mining) acceptable?

This should be part of a wider explorative process, probably as a first step into the understanding of the data set.

Being part of the Discovery Net platform, the distributed analysis process can be simply designed from the Discovery Net client software.


Future Works

First step towards more generic distributed data mining strategies (classification algorithms, association rules)

Need evaluation against real data sets ! Possible improvements including:

Refinement through feedback Use of a more complex intermediate summary

structure for the partial models (e.g. tree structures containing summary information)

Estimation of the number of clusters (using Bayesian Information Criteria)

Plenty of possible clustering algorithms to try to use.


Questions?

Documents

Scalable Clustering on the Data Grid