Weighted Chinese Restaurant Process

for clustering barcodes

Javier Cabrera John Lau Albert Lo

DIMACS, Bristol U, and HKUST

Cluster Analysis:

Group the observations into k distinct natural groups.

Non Bayesian Cluster Analysis:

Hierarchical clustering:  Build a hierarchical tree

- SIMILARITY: Inter point distance: Euclidean, Manhattan… - Inter cluster distance: Single Linkage, Complete, Average,

Ward- Build a hierarchical tree

Non Hierarchical clustering: - K-means- Divisive- PAM- Model Based- Many Other Methods

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Hierarchical Clustering1

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Weighted Chinese Restaurant Process

1. The Restaurant is full of tables.

2. Customers are sited on tables by a sitting rule.

3. Customers are allowed to move from one table to another or to a new empty one.

Partition: Each sitting arrangement for all the customers in the restaurant.

Partitions:p : Partition of specimens into species.p P : {Space of all possible partitions. All arrangements of specimens into species}

Bayes basics:Prior Distribution: π(p)

Likelihood: f(x|p) = 1in(p) k(xj, jCi).

Posterior: π(p|data) f(x|p) π(p)

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Weighted Chinese Restaurant ProcessApproximate Posterior

distribution with WCRP

• Run the process for a while and obtain frequency table of partitions visited.

• Estimate final partition with posterior mode.

• Compare posterior probabilities of most probable partitions.

New Specimens: - Placed in one existing

table.- Open a new table=>New

Species

Future WorkWCRP Algorithm for

Barcode data:

Data Visualization:Final partition => similarities => Euclidean Representation - Multidimensional Scaling- Multivariate Data Visualization (used in taxonomy) - Projection Pursuit

Entropy scanningLo (1984), Ishwaran and James (2003b), Cabrera, Lau, Lo (2006)

Javier Cabrera cabrera@stat.rutgers.edu John Lau john.lau@bristol.edu.ukAlbert Lo imaylo@ust.hk