Figure 2: An result of experiment I

Figure 3: An result of experiment II

### Branching Competitive Learning For Data Clustering

Irwin King, Ada Fu and Laiwan Chan

This project proposes a novel modification to the classical Competitive Learning (CL) by adding a dynamic branching mechanism to neutral networks so that the number of neurons can be increased over time until the networks reaches a good estimation of the cluster number in a data set.

- Key problems
- The number of clusters must be appropriately preselected, e.g., K-mean and classical CL
- Sensitive to the preselected cluster number and the initialization of synaptic vectors, e.g., RPCL0

The Branching Criterion

1. The angle criteria based on the angle between

current moving direction and the previous moving

direction of a synaptic vector:

2. The distance criteria based on the distance between

the input data and the winner:

where are an randomly selected data at

current step, the winner in current competition, angle

and distance threshold.

- Contributions
- Propose Branching Competitive Learning (BCL) algorithm
- Propose a neuron branching mechanism to estimate cluster number and cluster data
- Present a Branching Criteria
- Present a new way of hierarchical data clustering, i.e., multiresolution clustering
- The Advantages of BCL
- The ability to automatically detect cluster number
- Fast convergence of synaptic vectors
- Convergence to implement multiresolution data clustering

The Algorithm of BCL

1. Initialize the first synaptic vector.

2. Randomly take a sample from the

dataset, find the winner of the current

competition in the set of synaptic vector

i.e.,

where is the frequency that wins the

competition up to now.

3. If satisfies the branching criterion above, a new

neuron is spawn off from

otherwise, update by

An Illustration of BCL

Figure 1: An illustration of the procedure of the BCL

algorithm, where

(1) Initialization of the first synaptic vector.

(2) Branching points of synaptic vectors.

(3) Final convergence of synaptic vectors.

- Experiments
- Examine the ability of BCL to detect cluster number.
- Show a multiresolution clustering in BCL scheme.
- Compare the performance of BCL and RPCL for data clustering

- The experimental environment is Pentium II PC with 128 RAM under Windows98 using Visual C++6.0

Table 1: Results of experiment III

- Selected Publication
- Irwin King and Huilin Xiong. Branching competitive learning for clustering. In Proceedings to the International Conference on Neural Information Processing (ICONIP2000), pages WBP--27, Taejon, Korea, 2000.