Vector quantization / Clustering

1. Methods Overview [EN]

For every new sample :

• if the distance between the sample and a cluster is smaller than a given threshold, then add the sample to the cluster, else create a new cluster with the sample

Initially every sample is a cluster.
Repeat until the desired number of clusters is obtained :

• merge the two closest clusters

k-moyennes

Randomly chose k clusters.
For every sample :

• decrease the distance between the closest cluster to the sample, and the sample (using a learning rate)
• decrease the learning rate in time

A variant that initializes centers so that there is a guarantee in accuracy, and a faster convergence :

• chose the first center randomly with uniform distribution among the samples
• chose the next centers randomly with probability proportional to the minimum distance of the sample to the already chosen centers.

• 2006, Arthur-Vassilvitskii, k-means++: The Advantages of Careful Seeding

A way to chose the optimal number of clusters k.

Compute for different number of clusters the ratio of the intra-clusters variance to the total variance. The optimal number of clusters is when adding clusters do not bring significant decrease of the ratio.

Cartes auto-organisatrices de Kohonen