Lloyd Algorithm K-Means Clustering

Gene Expression

• Susumu Ohno: whole genome duplications

• The expression of genes can be measured over time.

• Identifying which genes are expressed at a given moment can help determine function.

Grouping

• Grouping genes by derivative.• Data must be clustered by derivative.

Clustering Problems

• Cluster d data points into k clusters, such that each point is closer to the points in its cluster than those of any other.

• Data is usually not that clearly organized.

Lloyd’s Algorithm

• Assign points to clusters, minimizing distance between points and centers of clusters.

• Assign cluster center of gravity as new center, repeat until centers do not change, minimize squared error distortion.

The Computational Problem

• Input: A matrix of points with dimensions m and the desired number of clusters k.

• Output: Points organized into k clusters, minimizing distance from center, and a visual representation of the data.

Pseudo-pseudocode

• Arbitrarily assign k centers.• Assign points to k clusters, minimizing

Euclidian distance from center.• Assign cluster center of gravity as new center.• Repeat until algorithm converges

Plotting

Plotting