Generalized Method to Produce Balanced Structures Through k-means Objective Function

Balanced structures are required in certain applications and clustering does not inherently aim at producing balanced partition of data. Two things are essentially required: definition of balance and modification to objective function to accommodate this definition. This paper proposes three definitions of balance in clusters: cardinality, variance and density; such that they can be directly interpreted for applications of balanced clustering. These are incorporated with objective function of standard k-means algorithm to demonstrate effect of balance in output over popular datasets. Paper also suggests method to measure the balance factor of any cluster structure.