Parameterized Complexity of Feature Selection for Categorical Data Clustering

We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While is one of the most common approaches reduce dimensionality practice, known are heuristics. study following mathematical model. assume that there some inadvertent (or undesirable) features input unnecessarily increase cost Consequently, we want select a subset original from such small-cost clustering on selected features. More precisely, given integers ℓ (the number irrelevant features) and k clusters), budget B , set n points (represented by m -dimensional vectors whose elements belong finite values Σ ), − relevant any optimal -clustering these does not exceed . Here cluster sum Hamming distances (ℓ 0 -distances) between its center. The total costs clusters. use framework parameterized complexity identify how problem depends parameters | |. Our main result an algorithm solves Feature Selection time f ( |) · g 2 functions In other words, fixed-parameter tractable when constants. based solution more general problem, Constrained Clustering Outliers. this delete certain outliers remaining could be clustered around centers satisfying specific constraints. One interesting fact about Outliers besides Selection, it encompasses many fundamental problems regarding as Robust Clustering, Binary Boolean Low-rank Matrix Approximation Thus byproduct our theorem, obtain algorithms all problems. also complement findings lower bounds.