  Clustering is a fundamental tool in unsupervised learning, used to group
objects by distinguishing between similar and dissimilar features of a given
data set. One of the most common clustering algorithms is k-means.
Unfortunately, when dealing with real-world data many traditional clustering
algorithms are compromised by lack of clear separation between groups, noisy
observations, and/or outlying data points. Thus, robust statistical algorithms
are required for successful data analytics. Current methods that robustify
k-means clustering are specialized for either single or multi-membership data,
but do not perform competitively in both cases. We propose an extension of the
k-means algorithm, which we call Robust Trimmed k-means (RTKM) that
simultaneously identifies outliers and clusters points and can be applied to
either single- or multi-membership data. We test RTKM on various real-world
datasets and show that RTKM performs competitively with other methods on single
membership data with outliers and multi-membership data without outliers. We
also show that RTKM leverages its relative advantages to outperform other
methods on multi-membership data containing outliers.
