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What to Do When K -Means Clustering Fails: A Simple yet Principled Alternative Algorithm

View Article: PubMed Central - PubMed

ABSTRACT

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism.

No MeSH data available.


Clustering solution obtained by K-means and MAP-DP for synthetic elliptical Gaussian data.The clusters are trivially well-separated, and even though they have different densities (12% of the data is blue, 28% yellow cluster, 60% orange) and elliptical cluster geometries, K-means produces a near-perfect clustering, as with MAP-DP. This shows that K-means can in some instances work when the clusters are not equal radii with shared densities, but only when the clusters are so well-separated that the clustering can be trivially performed by eye.
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pone.0162259.g005: Clustering solution obtained by K-means and MAP-DP for synthetic elliptical Gaussian data.The clusters are trivially well-separated, and even though they have different densities (12% of the data is blue, 28% yellow cluster, 60% orange) and elliptical cluster geometries, K-means produces a near-perfect clustering, as with MAP-DP. This shows that K-means can in some instances work when the clusters are not equal radii with shared densities, but only when the clusters are so well-separated that the clustering can be trivially performed by eye.

Mentions: This data is generated from three elliptical Gaussian distributions with different covariances and different number of points in each cluster. In this case, despite the clusters not being spherical, equal density and radius, the clusters are so well-separated that K-means, as with MAP-DP, can perfectly separate the data into the correct clustering solution (see Fig 5). So, for data which is trivially separable by eye, K-means can produce a meaningful result. However, it is questionable how often in practice one would expect the data to be so clearly separable, and indeed, whether computational cluster analysis is actually necessary in this case. Even in this trivial case, the value of K estimated using BIC is K = 4, an overestimate of the true number of clusters K = 3.


What to Do When K -Means Clustering Fails: A Simple yet Principled Alternative Algorithm
Clustering solution obtained by K-means and MAP-DP for synthetic elliptical Gaussian data.The clusters are trivially well-separated, and even though they have different densities (12% of the data is blue, 28% yellow cluster, 60% orange) and elliptical cluster geometries, K-means produces a near-perfect clustering, as with MAP-DP. This shows that K-means can in some instances work when the clusters are not equal radii with shared densities, but only when the clusters are so well-separated that the clustering can be trivially performed by eye.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036949&req=5

pone.0162259.g005: Clustering solution obtained by K-means and MAP-DP for synthetic elliptical Gaussian data.The clusters are trivially well-separated, and even though they have different densities (12% of the data is blue, 28% yellow cluster, 60% orange) and elliptical cluster geometries, K-means produces a near-perfect clustering, as with MAP-DP. This shows that K-means can in some instances work when the clusters are not equal radii with shared densities, but only when the clusters are so well-separated that the clustering can be trivially performed by eye.
Mentions: This data is generated from three elliptical Gaussian distributions with different covariances and different number of points in each cluster. In this case, despite the clusters not being spherical, equal density and radius, the clusters are so well-separated that K-means, as with MAP-DP, can perfectly separate the data into the correct clustering solution (see Fig 5). So, for data which is trivially separable by eye, K-means can produce a meaningful result. However, it is questionable how often in practice one would expect the data to be so clearly separable, and indeed, whether computational cluster analysis is actually necessary in this case. Even in this trivial case, the value of K estimated using BIC is K = 4, an overestimate of the true number of clusters K = 3.

View Article: PubMed Central - PubMed

ABSTRACT

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism.

No MeSH data available.