25,290 research outputs found
An efficient -means-type algorithm for clustering datasets with incomplete records
The -means algorithm is arguably the most popular nonparametric clustering
method but cannot generally be applied to datasets with incomplete records. The
usual practice then is to either impute missing values under an assumed
missing-completely-at-random mechanism or to ignore the incomplete records, and
apply the algorithm on the resulting dataset. We develop an efficient version
of the -means algorithm that allows for clustering in the presence of
incomplete records. Our extension is called -means and reduces to the
-means algorithm when all records are complete. We also provide
initialization strategies for our algorithm and methods to estimate the number
of groups in the dataset. Illustrations and simulations demonstrate the
efficacy of our approach in a variety of settings and patterns of missing data.
Our methods are also applied to the analysis of activation images obtained from
a functional Magnetic Resonance Imaging experiment.Comment: 21 pages, 12 figures, 3 tables, in press, Statistical Analysis and
Data Mining -- The ASA Data Science Journal, 201
Clustering Stability: An Overview
A popular method for selecting the number of clusters is based on stability
arguments: one chooses the number of clusters such that the corresponding
clustering results are "most stable". In recent years, a series of papers has
analyzed the behavior of this method from a theoretical point of view. However,
the results are very technical and difficult to interpret for non-experts. In
this paper we give a high-level overview about the existing literature on
clustering stability. In addition to presenting the results in a slightly
informal but accessible way, we relate them to each other and discuss their
different implications
Dynamic Tensor Clustering
Dynamic tensor data are becoming prevalent in numerous applications. Existing
tensor clustering methods either fail to account for the dynamic nature of the
data, or are inapplicable to a general-order tensor. Also there is often a gap
between statistical guarantee and computational efficiency for existing tensor
clustering solutions. In this article, we aim to bridge this gap by proposing a
new dynamic tensor clustering method, which takes into account both sparsity
and fusion structures, and enjoys strong statistical guarantees as well as high
computational efficiency. Our proposal is based upon a new structured tensor
factorization that encourages both sparsity and smoothness in parameters along
the specified tensor modes. Computationally, we develop a highly efficient
optimization algorithm that benefits from substantial dimension reduction. In
theory, we first establish a non-asymptotic error bound for the estimator from
the structured tensor factorization. Built upon this error bound, we then
derive the rate of convergence of the estimated cluster centers, and show that
the estimated clusters recover the true cluster structures with a high
probability. Moreover, our proposed method can be naturally extended to
co-clustering of multiple modes of the tensor data. The efficacy of our
approach is illustrated via simulations and a brain dynamic functional
connectivity analysis from an Autism spectrum disorder study.Comment: Accepted at Journal of the American Statistical Associatio
Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms
Clustering non-Euclidean data is difficult, and one of the most used
algorithms besides hierarchical clustering is the popular algorithm
Partitioning Around Medoids (PAM), also simply referred to as k-medoids. In
Euclidean geometry the mean-as used in k-means-is a good estimator for the
cluster center, but this does not hold for arbitrary dissimilarities. PAM uses
the medoid instead, the object with the smallest dissimilarity to all others in
the cluster. This notion of centrality can be used with any (dis-)similarity,
and thus is of high relevance to many domains such as biology that require the
use of Jaccard, Gower, or more complex distances.
A key issue with PAM is its high run time cost. We propose modifications to
the PAM algorithm to achieve an O(k)-fold speedup in the second SWAP phase of
the algorithm, but will still find the same results as the original PAM
algorithm. If we slightly relax the choice of swaps performed (at comparable
quality), we can further accelerate the algorithm by performing up to k swaps
in each iteration. With the substantially faster SWAP, we can now also explore
alternative strategies for choosing the initial medoids. We also show how the
CLARA and CLARANS algorithms benefit from these modifications. It can easily be
combined with earlier approaches to use PAM and CLARA on big data (some of
which use PAM as a subroutine, hence can immediately benefit from these
improvements), where the performance with high k becomes increasingly
important.
In experiments on real data with k=100, we observed a 200-fold speedup
compared to the original PAM SWAP algorithm, making PAM applicable to larger
data sets as long as we can afford to compute a distance matrix, and in
particular to higher k (at k=2, the new SWAP was only 1.5 times faster, as the
speedup is expected to increase with k)
- …