1,040,369 research outputs found
Adaptive Evolutionary Clustering
In many practical applications of clustering, the objects to be clustered
evolve over time, and a clustering result is desired at each time step. In such
applications, evolutionary clustering typically outperforms traditional static
clustering by producing clustering results that reflect long-term trends while
being robust to short-term variations. Several evolutionary clustering
algorithms have recently been proposed, often by adding a temporal smoothness
penalty to the cost function of a static clustering method. In this paper, we
introduce a different approach to evolutionary clustering by accurately
tracking the time-varying proximities between objects followed by static
clustering. We present an evolutionary clustering framework that adaptively
estimates the optimal smoothing parameter using shrinkage estimation, a
statistical approach that improves a naive estimate using additional
information. The proposed framework can be used to extend a variety of static
clustering algorithms, including hierarchical, k-means, and spectral
clustering, into evolutionary clustering algorithms. Experiments on synthetic
and real data sets indicate that the proposed framework outperforms static
clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox
available at http://tbayes.eecs.umich.edu/xukevin/affec
Factor PD-Clustering
Factorial clustering methods have been developed in recent years thanks to
the improving of computational power. These methods perform a linear
transformation of data and a clustering on transformed data optimizing a common
criterion. Factorial PD-clustering is based on Probabilistic Distance
clustering (PD-clustering). PD-clustering is an iterative, distribution free,
probabilistic, clustering method. Factor PD-clustering make a linear
transformation of original variables into a reduced number of orthogonal ones
using a common criterion with PD-Clustering. It is demonstrated that Tucker 3
decomposition allows to obtain this transformation. Factor PD-clustering makes
alternatively a Tucker 3 decomposition and a PD-clustering on transformed data
until convergence. This method could significantly improve the algorithm
performance and allows to work with large dataset, to improve the stability and
the robustness of the method
Statistical Properties of Convex Clustering
In this manuscript, we study the statistical properties of convex clustering.
We establish that convex clustering is closely related to single linkage
hierarchical clustering and -means clustering. In addition, we derive the
range of tuning parameter for convex clustering that yields a non-trivial
solution. We also provide an unbiased estimate of the degrees of freedom, and
provide a finite sample bound for the prediction error for convex clustering.
We compare convex clustering to some traditional clustering methods in
simulation studies.Comment: 20 pages, 5 figure
SOTXTSTREAM: Density-based self-organizing clustering of text streams
A streaming data clustering algorithm is presented building upon the density-based selforganizing stream clustering algorithm SOSTREAM. Many density-based clustering algorithms are limited by their inability to identify clusters with heterogeneous density. SOSTREAM addresses this limitation through the use of local (nearest neighbor-based) density determinations. Additionally, many stream clustering algorithms use a two-phase clustering approach. In the first phase, a micro-clustering solution is maintained online, while in the second phase, the micro-clustering solution is clustered offline to produce a macro solution. By performing self-organization techniques on micro-clusters in the online phase, SOSTREAM is able to maintain a macro clustering solution in a single phase. Leveraging concepts from SOSTREAM, a new density-based self-organizing text stream clustering algorithm, SOTXTSTREAM, is presented that addresses several shortcomings of SOSTREAM. Gains in clustering performance of this new algorithm are demonstrated on several real-world text stream datasets
Robust hierarchical k-center clustering
One of the most popular and widely used methods for data clustering is hierarchical clustering. This clustering technique has proved useful to reveal interesting structure in the data in several applications ranging from computational biology to computer vision. Robustness is an important feature of a clustering technique if we require the clustering to be stable against small perturbations in the input data. In most applications, getting a clustering output that is robust against adversarial outliers or stochastic noise is a necessary condition for the applicability and effectiveness of the clustering technique. This is even more critical in hierarchical clustering where a small change at the bottom of the hierarchy may propagate all the way through to the top. Despite all the previous work [2, 3, 6, 8], our theoretical understanding of robust hierarchical clustering is still limited and several hierarchical clustering algorithms are not known to satisfy such robustness properties. In this paper, we study the limits of robust hierarchical k-center clustering by introducing the concept of universal hierarchical clustering and provide (almost) tight lower and upper bounds for the robust hierarchical k-center clustering problem with outliers and variants of the stochastic clustering problem. Most importantly we present a constant-factor approximation for optimal hierarchical k-center with at most z outliers using a universal set of at most O(z2) set of outliers and show that this result is tight. Moreover we show the necessity of using a universal set of outliers in order to compute an approximately optimal hierarchical k-center with a diffierent set of outliers for each k
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