407,681 research outputs found
A New Coreset Framework for Clustering
Given a metric space, the -clustering problem consists of finding
centers such that the sum of the of distances raised to the power of every
point to its closest center is minimized. This encapsulates the famous
-median () and -means () clustering problems. Designing
small-space sketches of the data that approximately preserves the cost of the
solutions, also known as \emph{coresets}, has been an important research
direction over the last 15 years.
In this paper, we present a new, simple coreset framework that simultaneously
improves upon the best known bounds for a large variety of settings, ranging
from Euclidean space, doubling metric, minor-free metric, and the general
metric cases
Element-centric clustering comparison unifies overlaps and hierarchy
Clustering is one of the most universal approaches for understanding complex
data. A pivotal aspect of clustering analysis is quantitatively comparing
clusterings; clustering comparison is the basis for many tasks such as
clustering evaluation, consensus clustering, and tracking the temporal
evolution of clusters. In particular, the extrinsic evaluation of clustering
methods requires comparing the uncovered clusterings to planted clusterings or
known metadata. Yet, as we demonstrate, existing clustering comparison measures
have critical biases which undermine their usefulness, and no measure
accommodates both overlapping and hierarchical clusterings. Here we unify the
comparison of disjoint, overlapping, and hierarchically structured clusterings
by proposing a new element-centric framework: elements are compared based on
the relationships induced by the cluster structure, as opposed to the
traditional cluster-centric philosophy. We demonstrate that, in contrast to
standard clustering similarity measures, our framework does not suffer from
critical biases and naturally provides unique insights into how the clusterings
differ. We illustrate the strengths of our framework by revealing new insights
into the organization of clusters in two applications: the improved
classification of schizophrenia based on the overlapping and hierarchical
community structure of fMRI brain networks, and the disentanglement of various
social homophily factors in Facebook social networks. The universality of
clustering suggests far-reaching impact of our framework throughout all areas
of science
Electricity clustering framework for automatic classification of customer loads
Clustering in energy markets is a top topic with high significance on expert and intelligent systems. The main impact of is paper is the proposal of a new clustering framework for the automatic classification of electricity customers’ loads. An automatic selection of the clustering classification algorithm is also highlighted. Finally, new customers can be assigned to a predefined set of clusters in the classificationphase. The computation time of the proposed framework is less than that of previous classification tech- niques, which enables the processing of a complete electric company sample in a matter of minutes on a personal computer. The high accuracy of the predicted classification results verifies the performance of the clustering technique. This classification phase is of significant assistance in interpreting the results, and the simplicity of the clustering phase is sufficient to demonstrate the quality of the complete mining framework.Ministerio de Economía y Competitividad TEC2013-40767-RMinisterio de Economía y Competitividad IDI- 2015004
Innovation Pursuit: A New Approach to Subspace Clustering
In subspace clustering, a group of data points belonging to a union of
subspaces are assigned membership to their respective subspaces. This paper
presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of
subspace clustering using a new geometrical idea whereby subspaces are
identified based on their relative novelties. We present two frameworks in
which the idea of innovation pursuit is used to distinguish the subspaces.
Underlying the first framework is an iterative method that finds the subspaces
consecutively by solving a series of simple linear optimization problems, each
searching for a direction of innovation in the span of the data potentially
orthogonal to all subspaces except for the one to be identified in one step of
the algorithm. A detailed mathematical analysis is provided establishing
sufficient conditions for iPursuit to correctly cluster the data. The proposed
approach can provably yield exact clustering even when the subspaces have
significant intersections. It is shown that the complexity of the iterative
approach scales only linearly in the number of data points and subspaces, and
quadratically in the dimension of the subspaces. The second framework
integrates iPursuit with spectral clustering to yield a new variant of
spectral-clustering-based algorithms. The numerical simulations with both real
and synthetic data demonstrate that iPursuit can often outperform the
state-of-the-art subspace clustering algorithms, more so for subspaces with
significant intersections, and that it significantly improves the
state-of-the-art result for subspace-segmentation-based face clustering
A New Framework for Distance-based Functional Clustering
We develop a new framework for clustering functional data, based on a distance matrix similar to the approach in clustering multivariate data using spectral clustering. First, we smooth the raw observations using appropriate smoothing techniques with desired smoothness, through a penalized fit. The next step is to create an optimal distance matrix either from the smoothed curves or their available derivatives. The choice of the distance matrix depends on the nature of the data. Finally, we create and implement the spectral clustering algorithm. We applied our newly developed approach, Functional Spectral Clustering (FSC) on sets of simulated and real data. Our proposed method showed better performance than existing methods with respect to accuracy rates
A New Framework for Distance-based Functional Clustering
We develop a new framework for clustering functional data, based on a distance matrix similar to the approach in clustering multivariate data using spectral clustering. First, we smooth the raw observations using appropriate smoothing techniques with desired smoothness, through a penalized fit. The next step is to create an optimal distance matrix either from the smoothed curves or their available derivatives. The choice of the distance matrix depends on the nature of the data. Finally, we create and implement the spectral clustering algorithm. We applied our newly developed approach, Functional Spectral Clustering (FSC) on sets of simulated and real data. Our proposed method showed better performance than existing methods with respect to accuracy rates
- …