4,010 research outputs found
Optimal Clustering under Uncertainty
Classical clustering algorithms typically either lack an underlying
probability framework to make them predictive or focus on parameter estimation
rather than defining and minimizing a notion of error. Recent work addresses
these issues by developing a probabilistic framework based on the theory of
random labeled point processes and characterizing a Bayes clusterer that
minimizes the number of misclustered points. The Bayes clusterer is analogous
to the Bayes classifier. Whereas determining a Bayes classifier requires full
knowledge of the feature-label distribution, deriving a Bayes clusterer
requires full knowledge of the point process. When uncertain of the point
process, one would like to find a robust clusterer that is optimal over the
uncertainty, just as one may find optimal robust classifiers with uncertain
feature-label distributions. Herein, we derive an optimal robust clusterer by
first finding an effective random point process that incorporates all
randomness within its own probabilistic structure and from which a Bayes
clusterer can be derived that provides an optimal robust clusterer relative to
the uncertainty. This is analogous to the use of effective class-conditional
distributions in robust classification. After evaluating the performance of
robust clusterers in synthetic mixtures of Gaussians models, we apply the
framework to granular imaging, where we make use of the asymptotic
granulometric moment theory for granular images to relate robust clustering
theory to the application.Comment: 19 pages, 5 eps figures, 1 tabl
Clustering from Sparse Pairwise Measurements
We consider the problem of grouping items into clusters based on few random
pairwise comparisons between the items. We introduce three closely related
algorithms for this task: a belief propagation algorithm approximating the
Bayes optimal solution, and two spectral algorithms based on the
non-backtracking and Bethe Hessian operators. For the case of two symmetric
clusters, we conjecture that these algorithms are asymptotically optimal in
that they detect the clusters as soon as it is information theoretically
possible to do so. We substantiate this claim for one of the spectral
approaches we introduce
Transforming Graph Representations for Statistical Relational Learning
Relational data representations have become an increasingly important topic
due to the recent proliferation of network datasets (e.g., social, biological,
information networks) and a corresponding increase in the application of
statistical relational learning (SRL) algorithms to these domains. In this
article, we examine a range of representation issues for graph-based relational
data. Since the choice of relational data representation for the nodes, links,
and features can dramatically affect the capabilities of SRL algorithms, we
survey approaches and opportunities for relational representation
transformation designed to improve the performance of these algorithms. This
leads us to introduce an intuitive taxonomy for data representation
transformations in relational domains that incorporates link transformation and
node transformation as symmetric representation tasks. In particular, the
transformation tasks for both nodes and links include (i) predicting their
existence, (ii) predicting their label or type, (iii) estimating their weight
or importance, and (iv) systematically constructing their relevant features. We
motivate our taxonomy through detailed examples and use it to survey and
compare competing approaches for each of these tasks. We also discuss general
conditions for transforming links, nodes, and features. Finally, we highlight
challenges that remain to be addressed
A survey of machine learning techniques applied to self organizing cellular networks
In this paper, a survey of the literature of the past fifteen years involving Machine Learning (ML) algorithms applied to self organizing cellular networks is performed. In order for future networks to overcome the current limitations and address the issues of current cellular systems, it is clear that more intelligence needs to be deployed, so that a fully autonomous and flexible network can be enabled. This paper focuses on the learning perspective of Self Organizing Networks (SON) solutions and provides, not only an overview of the most common ML techniques encountered in cellular networks, but also manages to classify each paper in terms of its learning solution, while also giving some examples. The authors also classify each paper in terms of its self-organizing use-case and discuss how each proposed solution performed. In addition, a comparison between the most commonly found ML algorithms in terms of certain SON metrics is performed and general guidelines on when to choose each ML algorithm for each SON function are proposed. Lastly, this work also provides future research directions and new paradigms that the use of more robust and intelligent algorithms, together with data gathered by operators, can bring to the cellular networks domain and fully enable the concept of SON in the near future
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Models of incremental concept formation
Given a set of observations, humans acquire concepts that organize those observations and use them in classifying future experiences. This type of concept formation can occur in the absence of a tutor and it can take place despite irrelevant and incomplete information. A reasonable model of such human concept learning should be both incremental and capable of handling this type of complex experiences that people encounter in the real world. In this paper, we review three previous models of incremental concept formation and then present CLASSIT, a model that extends these earlier systems. All of the models integrate the process of recognition and learning, and all can be viewed as carrying out search through the space of possible concept hierarchies. In an attempt to show that CLASSIT is a robust concept formation system, we also present some empirical studies of its behavior under a variety of conditions
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
We present two graph-based algorithms for multiclass segmentation of
high-dimensional data. The algorithms use a diffuse interface model based on
the Ginzburg-Landau functional, related to total variation compressed sensing
and image processing. A multiclass extension is introduced using the Gibbs
simplex, with the functional's double-well potential modified to handle the
multiclass case. The first algorithm minimizes the functional using a convex
splitting numerical scheme. The second algorithm is a uses a graph adaptation
of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates
between diffusion and thresholding. We demonstrate the performance of both
algorithms experimentally on synthetic data, grayscale and color images, and
several benchmark data sets such as MNIST, COIL and WebKB. We also make use of
fast numerical solvers for finding the eigenvectors and eigenvalues of the
graph Laplacian, and take advantage of the sparsity of the matrix. Experiments
indicate that the results are competitive with or better than the current
state-of-the-art multiclass segmentation algorithms.Comment: 14 page
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