6,627 research outputs found
Document Clustering Based On Max-Correntropy Non-Negative Matrix Factorization
Nonnegative matrix factorization (NMF) has been successfully applied to many
areas for classification and clustering. Commonly-used NMF algorithms mainly
target on minimizing the distance or Kullback-Leibler (KL) divergence,
which may not be suitable for nonlinear case. In this paper, we propose a new
decomposition method by maximizing the correntropy between the original and the
product of two low-rank matrices for document clustering. This method also
allows us to learn the new basis vectors of the semantic feature space from the
data. To our knowledge, we haven't seen any work has been done by maximizing
correntropy in NMF to cluster high dimensional document data. Our experiment
results show the supremacy of our proposed method over other variants of NMF
algorithm on Reuters21578 and TDT2 databasets.Comment: International Conference of Machine Learning and Cybernetics (ICMLC)
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On Similarities between Inference in Game Theory and Machine Learning
In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoff-dominant but risk-dominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We first show that the standard update rule of mean field variational learning is analogous to a Cournot adjustment within game theory. By analogy with fictitious play, we then suggest an improved update rule, and show that this results in fictitious variational play, an improved mean field variational learning algorithm that exhibits better convergence in highly or strongly connected graphical models. Second, we use a recent advance in fictitious play, namely dynamic fictitious play, to derive a derivative action variational learning algorithm, that exhibits superior convergence properties on a canonical machine learning problem (clustering a mixture distribution)
Graph Regularized Non-negative Matrix Factorization By Maximizing Correntropy
Non-negative matrix factorization (NMF) has proved effective in many
clustering and classification tasks. The classic ways to measure the errors
between the original and the reconstructed matrix are distance or
Kullback-Leibler (KL) divergence. However, nonlinear cases are not properly
handled when we use these error measures. As a consequence, alternative
measures based on nonlinear kernels, such as correntropy, are proposed.
However, the current correntropy-based NMF only targets on the low-level
features without considering the intrinsic geometrical distribution of data. In
this paper, we propose a new NMF algorithm that preserves local invariance by
adding graph regularization into the process of max-correntropy-based matrix
factorization. Meanwhile, each feature can learn corresponding kernel from the
data. The experiment results of Caltech101 and Caltech256 show the benefits of
such combination against other NMF algorithms for the unsupervised image
clustering
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