1,578 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)
201
Computing a Nonnegative Matrix Factorization -- Provably
In the Nonnegative Matrix Factorization (NMF) problem we are given an nonnegative matrix and an integer . Our goal is to express
as where and are nonnegative matrices of size
and respectively. In some applications, it makes sense to ask
instead for the product to approximate -- i.e. (approximately)
minimize \norm{M - AW}_F where \norm{}_F denotes the Frobenius norm; we
refer to this as Approximate NMF. This problem has a rich history spanning
quantum mechanics, probability theory, data analysis, polyhedral combinatorics,
communication complexity, demography, chemometrics, etc. In the past decade NMF
has become enormously popular in machine learning, where and are
computed using a variety of local search heuristics. Vavasis proved that this
problem is NP-complete. We initiate a study of when this problem is solvable in
polynomial time:
1. We give a polynomial-time algorithm for exact and approximate NMF for
every constant . Indeed NMF is most interesting in applications precisely
when is small.
2. We complement this with a hardness result, that if exact NMF can be solved
in time , 3-SAT has a sub-exponential time algorithm. This rules
out substantial improvements to the above algorithm.
3. We give an algorithm that runs in time polynomial in , and
under the separablity condition identified by Donoho and Stodden in 2003. The
algorithm may be practical since it is simple and noise tolerant (under benign
assumptions). Separability is believed to hold in many practical settings.
To the best of our knowledge, this last result is the first example of a
polynomial-time algorithm that provably works under a non-trivial condition on
the input and we believe that this will be an interesting and important
direction for future work.Comment: 29 pages, 3 figure
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
A Broad Learning Approach for Context-Aware Mobile Application Recommendation
With the rapid development of mobile apps, the availability of a large number
of mobile apps in application stores brings challenge to locate appropriate
apps for users. Providing accurate mobile app recommendation for users becomes
an imperative task. Conventional approaches mainly focus on learning users'
preferences and app features to predict the user-app ratings. However, most of
them did not consider the interactions among the context information of apps.
To address this issue, we propose a broad learning approach for
\textbf{C}ontext-\textbf{A}ware app recommendation with \textbf{T}ensor
\textbf{A}nalysis (CATA). Specifically, we utilize a tensor-based framework to
effectively integrate user's preference, app category information and
multi-view features to facilitate the performance of app rating prediction. The
multidimensional structure is employed to capture the hidden relationships
between multiple app categories with multi-view features. We develop an
efficient factorization method which applies Tucker decomposition to learn the
full-order interactions within multiple categories and features. Furthermore,
we employ a group norm regularization to learn the group-wise
feature importance of each view with respect to each app category. Experiments
on two real-world mobile app datasets demonstrate the effectiveness of the
proposed method
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