6,660 research outputs found
A deep matrix factorization method for learning attribute representations
Semi-Non-negative Matrix Factorization is a technique that learns a
low-dimensional representation of a dataset that lends itself to a clustering
interpretation. It is possible that the mapping between this new representation
and our original data matrix contains rather complex hierarchical information
with implicit lower-level hidden attributes, that classical one level
clustering methodologies can not interpret. In this work we propose a novel
model, Deep Semi-NMF, that is able to learn such hidden representations that
allow themselves to an interpretation of clustering according to different,
unknown attributes of a given dataset. We also present a semi-supervised
version of the algorithm, named Deep WSF, that allows the use of (partial)
prior information for each of the known attributes of a dataset, that allows
the model to be used on datasets with mixed attribute knowledge. Finally, we
show that our models are able to learn low-dimensional representations that are
better suited for clustering, but also classification, outperforming
Semi-Non-negative Matrix Factorization, but also other state-of-the-art
methodologies variants.Comment: Submitted to TPAMI (16-Mar-2015
Is Simple Better? Revisiting Non-linear Matrix Factorization for Learning Incomplete Ratings
Matrix factorization techniques have been widely used as a method for
collaborative filtering for recommender systems. In recent times, different
variants of deep learning algorithms have been explored in this setting to
improve the task of making a personalized recommendation with user-item
interaction data. The idea that the mapping between the latent user or item
factors and the original features is highly nonlinear suggest that classical
matrix factorization techniques are no longer sufficient. In this paper, we
propose a multilayer nonlinear semi-nonnegative matrix factorization method,
with the motivation that user-item interactions can be modeled more accurately
using a linear combination of non-linear item features. Firstly, we learn
latent factors for representations of users and items from the designed
multilayer nonlinear Semi-NMF approach using explicit ratings. Secondly, the
architecture built is compared with deep-learning algorithms like Restricted
Boltzmann Machine and state-of-the-art Deep Matrix factorization techniques. By
using both supervised rate prediction task and unsupervised clustering in
latent item space, we demonstrate that our proposed approach achieves better
generalization ability in prediction as well as comparable representation
ability as deep matrix factorization in the clustering task.Comment: version
Distributed Low-rank Subspace Segmentation
Vision problems ranging from image clustering to motion segmentation to
semi-supervised learning can naturally be framed as subspace segmentation
problems, in which one aims to recover multiple low-dimensional subspaces from
noisy and corrupted input data. Low-Rank Representation (LRR), a convex
formulation of the subspace segmentation problem, is provably and empirically
accurate on small problems but does not scale to the massive sizes of modern
vision datasets. Moreover, past work aimed at scaling up low-rank matrix
factorization is not applicable to LRR given its non-decomposable constraints.
In this work, we propose a novel divide-and-conquer algorithm for large-scale
subspace segmentation that can cope with LRR's non-decomposable constraints and
maintains LRR's strong recovery guarantees. This has immediate implications for
the scalability of subspace segmentation, which we demonstrate on a benchmark
face recognition dataset and in simulations. We then introduce novel
applications of LRR-based subspace segmentation to large-scale semi-supervised
learning for multimedia event detection, concept detection, and image tagging.
In each case, we obtain state-of-the-art results and order-of-magnitude speed
ups
Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization
Nonnegative Matrix Factorization (NMF) has been continuously evolving in
several areas like pattern recognition and information retrieval methods. It
factorizes a matrix into a product of 2 low-rank non-negative matrices that
will define parts-based, and linear representation of nonnegative data.
Recently, Graph regularized NMF (GrNMF) is proposed to find a compact
representation,which uncovers the hidden semantics and simultaneously respects
the intrinsic geometric structure. In GNMF, an affinity graph is constructed
from the original data space to encode the geometrical information. In this
paper, we propose a novel idea which engages a Multiple Kernel Learning
approach into refining the graph structure that reflects the factorization of
the matrix and the new data space. The GrNMF is improved by utilizing the graph
refined by the kernel learning, and then a novel kernel learning method is
introduced under the GrNMF framework. Our approach shows encouraging results of
the proposed algorithm in comparison to the state-of-the-art clustering
algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible
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