47,821 research outputs found
Link Prediction via Generalized Coupled Tensor Factorisation
This study deals with the missing link prediction problem: the problem of
predicting the existence of missing connections between entities of interest.
We address link prediction using coupled analysis of relational datasets
represented as heterogeneous data, i.e., datasets in the form of matrices and
higher-order tensors. We propose to use an approach based on probabilistic
interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor
Factorisation, which can simultaneously fit a large class of tensor models to
higher-order tensors/matrices with com- mon latent factors using different loss
functions. Numerical experiments demonstrate that joint analysis of data from
multiple sources via coupled factorisation improves the link prediction
performance and the selection of right loss function and tensor model is
crucial for accurately predicting missing links
Multi-Target Prediction: A Unifying View on Problems and Methods
Multi-target prediction (MTP) is concerned with the simultaneous prediction
of multiple target variables of diverse type. Due to its enormous application
potential, it has developed into an active and rapidly expanding research field
that combines several subfields of machine learning, including multivariate
regression, multi-label classification, multi-task learning, dyadic prediction,
zero-shot learning, network inference, and matrix completion. In this paper, we
present a unifying view on MTP problems and methods. First, we formally discuss
commonalities and differences between existing MTP problems. To this end, we
introduce a general framework that covers the above subfields as special cases.
As a second contribution, we provide a structured overview of MTP methods. This
is accomplished by identifying a number of key properties, which distinguish
such methods and determine their suitability for different types of problems.
Finally, we also discuss a few challenges for future research
ACCAMS: Additive Co-Clustering to Approximate Matrices Succinctly
Matrix completion and approximation are popular tools to capture a user's
preferences for recommendation and to approximate missing data. Instead of
using low-rank factorization we take a drastically different approach, based on
the simple insight that an additive model of co-clusterings allows one to
approximate matrices efficiently. This allows us to build a concise model that,
per bit of model learned, significantly beats all factorization approaches to
matrix approximation. Even more surprisingly, we find that summing over small
co-clusterings is more effective in modeling matrices than classic
co-clustering, which uses just one large partitioning of the matrix.
Following Occam's razor principle suggests that the simple structure induced
by our model better captures the latent preferences and decision making
processes present in the real world than classic co-clustering or matrix
factorization. We provide an iterative minimization algorithm, a collapsed
Gibbs sampler, theoretical guarantees for matrix approximation, and excellent
empirical evidence for the efficacy of our approach. We achieve
state-of-the-art results on the Netflix problem with a fraction of the model
complexity.Comment: 22 pages, under review for conference publicatio
Image collection pop-up: 3D reconstruction and clustering of rigid and non-rigid categories
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Multi-body Non-rigid Structure-from-Motion
Conventional structure-from-motion (SFM) research is primarily concerned with
the 3D reconstruction of a single, rigidly moving object seen by a static
camera, or a static and rigid scene observed by a moving camera --in both cases
there are only one relative rigid motion involved. Recent progress have
extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid}
relative motions in the scene), as well as {non-rigid SFM} (where there is a
single non-rigid, deformable object or scene). Along this line of thinking,
there is apparently a missing gap of "multi-body non-rigid SFM", in which the
task would be to jointly reconstruct and segment multiple 3D structures of the
multiple, non-rigid objects or deformable scenes from images. Such a multi-body
non-rigid scenario is common in reality (e.g. two persons shaking hands,
multi-person social event), and how to solve it represents a natural
{next-step} in SFM research. By leveraging recent results of subspace
clustering, this paper proposes, for the first time, an effective framework for
multi-body NRSFM, which simultaneously reconstructs and segments each 3D
trajectory into their respective low-dimensional subspace. Under our
formulation, 3D trajectories for each non-rigid structure can be well
approximated with a sparse affine combination of other 3D trajectories from the
same structure (self-expressiveness). We solve the resultant optimization with
the alternating direction method of multipliers (ADMM). We demonstrate the
efficacy of the proposed framework through extensive experiments on both
synthetic and real data sequences. Our method clearly outperforms other
alternative methods, such as first clustering the 2D feature tracks to groups
and then doing non-rigid reconstruction in each group or first conducting 3D
reconstruction by using single subspace assumption and then clustering the 3D
trajectories into groups.Comment: 21 pages, 16 figure
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