25,836 research outputs found
Dictionary-based Tensor Canonical Polyadic Decomposition
To ensure interpretability of extracted sources in tensor decomposition, we
introduce in this paper a dictionary-based tensor canonical polyadic
decomposition which enforces one factor to belong exactly to a known
dictionary. A new formulation of sparse coding is proposed which enables high
dimensional tensors dictionary-based canonical polyadic decomposition. The
benefits of using a dictionary in tensor decomposition models are explored both
in terms of parameter identifiability and estimation accuracy. Performances of
the proposed algorithms are evaluated on the decomposition of simulated data
and the unmixing of hyperspectral images
Improving Negative Sampling for Word Representation using Self-embedded Features
Although the word-popularity based negative sampler has shown superb
performance in the skip-gram model, the theoretical motivation behind
oversampling popular (non-observed) words as negative samples is still not well
understood. In this paper, we start from an investigation of the gradient
vanishing issue in the skipgram model without a proper negative sampler. By
performing an insightful analysis from the stochastic gradient descent (SGD)
learning perspective, we demonstrate that, both theoretically and intuitively,
negative samples with larger inner product scores are more informative than
those with lower scores for the SGD learner in terms of both convergence rate
and accuracy. Understanding this, we propose an alternative sampling algorithm
that dynamically selects informative negative samples during each SGD update.
More importantly, the proposed sampler accounts for multi-dimensional
self-embedded features during the sampling process, which essentially makes it
more effective than the original popularity-based (one-dimensional) sampler.
Empirical experiments further verify our observations, and show that our
fine-grained samplers gain significant improvement over the existing ones
without increasing computational complexity.Comment: Accepted in WSDM 201
Spectral Unmixing with Multiple Dictionaries
Spectral unmixing aims at recovering the spectral signatures of materials,
called endmembers, mixed in a hyperspectral or multispectral image, along with
their abundances. A typical assumption is that the image contains one pure
pixel per endmember, in which case spectral unmixing reduces to identifying
these pixels. Many fully automated methods have been proposed in recent years,
but little work has been done to allow users to select areas where pure pixels
are present manually or using a segmentation algorithm. Additionally, in a
non-blind approach, several spectral libraries may be available rather than a
single one, with a fixed number (or an upper or lower bound) of endmembers to
chose from each. In this paper, we propose a multiple-dictionary constrained
low-rank matrix approximation model that address these two problems. We propose
an algorithm to compute this model, dubbed M2PALS, and its performance is
discussed on both synthetic and real hyperspectral images
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