36,244 research outputs found
Low-Rank Matrices on Graphs: Generalized Recovery & Applications
Many real world datasets subsume a linear or non-linear low-rank structure in
a very low-dimensional space. Unfortunately, one often has very little or no
information about the geometry of the space, resulting in a highly
under-determined recovery problem. Under certain circumstances,
state-of-the-art algorithms provide an exact recovery for linear low-rank
structures but at the expense of highly inscalable algorithms which use nuclear
norm. However, the case of non-linear structures remains unresolved. We revisit
the problem of low-rank recovery from a totally different perspective,
involving graphs which encode pairwise similarity between the data samples and
features. Surprisingly, our analysis confirms that it is possible to recover
many approximate linear and non-linear low-rank structures with recovery
guarantees with a set of highly scalable and efficient algorithms. We call such
data matrices as \textit{Low-Rank matrices on graphs} and show that many real
world datasets satisfy this assumption approximately due to underlying
stationarity. Our detailed theoretical and experimental analysis unveils the
power of the simple, yet very novel recovery framework \textit{Fast Robust PCA
on Graphs
Structural Embedding of Syntactic Trees for Machine Comprehension
Deep neural networks for machine comprehension typically utilizes only word
or character embeddings without explicitly taking advantage of structured
linguistic information such as constituency trees and dependency trees. In this
paper, we propose structural embedding of syntactic trees (SEST), an algorithm
framework to utilize structured information and encode them into vector
representations that can boost the performance of algorithms for the machine
comprehension. We evaluate our approach using a state-of-the-art neural
attention model on the SQuAD dataset. Experimental results demonstrate that our
model can accurately identify the syntactic boundaries of the sentences and
extract answers that are syntactically coherent over the baseline methods
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
Reading Wikipedia to Answer Open-Domain Questions
This paper proposes to tackle open- domain question answering using Wikipedia
as the unique knowledge source: the answer to any factoid question is a text
span in a Wikipedia article. This task of machine reading at scale combines the
challenges of document retrieval (finding the relevant articles) with that of
machine comprehension of text (identifying the answer spans from those
articles). Our approach combines a search component based on bigram hashing and
TF-IDF matching with a multi-layer recurrent neural network model trained to
detect answers in Wikipedia paragraphs. Our experiments on multiple existing QA
datasets indicate that (1) both modules are highly competitive with respect to
existing counterparts and (2) multitask learning using distant supervision on
their combination is an effective complete system on this challenging task.Comment: ACL2017, 10 page
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