74,932 research outputs found
Unsupervised Generative Adversarial Cross-modal Hashing
Cross-modal hashing aims to map heterogeneous multimedia data into a common
Hamming space, which can realize fast and flexible retrieval across different
modalities. Unsupervised cross-modal hashing is more flexible and applicable
than supervised methods, since no intensive labeling work is involved. However,
existing unsupervised methods learn hashing functions by preserving inter and
intra correlations, while ignoring the underlying manifold structure across
different modalities, which is extremely helpful to capture meaningful nearest
neighbors of different modalities for cross-modal retrieval. To address the
above problem, in this paper we propose an Unsupervised Generative Adversarial
Cross-modal Hashing approach (UGACH), which makes full use of GAN's ability for
unsupervised representation learning to exploit the underlying manifold
structure of cross-modal data. The main contributions can be summarized as
follows: (1) We propose a generative adversarial network to model cross-modal
hashing in an unsupervised fashion. In the proposed UGACH, given a data of one
modality, the generative model tries to fit the distribution over the manifold
structure, and select informative data of another modality to challenge the
discriminative model. The discriminative model learns to distinguish the
generated data and the true positive data sampled from correlation graph to
achieve better retrieval accuracy. These two models are trained in an
adversarial way to improve each other and promote hashing function learning.
(2) We propose a correlation graph based approach to capture the underlying
manifold structure across different modalities, so that data of different
modalities but within the same manifold can have smaller Hamming distance and
promote retrieval accuracy. Extensive experiments compared with 6
state-of-the-art methods verify the effectiveness of our proposed approach.Comment: 8 pages, accepted by 32th AAAI Conference on Artificial Intelligence
(AAAI), 201
Regular Tessellation Link Complements
By regular tessellation, we mean any hyperbolic 3-manifold tessellated by
ideal Platonic solids such that the symmetry group acts transitively on
oriented flags. A regular tessellation has an invariant we call the cusp
modulus. For small cusp modulus, we classify all regular tessellations. For
large cusp modulus, we prove that a regular tessellations has to be infinite
volume if its fundamental group is generated by peripheral curves only. This
shows that there are at least 19 and at most 21 link complements that are
regular tessellations (computer experiments suggest that at least one of the
two remaining cases likely fails to be a link complement, but so far we have no
proof). In particular, we complete the classification of all principal
congruence link complements given in Baker and Reid for the cases of
discriminant D=-3 and D=-4. We only describe the manifolds arising as
complements of links here with a future publication "Regular Tessellation
Links" giving explicit pictures of these links.Comment: 35 pages, 19 figures, 4 tables; version 2: minor chages; fixed title
in arxiv's metadata; version3: addresses referee's comments, in particular,
rewrite of discussion section; including ancillary file
Optimizing the double description method for normal surface enumeration
Many key algorithms in 3-manifold topology involve the enumeration of normal
surfaces, which is based upon the double description method for finding the
vertices of a convex polytope. Typically we are only interested in a small
subset of these vertices, thus opening the way for substantial optimization.
Here we give an account of the vertex enumeration problem as it applies to
normal surfaces, and present new optimizations that yield strong improvements
in both running time and memory consumption. The resulting algorithms are
tested using the freely available software package Regina.Comment: 27 pages, 12 figures; v2: Removed the 3^n bound from Section 3.3,
fixed the projective equation in Lemma 4.4, clarified "most triangulations"
in the introduction to section 5; v3: replace -ise with -ize for Mathematics
of Computation (note that this changes the title of the paper
Simplicial Nonlinear Principal Component Analysis
We present a new manifold learning algorithm that takes a set of data points
lying on or near a lower dimensional manifold as input, possibly with noise,
and outputs a simplicial complex that fits the data and the manifold. We have
implemented the algorithm in the case where the input data can be triangulated.
We provide triangulations of data sets that fall on the surface of a torus,
sphere, swiss roll, and creased sheet embedded in a fifty dimensional space. We
also discuss the theoretical justification of our algorithm.Comment: 21 pages, 6 figure
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