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Doubly Stochastic Neighbor Embedding on Spheres
[article]
2018
arXiv
pre-print
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Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely ...
This suggests replacing a flat space with spheres as the embedding space. ...
n×3 ; y 1 = · · · = y n ; i y i = 0 . (6) We call the new method DOubly Stochastic Neighbor Embedding on Spheres (DOSNES). ...
arXiv:1609.01977v2
fatcat:tkmni7oh6nae3fy4pvgbu62dpi
Doubly Stochastic Neighbor Embedding on Spheres
2019
Pattern Recognition Letters
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Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely ...
This suggests replacing a flat space with spheres as the embedding space. ...
∈ R n ×3 ; y 1 = · · · = y n ; i y i = 0 . (2) We call the new method Doubly Stochastic Neighbor Embedding on Spheres (DOSNES). ...
doi:10.1016/j.patrec.2019.08.026
fatcat:u2m5a63onzfwnf3tixtogrrppm
Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to Heteroskedastic Noise
[article]
2021
arXiv
pre-print
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That is, the doubly-stochastic normalization is advantageous in that it automatically accounts for observations with different noise variances. ...
We demonstrate that the doubly-stochastic normalization of the Gaussian kernel with zero main diagonal (i.e., no self loops) is robust to heteroskedastic noise. ...
The doubly-stochastic normalization In this work, we focus on the doubly-stochastic normalization of K: (Doubly-stochastic normalization) W (d) def = diag(d)K diag(d), (4) where d = [d 1 , . . . , d n ...
arXiv:2006.00402v2
fatcat:i6rkgslygrfetfp5gtiezkcxai
Accurate Image Search Using the Contextual Dissimilarity Measure
2010
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Experimental results show that our approach gives significantly better results than a standard distance and outperforms the state-of-the-art in terms of accuracy on the Nistér-Stewénius and Lola datasets ...
(b) Projection onto the sphere in IR 3 using Sinkhorn's algorithm to yield doubly stochastic distance matrix. Note the much more uniform density of the points on the sphere. ...
This new measure is based on a distance regularization algorithm in the spirit of the Sinkhorn's algorithm, which projects distance matrices on doubly-stochastic matrices. ...
doi:10.1109/tpami.2008.285
pmid:19926895
fatcat:rhpvp6h7dzbebgkicisgnkm6p4
Tight Relaxation of Quadratic Matching
2015
Computer graphics forum (Print)
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We focus on the latter and consider the Quadratic Assignment Matching (QAM) model. ...
Results of the proposed one-stage procedure for finding consistent correspondences between shapes in a collection showing strong variability and non-rigid deformations. ...
Relation to spectral and doubly-stochastic relaxations Two relaxation approaches to the QAM problem (1) have become standard -spectral and doubly-stochastic relaxations (e.g., [ABK14, LH05] ). ...
doi:10.1111/cgf.12701
fatcat:gd5rwuwzhnbj5ar3bnu5utp3tm
Ion transport in the gramicidin channel: molecular dynamics study of single and double occupancy
1995
Biophysical Journal
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The atomic system, which includes the gramicidin channel, a model membrane made of neutral Lennard-Jones particles and 190 explicit water molecules to form the bulk region, is similar to the one used in ...
The calculations reveal that the doubly occupied state is relatively more favorable for the larger ions. ...
neighbor is increased by only 0.04 A on average in going from the singly to the doubly occupied state (see Table 9 ). ...
doi:10.1016/s0006-3495(95)80264-x
pmid:7538804
pmcid:PMC1281812
fatcat:hfufxiowzfdbrdco4e6hhv4d3u
Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder
[article]
2019
bioRxiv
pre-print
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Here, we identified a framework of Graph Auto-Encoder (GAE) with hyper sphere distributer for functional data analysis in brain imaging studies that is underlying non-Euclidean structure, in learning of ...
stochastic matrices. ...
For learning both encoder, decoder in the figure 1 to map between the space of graph and their continuous embedding Z ε R C , stochastic graph encoder q Φ (Z|G) embed the graph into continuous representation ...
doi:10.1101/616367
fatcat:ro56rt37znbvblf6vw4vwyakjy
Graph-Based Method for Anomaly Prediction in Brain Network
[article]
2019
arXiv
pre-print
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stochastic matrices. ...
sphere (Sinha et al. 2016) . ...
arXiv:1904.07163v7
fatcat:xeraccrk25e6rf3hj2zibsaxum
Latent Variables on Spheres for Autoencoders in High Dimensions
[article]
2020
arXiv
pre-print
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We analyze the unique characteristics of random variables on spheres in high dimensions and argue that random variables on spheres are agnostic to various prior distributions and data modes when the dimension ...
Therefore, SAE can harness a high-dimensional latent space to improve the inference precision of latent codes while maintain the property of stochastic sampling from priors. ...
SAE: x f → z g →x, z ∈ S dz−1 , z 1 = 0, (3) where S dz−1 is the sphere embedded in R dz and 1 is the allone vector. Here we have no any probabilistic constraint on z. ...
arXiv:1912.10233v2
fatcat:7dttsmehkzhp3e3a6owdewdrda
Diffusion Maps Clustering for Magnetic Resonance Q-Ball Imaging Segmentation
2008
International Journal of Biomedical Imaging
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Finally, we show results on a real-brain dataset where we segment well-known fiber bundles. ...
We also show that our ODF diffusion maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. ...
One must imagine these functions as living on the surface of the sphere. Here, for visualization purposes, the radius of the respective spheres are scaled by the corresponding value on the surface. ...
doi:10.1155/2008/526906
pmid:18317506
pmcid:PMC2246070
fatcat:yrg7n4vkzneuhg4pcemtzovcjm
Universality in Two-Dimensional Enhancement Percolation
[article]
2007
arXiv
pre-print
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For the case of site percolation on the triangular lattice, we also prove a stronger form of universality by showing that the full scaling limit is not affected by any monotonic enhancement that does not ...
Work on this paper began during a visit in 2002/2003 to the Forschungsinstitut für Mathematik of ETH-Zürich, and continued during a postdoc at EURANDOM, Eindhoven. ...
The author also thanks Rob van den Berg and Frank den Hollander for their advice, and Ronald Meester and the anonymous referees for their comments on the presentation of the results. ...
arXiv:0712.3412v1
fatcat:6j47qclvdvdl5dvrj6eczkjpni
Stochastic reaction-diffusion kinetics in the microscopic limit
2010
Proceedings of the National Academy of Sciences of the United States of America
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In this framework, molecules are treated as nonoverlapping spheres that diffuse as Brownian particles with diffusion rate ...
In this paper we identify and resolve this inconsistency by embedding the microscopic description into the RDME framework. ...
Because the doubly phosphorylated species typically regulates the downstream process in a nonlinear manner, such as in a MAPK cascade, the activity of the downstream processes will depend on the whole ...
doi:10.1073/pnas.1006565107
pmid:21041672
pmcid:PMC2993376
fatcat:a4jimgumfrcqpd4hemriqjxeju
Object Recognition as Many-to-Many Feature Matching
2006
International Journal of Computer Vision
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This is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure. ...
When recognition is exemplar-based, feature correspondence is one-to-one. ...
Although we seek a canonical node as root, we note that the shortest-path distance matrix, and hence the structure of the embedding, is invariant to the choice of root. 4. ...
doi:10.1007/s11263-006-6993-y
fatcat:35o2peidqbcoxo7tfnciluu7lm
AMC-Loss: Angular Margin Contrastive Loss for Improved Explainability in Image Classification
[article]
2020
arXiv
pre-print
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The AMC-Loss employs the discriminative angular distance metric that is equivalent to geodesic distance on a hypersphere manifold such that it can serve a clear geometric interpretation. ...
We find that although the proposed geometrically constrained loss-function improves quantitative results modestly, it has a qualitatively surprisingly beneficial effect on increasing the interpretability ...
To address this issue, following [9] , we adopt the doubly stochastic sampled data pairs in computing the geodesic. ...
arXiv:2004.09805v1
fatcat:d4ujgsgtffdjbg7uqxyhs4zv5i
Heat diffusion: Thermodynamic depth complexity of networks
2012
Physical Review E
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Our study is based on 217 protein-protein interaction (PPI) networks including histidine kinases from several species of bacteria. ...
The procedure is as follows: (i) initially express the doubly stochastic matrix K(G) as a convex combination of a single permutation matrix and residual doubly stochastic matrix K(G) ≡ K 1 = λ 1 P 1 + ...
Thus K β ij = n k=1 φ k (i)φ k (j )e −λ k β , (9) and K β ij ∈ [0,1] is the (i,j ) entry of a doubly stochastic matrix. ...
doi:10.1103/physreve.85.036206
pmid:22587160
fatcat:syv4qtuyoze2rdggpg2bqhmd2y
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