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Multilinear Hyperplane Hashing

Xianglong Liu, Xinjie Fan, Cheng Deng, Zhujin Li, Hao Su, Dacheng Tao
2016 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
To overcome this problem, this paper proposes a multilinear hyperplane hashing that generates a hash bit using multiple linear projections.  ...  Our theoretical analysis shows that with an even number of random linear projections, the multilinear hash function possesses strong locality sensitivity to hyperplane queries.  ...  The multilinear form enjoys several advantages in hyperplane hashing.  ... 
doi:10.1109/cvpr.2016.553 dblp:conf/cvpr/LiuFDLST16 fatcat:ylgakpbr6zf7ddk2kv2vaurdbu

AMM: Adaptive Multilinear Meshes [article]

Harsh Bhatia, Duong Hoang, Nate Morrical, Valerio Pascucci, Peer-Timo Bremer, Peter Lindstrom
2022 arXiv   pre-print
Through novelties in spatial hierarchy, our representation, Adaptive Multilinear Meshes (AMM), provides considerable reduction in the mesh size.  ...  AMM creates a piecewise multilinear representation of uniformly sampled scalar data and can selectively relax or enforce constraints on conformity, continuity, and coverage, delivering a flexible adaptive  ...  Improper nodes are also stored separately using a similar hashed set. Vertices are stored as hash maps, from vertex index (in row-major order) to function value.  ... 
arXiv:2007.15219v3 fatcat:w6ijdinqfbbsxjdy2koj4vi6ei

An invariance principle for polytopes

Prahladh Harsha, Adam Klivans, Raghu Meka
2012 Journal of the ACM  
We first partition [n] into blocks using a random hash function h ∈ u H and then use a blockwise-hybrid argument. Fix a hash function h ∈ H.  ...  Let P be a multilinear polynomial such that P = 1. Then, for any t ∈ R, Pr x∈u{−1,1} n [P (x) > t] − Pr x←N n [P (x) > t] ≤ τ.  ... 
doi:10.1145/2395116.2395118 fatcat:oh5uhclnrvfsdpowse3nimjvzi

Interactive proofs and the hardness of approximating cliques

Uriel Feige, Shafi Goldwasser, Laszlo Lovász, Shmuel Safra, Mario Szegedy
1996 Journal of the ACM  
Of independent interest is our proof of correctness for the multilinearity test of functions.  ...  We thank Sasha Shen for clarifying observations on multilinearity tests.  ...  to direction x 1 are "far" from multilinear, in which case we can proceed by induction on these hyperplanes (having only m − 1 dimensions).  ... 
doi:10.1145/226643.226652 fatcat:hlis7vvav5bmnn34hhm3riqg4u

Obfuscating Conjunctions

Zvika Brakerski, Guy N. Rothblum
2015 Journal of Cryptology  
Security follows from multilinear entropic variants of the Diffie-Hellman assumption.  ...  Our construction is based on multilinear maps, and can be instantiated using the recent candidates proposed by Garg, Gentry and Halevi (EUROCRYPT 2013) and by Coron, Lepoint and Tibouchi (CRYPTO 2013).  ...  These include the class of point functions, and extensions such as multi-point functions, "lockers" and constant-dimension hyperplanes.  ... 
doi:10.1007/s00145-015-9221-5 fatcat:s2jt4vvpdvb5xix3er7c2dbweq

Obfuscating Conjunctions [chapter]

Zvika Brakerski, Guy N. Rothblum
2013 Lecture Notes in Computer Science  
Security follows from multilinear entropic variants of the Diffie-Hellman assumption.  ...  Our construction is based on multilinear maps, and can be instantiated using the recent candidates proposed by Garg, Gentry and Halevi (EUROCRYPT 2013) and by Coron, Lepoint and Tibouchi (CRYPTO 2013).  ...  These include the class of point functions, and extensions such as multi-point functions, "lockers" and constant-dimension hyperplanes.  ... 
doi:10.1007/978-3-642-40084-1_24 fatcat:pmltma7cpvb53f6dzrafjnbyi4

An Illuminating Algorithm for the Light Bulb Problem

Josh Alman, Michael Wagner
2018 ACM-SIAM Symposium on Discrete Algorithms  
Algorithms based on techniques like Locality-Sensitive Hashing achieve runtimes of n 2−O(ρ) ; as ρ gets small, these approach quadratic.  ...  The hash function simply picks a uniformly random hyperplane through the origin, and outputs 1 or −1 depending on which side of the J. Alman 2:5 hyperplane a point lies on.  ...  Polynomial Multilinearization For a multivariate polynomial p : R d → R, its multilinearization is the polynomial p : R d → R which one gets when one expands p into a sum of monomials, and then for each  ... 
doi:10.4230/oasics.sosa.2019.2 dblp:conf/soda/Alman19 fatcat:o5nipprcxffundskhe62hhcqwu

An Illuminating Algorithm for the Light Bulb Problem [article]

Josh Alman
2018 arXiv   pre-print
Algorithms based on techniques like Locality-Sensitive Hashing achieve runtimes of n^2 - O(ρ); as ρ gets small, these approach quadratic.  ...  The hash function simply picks a uniformly random hyperplane through the origin, and outputs 1 or −1 depending on which side of the hyperplane a point lies on.  ...  Polynomial Multilinearization For a multivariate polynomial p : R d → R, its multilinearization is the polynomialp : R d → R which one gets when one expands p into a sum of monomials, and then for each  ... 
arXiv:1810.06740v1 fatcat:q3ef37n3knb6np2omjfjr7tssa

Linear and Kernel Classification: When to Use Which?

Hsin-Yuan Huang, Chih-Jen Lin
2016 Proceedings of the 2016 SIAM International Conference on Data Mining  
Our idea is to break the boundary into finite pieces, say K pieces, of hyperplanes.  ...  People remedy this problem by hashing the expanded features into a smaller dimension d (e.g., [19] ), but d is very hard to tune in practice.  ... 
doi:10.1137/1.9781611974348.25 dblp:conf/sdm/HuangL16 fatcat:bnpbdqph6refjgs7b6sfu7xrby

Expanding the Family of Grassmannian Kernels: An Embedding Perspective [chapter]

Mehrtash T. Harandi, Mathieu Salzmann, Sadeep Jayasumana, Richard Hartley, Hongdong Li
2014 Lecture Notes in Computer Science  
positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing  ...  Definition 4 (Alternating Multilinear Map). Let V and W be two vector spaces.  ...  For example, in SVMs, maximizing the margin of the separating hyperplane between two classes is independent of the position of the origin.  ... 
doi:10.1007/978-3-319-10584-0_27 fatcat:5nyxoiicrfcnhmbosqn27pmynq

Gated Linear Networks [article]

Joel Veness, Tor Lattimore, David Budden, Avishkar Bhoopchand, Christopher Mattern, Agnieszka Grabska-Barwinska, Eren Sezener, Jianan Wang, Peter Toth, Simon Schmitt, Marcus Hutter
2020 arXiv   pre-print
As we are interested in higher dimensional applications, it is necessary to sample hyperplanes in a manner that addresses the curse of dimensionality.  ...  task-specific cluster of examples is far from each other in signature space, the amount of interference between tasks is significantly reduced, with the gating essentially acting as an implicit weight hashing  ... 
arXiv:1910.01526v2 fatcat:fbgnq4rfwzbspis4jmv6qeudgq

Individual and Group Dynamics in the Reality Mining Corpus

Charlie K. Dagli, William M. Campbell
2012 2012 International Conference on Privacy, Security, Risk and Trust and 2012 International Confernece on Social Computing  
Additionally, we show how proximity information can be used in a multilinear clustering framework to detect interesting group behavior over time.  ...  For a separable data set, SVM optimization chooses a hyperplane in the expansion space with maximum margin.  ...  Multilinear Semantic Indexing Multilinear Semantic Indexing is a generalization of traditional Latent Semantic Indexing (LSI).  ... 
doi:10.1109/socialcom-passat.2012.75 dblp:conf/socialcom/DagliC12 fatcat:qkrj7wv2rbctrdltludeletghm

Expanding the Family of Grassmannian Kernels: An Embedding Perspective [article]

Mehrtash T. Harandi and Mathieu Salzmann and Sadeep Jayasumana and Richard Hartley and Hongdong Li
2014 arXiv   pre-print
positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing  ...  Video hashing.  ...  Definition 4 (Alternating Multilinear Map). Let V and W be two vector spaces.  ... 
arXiv:1407.1123v1 fatcat:2wavgwto7rfjtczeddq64qriaq

The closest solution to the shadow minimum of a cooperative dynamic game

K. Tanaka
1989 Computers and Mathematics with Applications  
both Q(A Is, fi), p(s, fi) and d(s, fi) are multilinear in p = (#', #2,..., gin).  ...  If a(dlKs)> 0, the positive half space H+ hasH+ = {x ~ R'l<< x> ~ 6(digs)} = Ks. And 0 ~ H+ because of (d, 0) = 0.  ... 
doi:10.1016/0898-1221(89)90135-1 fatcat:zlytj45s45eidkqfrc27rpm2uq

Geometric Optimization of the Evaluation of Finite Element Matrices

Robert C. Kirby, L. Ridgway Scott
2007 SIAM Journal on Scientific Computing  
These techniques are applicable to multilinear variational forms over affine elements using general basis functions.  ...  The current implementation of FFC is fully functional for multilinear forms with arbitrary order Lagrange elements, and works for general unstructured meshes in one, two, or three space dimensions.  ...  Instead of a plane graph, we make use of a "hyperplane graph" with edges weighted based on the length of intersection (between 0 and k − 1, inclusive).  ... 
doi:10.1137/060660722 fatcat:ted3nonl5jdzff75ntfe5hx6gm
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