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An Analysis of the Anti-learning Phenomenon for the Class Symmetric Polyhedron [chapter]

Adam Kowalczyk, Olivier Chapelle
2005 Lecture Notes in Computer Science  
The initial analysis presented in this paper shows that anti-learning is a property of data sets and is quite distinct from over-fitting of a training data.  ...  Moreover, the analysis leads to a specification of some machine learning procedures which can overcome anti-learning and generate machines able to classify training and test data consistently.  ...  Acknowlegements Many thanks to Cheng Soon Ong, Alex Smola and Grant Baldwin for help in preparation of this paper and to Manfred Warmuth and S.V.N. Vishwanathan for clarifying discussions.  ... 
doi:10.1007/11564089_8 fatcat:v32mzx4xxffyzp3sz6kcvfmdn4

Classification of polyhedral shapes from individual anisotropically resolved cryo-electron tomography reconstructions

Sukantadev Bag, Michael B Prentice, Mingzhi Liang, Martin J Warren, Kingshuk Roy Choudhury
2016 BMC Bioinformatics  
In studies with simulated data, a Bayes classifier constructed using these distributions has an average test set misclassification error of < 5 % with upto 30 % of the object missing, suggesting accurate  ...  Reconstructed cryo-ET images have a "missing wedge" of data loss due to limitations in rotation of the mounting stage.  ...  Each line in the graph represents a polyhedron from the family P. Only polyhedra with ≤ 20 vertices are shown (55 such).  ... 
doi:10.1186/s12859-016-1107-5 pmid:27296169 pmcid:PMC4904361 fatcat:n6lsljojabarxnf3ll2573ylw4

The Eisenlohr-Farris Algorithm for Fully Transitive Polyhedra [article]

Eric Pauli Pérez-Contreras
2021 arXiv   pre-print
We also apply this algorithm to construct a new polyhedron in the euclidean space 𝔼^3.  ...  In this note we describe the algorithm proposed by J. M. Eisenlohr and S. L. Farris for generating every fully transitive polyhedra in 𝔼^d.  ...  In this way we obtain a fully transitive family F of polygons that induces a fully transitive polyhedron.  ... 
arXiv:2109.08951v1 fatcat:ts54wcjzgfefjbzv6tmle3ws7u

Incremental learning with sample queries

J. Ratsaby
1998 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The classical theory of pattern recognition assumes labeled examples appear according to unknown underlying class conditional probability distributions where the pattern classes are picked randomly in  ...  This paper presents experimental results for an incremental nearest-neighbor learning algorithm which actively selects samples from different pattern classes according to a querying rule as opposed to  ...  in the family of learnable classifiers.  ... 
doi:10.1109/34.709619 fatcat:mlynhxv42fdp7cibrllyxdq7rm

Simple Kinesthetic Haptics for Object Recognition [article]

Avishai Sintov, Inbar Ben-David
2022 arXiv   pre-print
To train a classifier, training data is generated rapidly and solely in a computational process without interaction with real objects.  ...  Similarly, a global classifier is trained to identify general geometries (e.g., an ellipsoid or a box) rather than particular ones and demonstrated on a large set of objects.  ...  First, we train a classifier using three selected primitive geometries: a box, a sphere and a cylinder.  ... 
arXiv:2206.05601v1 fatcat:igccq4edjva4tc6y7qfvscbsq4

Construction of convex hull classifiers in high dimensions

Tetsuji Takahashi, Mineichi Kudo, Atsuyoshi Nakamura
2011 Pattern Recognition Letters  
We also propose a model selection procedure to control the number of faces of convex hulls for avoiding over-fitting, in which a fast procedure is adopted to calculate an upper-bound of the leave-one-out  ...  The classifier is one of non-kernel maximum margin classifiers. It keeps the maximum margin in the original feature space, unlike support vector machines with a kernel.  ...  This randomness does not affect much to the resultant 357 classifier, but needs an appropriate control to reduce its bad effect. paper, a model selection procedure for a family of polyhedron clas-360 sifiers  ... 
doi:10.1016/j.patrec.2011.06.020 fatcat:5g5eqcuht5dkziv6vvlv2wdo4q

Reconstruction of Branching Surface and Its Smoothness by Reversible Catmull-Clark Subdivision [chapter]

Kailash Jha
2009 Lecture Notes in Computer Science  
Number of control points at different layer for contours and 3D curves may not be the same, in this case a special polyhedron construction technique has been developed.  ...  In the next step, 3D composite curves are converted into different polyhedrons by the help of the contours at adjacent layers.  ...  The research has been concluded in section 6. Previous Works The literature that is devoted to many-to-one branching problem can be classified into four main families.  ... 
doi:10.1007/978-3-642-01973-9_85 fatcat:jke7aywmhfdj7edxauuiw2pgye

Classification of (1.2)-reflective anisotropic hyperbolic lattices of rank 4
Классификация (1.2)-рефлективных анизотропных гиперболических решёток ранга 4

Nikolay Vladimirovich Bogachev
2019 Izvestiya: Mathematics  
In this paper we prove that the fundamental polyhedron of a Q-arithmetic cocompact reflection group in the three-dimensional Lobachevsky space contains an edge such that the distance between its framing  ...  Using this fact we obtain a classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4.  ...  In order to select only anisotropic lattices, we use a computer program 8 , based on the results and methods formulated in § 3 of this paper.  ... 
doi:10.1070/im8766 fatcat:mtmli5r34rc3dalkzfard3ekje

Super-k: A Piecewise Linear Classifier Based on Voronoi Tessellations [article]

Rahman Salim Zengin
2021 arXiv   pre-print
It is called Supervised k-Voxels or in short Super-k. We are introducing Super-k as a foundational new algorithm and opening the possibility of a new family of algorithms.  ...  In this paper, it is shown via comparisons on certain datasets that the Super-k algorithm has the potential of providing comparable performance of the well-known SVM family of algorithms with less complexity  ...  A Voronoi polyhedron is a convex region defined by an inner generator point and some outer generator points, as shown in (1) .  ... 
arXiv:2012.15492v3 fatcat:2v73zg4tenczvgkydccvqxpb2y

Page 3926 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
The abstract of the e-print: “Let XY be a space of constant curvature and P be a convex polyhedron in X.  ...  In this paper we classify Coxeter decompositions of simplices in hyperbolic space of dimension greater than 3.  ... 

Page 4844 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
A combinatorial polyhedron A. is a graph (the 1-skeleton Sk'(.)) together with a collection of cycles (the faces of F.) satisfying the usual incidence properties, but double edges in Sk'(P.) are now allowed  ...  The authors define a regular projective polyhedron FY as a regu- lar combinatorial polyhedron A. together with an embedding g of Sk'(P.) into the 3-dimensional projective space P® for which there exists  ... 

An Incremental Nearest Neighbor Algorithm with Queries

Joel Ratsaby
1997 Neural Information Processing Systems  
The principle on which this algorithm is based is general enough to be used in any learning algorithm which permits a model-selection criterion and for which the error rate of the classifier is calculable  ...  in terms of the complexity of the model.  ...  computing the adjacencies of facets of a polyhedron, d.  ... 
dblp:conf/nips/Ratsaby97 fatcat:s7zwiqrcczdubkxxkgc7ps3u7u

Super-k: A Piecewise Linear Classifier Based on Voronoi Tessellations

Rahman Salim Zengin, Volkan Sezer
2021 Zenodo  
It is called Supervised k-Voxels or in short Super-k. We are introducing Super-k as a foundational new algorithm and opening the possibility of a new family of algorithms.  ...  In this paper, it is shown via comparisons on certain datasets that the Super-k algorithm has the potential of providing similar accuracy and training performance of the well-known SVM family of algorithms  ...  A detailed literature review about PWL classifiers can be found in [1] .  ... 
doi:10.5281/zenodo.4460307 fatcat:jh6tiebarvcz5outzt3x6cjru4

Thermodynamic Symmetry and Its Applications ‐ Search for Beauty in Science [chapter]

Zhen-Chuan Li
2018 Symmetry (Group Theory) and Mathematical Treatment in Chemistry  
(Albert Einstein, 1946) Abstract A variety of thermodynamic variables are properly arranged at vertices of an extended concentric multi-polyhedron diagram based on their physical meanings.  ...  Any desired partial derivatives can be derived in terms of several available quantities by a foolproof graphic method.  ...  An extended polyhedron Total 24 members of the C P 's family can be constructed as an extended 26-face polyhedron (rhombicuboctahedron) shown in Physically, such a scheme shown in Figure 4 to arrange  ... 
doi:10.5772/intechopen.72839 fatcat:3hczic53jzbhtp7dolpp2zavpm

Boolean operations of 2-manifolds through vertex neighborhood classification

Martti Mäntylä
1986 ACM Transactions on Graphics  
The classifier works by means of decision rules that guarantee the topological consistency and regularity of the resulting polyhedron.  ...  By virtue of the classifier, the various special cases can be reduced into a collection of classification problems involving a pair of coincident vertices.  ...  ACKNOWLEDGMENTS The thorough and helpful comments of the reviewers on preliminary versions of  ... 
doi:10.1145/7529.7530 fatcat:3ocen6mwjbd3hcl5arbp2m6vwi
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