The Separating Hyperplane Theorem

1998 ◽  
pp. 281-282
Author(s):  
Nicholas H. Bingham ◽  
Rüdiger Kiesel
Keyword(s):  
Separating Hyperplane

scholarly journals Afriat and arbitrage

2021 ◽  
Author(s):  
Alan Beggs
Keyword(s):  
Revealed Preference ◽  
Mathematical Tool ◽  
Separating Hyperplane

AbstractThis paper presents a proof of Afriat’s (Int Econ Rev 8:67–77) theorem on revealed preference by using the idea that a rational consumer should not be vulnerable to arbitrage. The main mathematical tool is the separating hyperplane theorem.

scholarly journals Controllability of Continuous Bimodal Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Josep Ferrer ◽  
Juan R. Pacha ◽  
Marta Peña
Keyword(s):  
Linear Systems ◽  
Higher Dimensions ◽  
Linear Dynamics ◽  
Explicit Characterization ◽  
Separating Hyperplane

We consider bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. We prove that the study of controllability can be reduced to the unobservable case, and for these ones we obtain a simple explicit characterization of controllability for dimensions 2 and 3, as well as some partial criteria for higher dimensions.

An Effective K-Means Clustering Based SVM Algorithm

2013 ◽  
Vol 333-335 ◽  
pp. 1344-1348
Author(s):  
Yu Kai Yao ◽  
Yang Liu ◽  
Zhao Li ◽  
Xiao Yun Chen
Keyword(s):  
Support Vector ◽  
Svm Classifier ◽  
Small Subset ◽  
Training Set ◽  
Data Mining Algorithms ◽  
Svm Algorithm ◽  
Svm Model ◽  
Separating Hyperplane ◽  
Regression Problems ◽  
Mining Algorithms

Support Vector Machine (SVM) is one of the most popular and effective data mining algorithms which can be used to resolve classification or regression problems, and has attracted much attention these years. SVM could find the optimal separating hyperplane between classes, which afford outstanding generalization ability with it. Usually all the labeled records are used as training set. However, the optimal separating hyperplane only depends on a few crucial samples (Support Vectors, SVs), we neednt train SVM model on the whole training set. In this paper a novel SVM model based on K-means clustering is presented, in which only a small subset of the original training set is selected to constitute the final training set, and the SVM classifier is built through training on these selected samples. This greatly decrease the scale of the training set, and effectively saves the training and predicting cost of SVM, meanwhile guarantees its generalization performance.

SUPPORT VECTOR MACHINES FOR THAI PHONEME RECOGNITION

2001 ◽  
Vol 09 (06) ◽  
pp. 803-813 ◽  
Author(s):  
NUTTAKORN THUBTHONG ◽  
BOONSERM KIJSIRIKUL
Keyword(s):  
Support Vector Machine ◽  
Dimensional Space ◽  
High Dimensional ◽  
Support Vector ◽  
Phoneme Recognition ◽  
Classification Technique ◽  
Separating Hyperplane ◽  
Vector Machines ◽  
Tone Recognition ◽  
Vowel Recognition

The Support Vector Machine (SVM) has recently been introduced as a new pattern classification technique. It learns the boundary regions between samples belonging to two classes by mapping the input samples into a high dimensional space, and seeking a separating hyperplane in this space. This paper describes an application of SVMs to two phoneme recognition problems: 5 Thai tones, and 12 Thai vowels spoken in isolation. The best results on tone recognition are 96.09% and 90.57% for the inside test and outside test, respectively, and on vowel recognition are 95.51% and 87.08% for the inside test and outside test, respectively.

Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem

2002 ◽  
Vol 105 (2) ◽  
pp. 435-449 ◽  
Author(s):  
Andrew McLennan
Keyword(s):  
Separating Hyperplane

Structure and Visualization of High-Dimensional Conductance Spaces

2006 ◽  
Vol 96 (2) ◽  
pp. 891-905 ◽  
Author(s):  
Adam L. Taylor ◽  
Timothy J. Hickey ◽  
Astrid A. Prinz ◽  
Eve Marder
Keyword(s):  
Connected Components ◽  
High Dimensional ◽  
Intrinsic Properties ◽  
Calcium Dependent ◽  
Linear Classifier ◽  
Burst Period ◽  
Separating Hyperplane ◽  
Different Types ◽  
Components Analysis ◽  
Connected Components Analysis

Neurons, and realistic models of neurons, typically express several different types of voltage-gated conductances. These conductances are subject to continual regulation. Therefore it is essential to understand how changes in the conductances of a neuron affect its intrinsic properties, such as burst period or delay to firing after inhibition of a particular duration and magnitude. Even in model neurons, it can be difficult to visualize how the intrinsic properties vary as a function of their underlying maximal conductances. We used a technique, called clutter-based dimension reordering (CBDR), which enabled us to visualize intrinsic properties in high-dimensional conductance spaces. We applied CBDR to a family of models with eight different types of voltage- and calcium-dependent channels. CBDR yields images that reveal structure in the underlying conductance space. CBDR can also be used to visualize the results of other types of analysis. As examples, we use CBDR to visualize the results of a connected-components analysis, and to visually evaluate the results of a separating-hyperplane (i.e., linear classifier) analysis. We believe that CBDR will be a useful tool for visualizing the conductance spaces of neuronal models in many systems.

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