scholarly journals Robustness Analysis of Eleven Linear Classifiers in Extremely High–Dimensional Feature Spaces

2010 ◽  
pp. 72-83 ◽  
Author(s):  
Ludwig Lausser ◽  
Hans A. Kestler
Keyword(s):  
Robustness Analysis ◽  
High Dimensional ◽  
Linear Classifiers ◽  
Feature Spaces

Contour Reconstruction

2020 ◽  
pp. 584-618
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Probability Distribution ◽  
Image Retrieval ◽  
Probability Distribution Function ◽  
Feature Space ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
High Dimensional ◽  
Feature Spaces ◽  
Contour Reconstruction ◽  
Multidimensional Feature Spaces

The method of Probabilistic Features Combination (PFC) enables interpolation and modeling of high-dimensional N data using features' combinations and different coefficients γ: polynomial, sinusoidal, cosinusoidal, tangent, cotangent, logarithmic, exponential, arc sin, arc cos, arc tan, arc cot or power function. Functions for γ calculations are chosen individually at each data modeling and it is treated as N-dimensional probability distribution function: γ depends on initial requirements and features' specifications. PFC method leads to data interpolation as handwriting or signature identification and image retrieval via discrete set of feature vectors in N-dimensional feature space. So PFC method makes possible the combination of two important problems: interpolation and modeling in a matter of image retrieval or writer identification. Main features of PFC method are: PFC interpolation develops a linear interpolation in multidimensional feature spaces into other functions as N-dimensional probability distribution functions.

A MULTI-CLASS SUPPORT VECTOR MACHINE: THEORY AND MODEL

2013 ◽  
Vol 12 (06) ◽  
pp. 1175-1199 ◽  
Author(s):  
MINGHE SUN
Keyword(s):  
Support Vector Machine ◽  
Quadratic Programming ◽  
Programming Model ◽  
Inner Product ◽  
High Dimensional ◽  
Support Vector ◽  
Test Problems ◽  
Discriminant Functions ◽  
Input Space ◽  
Feature Spaces

A multi-class support vector machine (M-SVM) is developed, its dual is derived, its dual is mapped to high dimensional feature spaces using inner product kernels, and its performance is tested. The M-SVM is formulated as a quadratic programming model. Its dual, also a quadratic programming model, is very elegant and is easier to solve than the primal. The discriminant functions can be directly constructed from the dual solution. By using inner product kernels, the M-SVM can be built and nonlinear discriminant functions can be constructed in high dimensional feature spaces without carrying out the mappings from the input space to the feature spaces. The size of the dual, measured by the number of variables and constraints, is independent of the dimension of the input space and stays the same whether the M-SVM is built in the input space or in a feature space. Compared to other models published in the literature, this M-SVM is equally or more effective. An example is presented to demonstrate the dual formulation and solution in feature spaces. Very good results were obtained on benchmark test problems from the literature.

scholarly journals Cleaning Data Sets with Diagnostic Errors in the High-Dimensional Feature Spaces

2019 ◽  
Vol 14 (2) ◽  
pp. 464-476
Author(s):  
I.A. Borisova ◽  
O.A. Kutnenko
Keyword(s):  
Diagnostic Errors ◽  
Medical Diagnostics ◽  
Maximal Class ◽  
High Dimensional ◽  
Data Sets ◽  
Local Similarity ◽  
Data Set ◽  
Feature Spaces ◽  
Feature Subspace ◽  
Low Dimensional

The paper proposes a new approach in data censoring, which allows correcting diagnostic errors in the data sets in case when these samples are described in high-dimensional feature spaces. Considering this case as a separate task is explained by the fact that in high-dimensional spaces most of the methods of outliers detection and data filtering, both statistical and metric, stop working. At the same time, for the tasks of medical diagnostics, given the complexity of the objects and phenomena studied, a large number of descriptive characteristics are the norm rather than the exception. To solve this problem, an approach that focuses on local similarity between objects belonging to the same class and uses the function of rival similarity (FRiS function) as a measure of similarity has been proposed. In this approach for efficient data cleaning from misclassified objects, the most informative and relevant low-dimensional feature subspace is selected, in which the separability of classes after their correction will be maximal. Class separability here means the similarity of objects of one class to each other and their dissimilarity to objects of another class. Cleaning data from class errors can consist both in their correction and removing the objects-outliers from the data set. The described method was implemented as a FRiS-LCFS algorithm (FRiS Local Censoring with Feature Selection) and tested on model and real biomedical problems, including the problem of diagnosing prostate cancer based on DNA microarray analysis. The developed algorithm showed its competitiveness in comparison with the standard methods for filtering data in high-dimensional spaces.

Git Recognition with Incomplete GEI Based on Random Forests

2014 ◽  
Vol 519-520 ◽  
pp. 661-666
Author(s):  
Qing Zhu ◽  
Jie Zhang
Keyword(s):  
Random Forests ◽  
Gait Recognition ◽  
Feature Space ◽  
High Dimensional ◽  
Random Forest Algorithm ◽  
Recognition Method ◽  
Locality Preserving ◽  
Feature Spaces ◽  
Feature Subspace ◽  
Low Dimensional

Abstract. This paper proposes an incomplete GEI gait recognition method based on Random Forests. There are numerous methods exist for git recognition,but they all lead to high dimensional feature spaces. To address the problem of high dimensional feature space, we propose the use of the Random Forest algorithm to rank features' importance . In order to efficiently search throughout subspaces, we apply a backward feature elimination search strategy.This demonstrate static areas of a GEI also contain useful information.Then, we project the selected feature to a low-dimensional feature subspace via the newly proposed two-dimensional locality preserving projections (2DLPP) method.Asa sequence,we further improve the discriminative power of the extracted features. Experimental results on the CASIA gait database demonstrate the effectiveness of the proposed method.

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