Chapter 2. Basics of single parameter regularization schemes

2013 ◽  
Keyword(s):  
Single Parameter ◽  
Parameter Regularization

TWO-STEP SINGLE PARAMETER REGULARIZATION FISHER DISCRIMINANT METHOD FOR FACE RECOGNITION

2006 ◽  
Vol 20 (02) ◽  
pp. 189-207 ◽  
Author(s):  
WEN-SHENG CHEN ◽  
PONG CHI YUEN ◽  
JIAN HUANG ◽  
BIN FANG
Keyword(s):  
Face Recognition ◽  
Small Sample Size ◽  
Small Sample ◽  
Single Parameter ◽  
Fisher Discriminant Analysis ◽  
Scatter Matrix ◽  
Second Stage ◽  
Fisher Discriminant ◽  
Optimal Projection ◽  
Parameter Regularization

In face recognition tasks, Fisher discriminant analysis (FDA) is one of the promising methods for dimensionality reduction and discriminant feature extraction. The objective of FDA is to find an optimal projection matrix, which maximizes the between-class-distance and simultaneously minimizes within-class-distance. The main limitation of traditional FDA is the so-called Small Sample Size (3S) problem. It induces that the within-class scatter matrix is singular and then the traditional FDA fails to perform directly for pattern classification. To overcome 3S problem, this paper proposes a novel two-step single parameter regularization Fisher discriminant (2SRFD) algorithm for face recognition. The first semi-regularized step is based on a rank lifting theorem. This step adjusts both the projection directions and their corresponding weights. Our previous three-to-one parameter regularized technique is exploited in the second stage, which just changes the weights of projection directions. It is shown that the final regularized within-class scatter matrix approaches the original within-class scatter matrix as the single parameter tends to zero. Also, our method has good computational complexity. The proposed method has been tested and evaluated with three public available databases, namely ORL, CMU PIE and FERET face databases. Comparing with existing state-of-the-art FDA-based methods in solving the S3 problem, the proposed 2SRFD approach gives the best performance.

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

A parameter hierarchy for agreement

2017 ◽  
Author(s):  
András Bárány
Keyword(s):  
Full Range ◽  
Single Parameter

This chapter models some of the results of the previous chapter. It builds on the recently developed notion of parameter hierarchies. Parameter hierarchies are sets of dependent parameters giving rise to chains of implicational relations among languages. The languages discussed in this book are positioned on a parameter hierarchy of ϕ‎-probes: some languages do not show any kind of agreement, others with a single ϕ‎-probe can agree with one argument, yet others with more than one probe with more arguments. It is argued that this hierarchy restricts agreement across languages in some ways, but that other parameters are needed to account for the full range of data studied in the book. This chapter concludes that there is no single parameter that governs differential object and differential subject marking.

scholarly journals Study on the Influence of Geometric Characteristics of Grain Membranes on Permeability Properties in Porous Sandstone

Membranes ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 587
Author(s):  
Run Shi ◽  
Huaiguang Xiao ◽  
Chengmeng Shao ◽  
Mingzheng Huang ◽  
Lei He
Keyword(s):  
Fluid Flow ◽  
Single Parameter ◽  
Control Group ◽  
Porous Rock ◽  
Permeability Characteristics ◽  
Natural Rock ◽  
Porous Sandstone ◽  
Novel Method ◽  
Boltzmann Method ◽  
Flow Laws

Studying the influence of grain characteristics on fluid flow in complex porous rock is one of the most important premises to reveal the permeability mechanism. Previous studies have mainly investigated the fluid flow laws in complex rock structures using an uncontrollable one single parameter of natural rock models or oversimplified control group models. In order to solve these problems, this paper proposes a novel method to reconstruct models that can independently control one single parameter of rock grain membranes based on mapping and reverse-mapping ideas. The lattice Boltzmann method is used to analyze the influence of grain parameters (grain radius, space, roundness, orientation, and model resolution) on the permeability characteristics (porosity, connectivity, permeability, flow path, and flow velocity). Results show that the grain radius and space have highly positive and negative correlations with permeability properties. The effect of grain roundness and resolution on permeability properties shows a strong regularity, while grain orientation on permeability properties shows strong randomness. This study is of great significance to reveal the fluid flow laws of natural rock structures.

Magnetic Field Synthesis and Parameter Regularization by Fuzzy Inference

2008 ◽  
Author(s):  
Andrei Ceclan ◽  
Constantin Barbulescu ◽  
Dan. D. Micu ◽  
Levente Czumbil
Keyword(s):  
Magnetic Field ◽  
Fuzzy Inference ◽  
Parameter Regularization

scholarly journals A single parameter approach to enhance the microstructural and mechanical properties of beta Ti-Nb alloy via open-air fiber laser nitriding

2020 ◽  
Vol 383 ◽  
pp. 125269 ◽  
Author(s):  
Chi-Wai Chan ◽  
Xianwen Chang ◽  
Mohammad Amin Bozorgzadeh ◽  
Graham C. Smith ◽  
Seunghwan Lee
Keyword(s):  
Mechanical Properties ◽  
Fiber Laser ◽  
Single Parameter ◽  
Laser Nitriding ◽  
Parameter Approach

Adsorption energy as a promising single-parameter descriptor for single atom catalysis in the oxygen evolution reaction

2021 ◽  
Author(s):  
Hai-Cai Huang ◽  
Jun Li ◽  
Yang Zhao ◽  
Jing Chen ◽  
Yu-Xiang Bu ◽  
...  
Keyword(s):  
Oxygen Evolution ◽  
Adsorption Energy ◽  
Oxygen Evolution Reaction ◽  
Single Parameter ◽  
Single Atom ◽  
Highly Efficient

A highly efficient and reliable single-parameter descriptor for offering a strategy to rationally design SACs for the OER.

Water-Quality Assessment of Lv-Tang River in Zhanjiang, China

2013 ◽  
Vol 295-298 ◽  
pp. 755-758 ◽  
Author(s):  
Ya Yun Liu ◽  
Zhi Hong Li ◽  
Xiao Jian Liang ◽  
Yan Peng Lin ◽  
Rong Hao Wu ◽  
...  
Keyword(s):  
Water Quality ◽  
Water Quality Index ◽  
Quality Index ◽  
Oxygen Demand ◽  
Pollution Index ◽  
Ammonia Nitrogen ◽  
Single Parameter ◽  
Water Quality Parameter ◽  
National Quality

Based on the water quality investigation data of December in 2010, the water environment quality of Lv-tang River in Zhanjiang national urban wetland park was assessed using single water quality parameter model and integrated water quality index model. The results show that the water quality of Lv-tang River is worse than the national quality standards for Grade V. The water is polluted seriously. The main pollutants are total nitrogen (TN), ammonia nitrogen (NH3-N) and chemical oxygen demand CODCr with their average concentrations of 60.49 mg/L, 30.57 mg/L and 227.38mg/L, respectively. The averages of their single parameter pollution index are 30.25 , 19.79 and 8.74. The average of single parameter pollution index of the river is 8.23 which indicated that the river belongs to heavy pollution zone. The integrated water quality index was 22.5 showing that the river belongs to serious pollution zone.

scholarly journals A simple clustering technique to extract subsets of data for function approximation

2015 ◽  
Vol 17 (5) ◽  
pp. 719-732
Author(s):  
Dulakshi Santhusitha Kumari Karunasingha ◽  
Shie-Yui Liong
Keyword(s):  
Function Approximation ◽  
Prediction Models ◽  
Data Extraction ◽  
Single Parameter ◽  
Subtractive Clustering ◽  
Data Sets ◽  
Clustering Methods ◽  
Clustering Method ◽  
Data Set ◽  
Functional Relationships

A simple clustering method is proposed for extracting representative subsets from lengthy data sets. The main purpose of the extracted subset of data is to use it to build prediction models (of the form of approximating functional relationships) instead of using the entire large data set. Such smaller subsets of data are often required in exploratory analysis stages of studies that involve resource consuming investigations. A few recent studies have used a subtractive clustering method (SCM) for such data extraction, in the absence of clustering methods for function approximation. SCM, however, requires several parameters to be specified. This study proposes a clustering method, which requires only a single parameter to be specified, yet it is shown to be as effective as the SCM. A method to find suitable values for the parameter is also proposed. Due to having only a single parameter, using the proposed clustering method is shown to be orders of magnitudes more efficient than using SCM. The effectiveness of the proposed method is demonstrated on phase space prediction of three univariate time series and prediction of two multivariate data sets. Some drawbacks of SCM when applied for data extraction are identified, and the proposed method is shown to be a solution for them.

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