Angle Principal Component Analysis

Recently, many ℓ1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed. Angle PCA employs ℓ2-norm to measure reconstruction error and variance of projected da-ta and maximizes the summation of ratio between variance and reconstruction error of each data. Angle PCA not only is robust to outliers but also retains PCA’s desirable property such as rotational invariance. To solve Angle PCA, we propose an iterative algorithm, which has closed-form solution in each iteration. Extensive experiments on several face image databases illustrate that our method is overall superior to the other robust PCA algorithms, such as PCA, PCA-L1 greedy, PCA-L1 nongreedy and HQ-PCA.

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Comparing Ranking Methods for Tensor Components in Multilinear and Concurrent Subspace Analysis with Applications in Face Images

International Journal of Image and Graphics ◽

10.1142/s0219467815500060 ◽

2015 ◽

Vol 15 (01) ◽

pp. 1550006 ◽

Cited By ~ 3

Author(s):

Tiene A. Filisbino ◽

Gilson A. Giraldi ◽

Carlos E. Thomaz

Keyword(s):

Principal Component Analysis ◽

Image Analysis ◽

Gait Recognition ◽

Principal Component ◽

Component Analysis ◽

Face Image ◽

Image Databases ◽

Subspace Analysis ◽

Raw Data ◽

Face Image Analysis

In the area of multi-dimensional image databases modeling, the multilinear principal component analysis (MPCA) and concurrent subspace analysis (CSA) approaches were independently proposed and applied for mining image databases. The former follows the classical principal component analysis (PCA) paradigm that centers the sample data before subspace learning. The CSA, on the other hand, performs the learning procedure using the raw data. Besides, the corresponding tensor components have been ranked in order to identify the principal tensor subspaces for separating sample groups for face image analysis and gait recognition. In this paper, we first demonstrate that if CSA receives centered input samples and we consider full projection matrices then the obtained solution is equal to the one generated by MPCA. Then, we consider the general problem of ranking tensor components. We examine the theoretical aspects of typical solutions in this field: (a) Estimating the covariance structure of the database; (b) Computing discriminant weights through separating hyperplanes; (c) Application of Fisher criterium. We discuss these solutions for tensor subspaces learned using centered data (MPCA) and raw data (CSA). In the experimental results we focus on tensor principal components selected by the mentioned techniques for face image analysis considering gender classification as well as reconstruction problems.

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ROBUST ADAPTED PRINCIPAL COMPONENT ANALYSIS FOR FACE RECOGNITION

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001409007284 ◽

2009 ◽

Vol 23 (03) ◽

pp. 491-520 ◽

Cited By ~ 4

Author(s):

SHAOKANG CHEN ◽

BRIAN C. LOVELL ◽

TING SHAN

Keyword(s):

Principal Component Analysis ◽

Recognition Rate ◽

Principal Component ◽

Component Analysis ◽

Face Image ◽

The Other ◽

Appearance Model ◽

Lighting Conditions ◽

Highly Sensitive ◽

Gallery Image

Recognizing faces with uncontrolled pose, illumination, and expression is a challenging task due to the fact that features insensitive to one variation may be highly sensitive to the other variations. Existing techniques dealing with just one of these variations are very often unable to cope with the other variations. The problem is even more difficult in applications where only one gallery image per person is available. In this paper, we describe a recognition method, Adapted Principal Component Analysis (APCA), that can simultaneously deal with large variations in both illumination and facial expression using only a single gallery image per person. We have now extended this method to handle head pose variations in two steps. The first step is to apply an Active Appearance Model (AAM) to the non-frontal face image to construct a synthesized frontal face image. The second is to use APCA for classification robust to lighting and pose. The proposed technique is evaluated on three public face databases — Asian Face, Yale Face, and FERET Database — with images under different lighting conditions, facial expressions, and head poses. Experimental results show that our method performs much better than other recognition methods including PCA, FLD, PRM and LTP. More specifically, we show that by using AAM for frontal face synthesis from high pose angle faces, the recognition rate of our APCA method increases by up to a factor of 4.

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An augmented Lagrangian method for solving total variation (TV)-based image registration model

Journal of Algorithms & Computational Technology ◽

10.1177/1748302620973534 ◽

2020 ◽

Vol 14 ◽

pp. 174830262097353

Author(s):

Noppadol Chumchob ◽

Ke Chen

Keyword(s):

Image Registration ◽

Augmented Lagrangian ◽

Numerical Solutions ◽

Augmented Lagrangian Method ◽

Closed Form Solution ◽

Numerical Algorithms ◽

Lagrangian Method ◽

Form Solution ◽

The Other ◽

Other Hand

Variational methods for image registration basically involve a regularizer to ensure that the resulting well-posed problem admits a solution. Different choices of regularizers lead to different deformations. On one hand, the conventional regularizers, such as the elastic, diffusion and curvature regularizers, are able to generate globally smooth deformations and generally useful for many applications. On the other hand, these regularizers become poor in some applications where discontinuities or steep gradients in the deformations are required. As is well-known, the total (TV) variation regularizer is more appropriate to preserve discontinuities of the deformations. However, it is difficult in developing an efficient numerical method to ensure that numerical solutions satisfy this requirement because of the non-differentiability and non-linearity of the TV regularizer. In this work we focus on computational challenges arising in approximately solving TV-based image registration model. Motivated by many efficient numerical algorithms in image restoration, we propose to use augmented Lagrangian method (ALM). At each iteration, the computation of our ALM requires to solve two subproblems. On one hand for the first subproblem, it is impossible to obtain exact solution. On the other hand for the second subproblem, it has a closed-form solution. To this end, we propose an efficient nonlinear multigrid (NMG) method to obtain an approximate solution to the first subproblem. Numerical results on real medical images not only confirm that our proposed ALM is more computationally efficient than some existing methods, but also that the proposed ALM delivers the accurate registration results with the desired property of the constructed deformations in a reasonable number of iterations.

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Quantify Coal Macrolithotypes of a Whole Coal Seam: A Method Combing Multiple Geophysical Logging and Principal Component Analysis

Energies ◽

10.3390/en14010213 ◽

2021 ◽

Vol 14 (1) ◽

pp. 213

Author(s):

Chao Cui ◽

Suoliang Chang ◽

Yanbin Yao ◽

Lutong Cao

Keyword(s):

Principal Component Analysis ◽

Coal Seam ◽

Coalbed Methane ◽

Principal Component ◽

Component Analysis ◽

Gas Production ◽

Index Model ◽

Geophysical Logging ◽

The Relationship ◽

Observation Results

Coal macrolithotypes control the reservoir heterogeneity, which plays a significant role in the exploration and development of coalbed methane. Traditional methods for coal macrolithotype evaluation often rely on core observation, but these techniques are non-economical and insufficient. The geophysical logging data are easily available for coalbed methane exploration; thus, it is necessary to find a relationship between core observation results and wireline logging data, and then to provide a new method to quantify coal macrolithotypes of a whole coal seam. In this study, we propose a L-Index model by combing the multiple geophysical logging data with principal component analysis, and we use the L-Index model to quantitatively evaluate the vertical and regional distributions of the macrolithotypes of No. 3 coal seam in Zhengzhuang field, southern Qinshui basin. Moreover, we also proposed a S-Index model to quantitatively evaluate the general brightness of a whole coal seam: the increase of the S-Index from 1 to 3.7, indicates decreasing brightness, i.e., from bright coal to dull coal. Finally, we discussed the relationship between S-Index and the hydro-fracturing effect. It was found that the coal seam with low S-Index values can easily form long extending fractures during hydraulic fracturing. Therefore, the lower S-Index values indicate much more favorable gas production potential in the Zhengzhuang field. This study provides a new methodology to evaluate coal macrolithotypes by using geophysical logging data.

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Discrimination of brazilian red varietal wines according to their sensory descriptors

Ciência e Agrotecnologia ◽

10.1590/s1413-70542011000600018 ◽

2011 ◽

Vol 35 (6) ◽

pp. 1172-1176 ◽

Cited By ~ 4

Author(s):

Alberto Miele ◽

Luiz Antenor Rizzon

Keyword(s):

Principal Component Analysis ◽

Total Variation ◽

Principal Component ◽

Pinot Noir ◽

The Other ◽

Sensory Characteristics ◽

Cabernet Sauvignon ◽

Sensory Panel ◽

Red Grape ◽

Grape Varieties

The purpose of this paper was to establish the sensory characteristics of wines made from old and newly introduced red grape varieties. To attain this objective, 16 Brazilian red varietal wines were evaluated by a sensory panel of enologists who assessed wines according to their aroma and flavor descriptors. A 90 mm unstructured scale was used to quantify the intensity of 26 descriptors, which were analyzed by means of the Principal Component Analysis (PCA). The PCA showed that three important components represented 74.11% of the total variation. PC 1 discriminated Tempranillo, Marselan and Ruby Cabernet wines, with Tempranillo being characterized by its equilibrium, quality, harmony, persistence and body, as well as by, fruity, spicy and oaky characters. The other two varietals were defined by vegetal, oaky and salty characteristics; PC 2 discriminated Pinot Noir, Sangiovese, Cabernet Sauvignon and Arinarnoa, where Pinot Noir was characterized by its floral flavor; PC 3 discriminated only Malbec, which had weak, floral and fruity characteristics. The other varietal wines did not show important discriminating effects.

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Air Pollution and Human Development in Europe: A New Index Using Principal Component Analysis

Sustainability ◽

10.3390/su10020312 ◽

2018 ◽

Vol 10 (2) ◽

pp. 312 ◽

Cited By ~ 7

Author(s):

Ana-Maria Săndică ◽

Monica Dudian ◽

Aurelia Ştefănescu

Keyword(s):

Principal Component Analysis ◽

Human Development ◽

Quantitative Measure ◽

Principal Component ◽

Component Analysis ◽

Life Expectancy At Birth ◽

Real Gdp ◽

Development Indicator ◽

The Relationship ◽

Pm2.5 Concentration

EU countries to measure human development incorporating the ambient PM2.5 concentration effect. Using a principal component analysis, we extract the information for 2010 and 2015 using the Real GDP/capita, the life expectancy at birth, tertiary educational attainment, ambient PM2.5 concentration, and the death rate due to exposure to ambient PM2.5 concentration for 29 European countries. This paper has two main results: it gives an overview about the relationship between human development and ambient PM2.5 concentration, and second, it provides a new quantitative measure, PHDI, which reshapes the concept of human development and the exposure to ambient PM2.5 concentration. Using rating classes, we defined thresholds for both HDI and PHDI values to group the countries in four categories. When comparing the migration matrix from 2010 to 2015 for HDI values, some countries improved the development indicator (Romania, Poland, Malta, Estonia, Cyprus), while no downgrades were observed. When comparing the transition matrix using the newly developed indicator, PHDI, the upgrades observed were for Denmark and Estonia, while some countries like Spain and Italy moved to a lower rating class due to ambient PM2.5 concentration.

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Correlation of environmental factors and spatial distribution of moluscs communities in mangrove reboisation areas of Seribu Islands, Indonesia

TORANI: Journal of Fisheries and Marine Science ◽

10.35911/torani.v2i2.7051 ◽

2019 ◽

Vol 2 (2) ◽

Cited By ~ 1

Author(s):

Syahrial Syahrial ◽

Eryc Pranata ◽

Hendri Susilo

Keyword(s):

Principal Component Analysis ◽

Spatial Distribution ◽

Environmental Factors ◽

Principal Component ◽

Quality Standard ◽

Small Plot ◽

Line Transects ◽

Relationship Of ◽

The Relationship ◽

Mangrove Reforestation

Mangrove reforestation is often carried out in various regions or regions, but information about the relationship of environmental factors and the distribution of fauna associations is still very minimal. The Principal Component Analysis (PCA) study on the correlation of environmental factors and the spatial distribution of the molusks community in the Seribu Islands mangrove reforestation area was conducted in March 2014 with the aim of analyzing environmental factors for the diversity and presence of the molusks. Environmental factors are measured insecurely, while the moluccan community is collected by making line transects and plots measuring 10 x 10 m2 and in the size of 10 x 10 m2, a small plot of 1 x 1 m2 is made. The results of the study show that environmental factors are not so different between stations and do not exceed the quality standard for the lives of 4 species of mollusks, where the parameters of aquatic pH are the environmental factors that most influence their distribution.Keywords: environmental factors, distribution, mollusks community, mangrove reforestation, Seribu Islands

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Comparative analysis of populations of the Balkan endemic species Daphne malyana Blecic (Thymeleaceae)

Archives of Biological Sciences ◽

10.2298/abs1004151j ◽

2010 ◽

Vol 62 (4) ◽

pp. 1151-1162 ◽

Cited By ~ 2

Author(s):

Marina Juskovic ◽

P. Vasiljevic ◽

V. Randjelovic ◽

V. Stevanovic ◽

Branka Stevanovic

Keyword(s):

Principal Component Analysis ◽

Comparative Analysis ◽

Endemic Species ◽

Morphological Variability ◽

Principal Component ◽

Balkan Peninsula ◽

Canonical Discriminant Analysis ◽

The Other ◽

Isolated Populations ◽

Microclimate Conditions

Daphne malyana Blecic (Thymeleaceae) is an endemic species of the western part of the Balkan Peninsula, distributed in the mountains, canyons and gorges of N. Montenegro, E. Bosnia and W. Serbia. The comparative morphoanatomic investigations have included four distantly separated populations of the species D. malyana, i.e. two from Serbia, from the ravines of Sokoline and Vranjak on Mt. Tara, and two from Montenegro, in the canyons of the Tara and Piva rivers. Comparative morphoanatomical studies have shown the presence of general adaptive characteristics of a specific, conservative xeromorphic type, slightly differing in each population. Principal component analysis (PCA) and canonical discriminant analysis (CDA) of 20 morphoanatomical characteristics of the leaves and stems have shown a clear distinction between the populations from the river Piva canyon (Montenegro) and those from the Sokoline ravine (Serbia), on one side, and those of Vranjak gorge (Serbia) and of the river Tara canyon (Montenegro) on the other side. It may be assumed that the mild morphological variability of the isolated populations of the Balkan endemic species D. malyana in the canyons and gorges seem to have been affected by the microclimate conditions in their habitats.

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An Analytical Solution for Flexible Substrates Undergoing Small Equibiaxial Strains

ASME 2009 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2009-206285 ◽

2009 ◽

Author(s):

Martin Y. M. Chiang ◽

Joy Dunkers

Keyword(s):

Fluid Shear Stress ◽

Flexible Substrate ◽

Closed Form Solution ◽

Form Solution ◽

Controlled Delivery ◽

Cell Culture Systems ◽

Substrate Strain ◽

Elastic Responses ◽

The Relationship

Cells can distinguish between different types of mechanical signals, such as stretch (tension), pressure (compression), and shear, to guide mechanosensitive cellular activities. Cell culture systems with controlled delivery of a mechanical input such as substrate strain, hydrostatic pressure, or fluid shear stress are used for the in vitro application of these forces. The work reported here uses a system that imparts equibiaxial loading on a flexible substrate to study cell response to stretch, similar to the Bioflex in the Flexcell [1] family of products. The objective of this study is to introduce an analytical (closed-form) solution of the relationship between the substrate strain and pressure under small strains, less than 2%. The solution is derived from the superposition of two elastic responses induced in the equibiaxial strain culture system after applying pressure.

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Effects of Differential Tax Rates on Transfer Pricing

Journal of Accounting Auditing & Finance ◽

10.1177/0148558x9601100203 ◽

1996 ◽

Vol 11 (2) ◽

pp. 183-196 ◽

Cited By ~ 5

Author(s):

Shu-hsing Li ◽

Kashi R. Balachandran

Keyword(s):

Internal Control ◽

Transfer Pricing ◽

Closed Form Solution ◽

Form Solution ◽

Price System ◽

The Other ◽

Tax Rates ◽

Tax Rate ◽

Optimal Mechanism ◽

Pricing System

The purpose of this paper is to study transfer pricing under asymmetric information and taxation. In accordance with the empirical evidence documented in accounting literature, this paper assumes that the firm uses one pricing system instead of two pricing systems—one for the tax purposes and the other for internal control. We provide a closed-form solution for the optimal mechanism under a dual-price system, which allows for the price credited to the manufacturing division to not equal the price charged to the distribution division. The equilibrium outcomes of the analysis suggest several interesting findings. Under a dual-price system, both divisional accounting profits at equilibrium change in the same direction with respect to the change of tax rate. However, the direct effect is larger than the indirect effect. Under a dual-price system, the division with the lower tax rate should be credited more profits than the division with the higher tax rate, but it would not fully bear all the profits.

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