• Title/Summary/Keyword: $L_{2,1}$-norm regression

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Two Dimensional Slow Feature Discriminant Analysis via L2,1 Norm Minimization for Feature Extraction

  • Gu, Xingjian;Shu, Xiangbo;Ren, Shougang;Xu, Huanliang
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.7
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    • pp.3194-3216
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    • 2018
  • Slow Feature Discriminant Analysis (SFDA) is a supervised feature extraction method inspired by biological mechanism. In this paper, a novel method called Two Dimensional Slow Feature Discriminant Analysis via $L_{2,1}$ norm minimization ($2DSFDA-L_{2,1}$) is proposed. $2DSFDA-L_{2,1}$ integrates $L_{2,1}$ norm regularization and 2D statically uncorrelated constraint to extract discriminant feature. First, $L_{2,1}$ norm regularization can promote the projection matrix row-sparsity, which makes the feature selection and subspace learning simultaneously. Second, uncorrelated features of minimum redundancy are effective for classification. We define 2D statistically uncorrelated model that each row (or column) are independent. Third, we provide a feasible solution by transforming the proposed $L_{2,1}$ nonlinear model into a linear regression type. Additionally, $2DSFDA-L_{2,1}$ is extended to a bilateral projection version called $BSFDA-L_{2,1}$. The advantage of $BSFDA-L_{2,1}$ is that an image can be represented with much less coefficients. Experimental results on three face databases demonstrate that the proposed $2DSFDA-L_{2,1}/BSFDA-L_{2,1}$ can obtain competitive performance.

Power Failure Sensitivity Analysis via Grouped L1/2 Sparsity Constrained Logistic Regression

  • Li, Baoshu;Zhou, Xin;Dong, Ping
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.15 no.8
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    • pp.3086-3101
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    • 2021
  • To supply precise marketing and differentiated service for the electric power service department, it is very important to predict the customers with high sensitivity of electric power failure. To solve this problem, we propose a novel grouped 𝑙1/2 sparsity constrained logistic regression method for sensitivity assessment of electric power failure. Different from the 𝑙1 norm and k-support norm, the proposed grouped 𝑙1/2 sparsity constrained logistic regression method simultaneously imposes the inter-class information and tighter approximation to the nonconvex 𝑙0 sparsity to exploit multiple correlated attributions for prediction. Firstly, the attributes or factors for predicting the customer sensitivity of power failure are selected from customer sheets, such as customer information, electric consuming information, electrical bill, 95598 work sheet, power failure events, etc. Secondly, all these samples with attributes are clustered into several categories, and samples in the same category are assumed to be sharing similar properties. Then, 𝑙1/2 norm constrained logistic regression model is built to predict the customer's sensitivity of power failure. Alternating direction of multipliers (ADMM) algorithm is finally employed to solve the problem by splitting it into several sub-problems effectively. Experimental results on power electrical dataset with about one million customer data from a province validate that the proposed method has a good prediction accuracy.

A Robust Estimation Procedure for the Linear Regression Model

  • Kim, Bu-Yong
    • Journal of the Korean Statistical Society
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    • v.16 no.2
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    • pp.80-91
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    • 1987
  • Minimum $L_i$ norm estimation is a robust procedure ins the sense that it leads to an estimator which has greater statistical eficiency than the least squares estimator in the presence of outliers. And the $L_1$ norm estimator has some desirable statistical properties. In this paper a new computational procedure for $L_1$ norm estimation is proposed which combines the idea of reweighted least squares method and the linear programming approach. A modification of the projective transformation method is employed to solve the linear programming problem instead of the simplex method. It is proved that the proposed algorithm terminates in a finite number of iterations.

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Band Selection Using L2,1-norm Regression for Hyperspectral Target Detection (초분광 표적 탐지를 위한 L2,1-norm Regression 기반 밴드 선택 기법)

  • Kim, Joochang;Yang, Yukyung;Kim, Jun-Hyung;Kim, Junmo
    • Korean Journal of Remote Sensing
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    • v.33 no.5_1
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    • pp.455-467
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    • 2017
  • When performing target detection using hyperspectral imagery, a feature extraction process is necessary to solve the problem of redundancy of adjacent spectral bands and the problem of a large amount of calculation due to high dimensional data. This study proposes a new band selection method using the $L_{2,1}$-norm regression model to apply the feature selection technique in the machine learning field to the hyperspectral band selection. In order to analyze the performance of the proposed band selection technique, we collected the hyperspectral imagery and these were used to analyze the performance of target detection with band selection. The Adaptive Cosine Estimator (ACE) detection performance is maintained or improved when the number of bands is reduced from 164 to about 30 to 40 bands in the 350 nm to 2500 nm wavelength band. Experimental results show that the proposed band selection technique extracts bands that are effective for detection in hyperspectral images and can reduce the size of the data without reducing the performance, which can help improve the processing speed of real-time target detection system in the future.

Feature Selection via Embedded Learning Based on Tangent Space Alignment for Microarray Data

  • Ye, Xiucai;Sakurai, Tetsuya
    • Journal of Computing Science and Engineering
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    • v.11 no.4
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    • pp.121-129
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    • 2017
  • Feature selection has been widely established as an efficient technique for microarray data analysis. Feature selection aims to search for the most important feature/gene subset of a given dataset according to its relevance to the current target. Unsupervised feature selection is considered to be challenging due to the lack of label information. In this paper, we propose a novel method for unsupervised feature selection, which incorporates embedded learning and $l_{2,1}-norm$ sparse regression into a framework to select genes in microarray data analysis. Local tangent space alignment is applied during embedded learning to preserve the local data structure. The $l_{2,1}-norm$ sparse regression acts as a constraint to aid in learning the gene weights correlatively, by which the proposed method optimizes for selecting the informative genes which better capture the interesting natural classes of samples. We provide an effective algorithm to solve the optimization problem in our method. Finally, to validate the efficacy of the proposed method, we evaluate the proposed method on real microarray gene expression datasets. The experimental results demonstrate that the proposed method obtains quite promising performance.

Correlates of Subjective Well-being in Korean Culture (한국문화에서 주관안녕에 영향을 미치는 사회심리 요인들)

  • Hahn, Doug-Woong
    • Korean Journal of Culture and Social Issue
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    • v.12 no.5_spc
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    • pp.45-79
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    • 2006
  • The purpose of this paper was to review the results of the subjective well-being(swb) studies performed by Hahn and coworkers in Korean culture. As the correlates of swb, we dealt with demographic/individual difference variables, intrapersonal variables, interpersonal process variables, and Korean cultural variables. We proposed that the components of swb were consisted of quality of life(cognitive swb) and overall happy feelings about one's own life(emotional swb). It was also assumed that a measure of total swb could be calculated by summated mean of cognitive swb and emotional swb measures. The data of the swb studies were analyzed and interpreted according to the above three measures of swb. The results of a nationwide survey(Hahn, 2004) from age of 19 to 75 years ald(n=2,230) showed significant simple correlation coefficients between the following demographic/individual difference variables and swb: Gender difference in swb was found(total swb r=.08, p<.001; life satisfaction r=.10, p<.001; overall emotional swb r=.05, p<.05). Men were happier than women in terms of all three measures of swb. It was also found that women appeared to experience greater positive and negative emotions. Correlation between age and emotional swb(r=.09, p<.001) was significant, but life satisfaction was not significant(r=.04, n.s). Correlations between economic status and swb were also significant(total swb r =.23, p<.001; life satisfaction r=.15 p<.001; overall emotional swb r=.15, p<.001l). Although existence of father was negatively related to emotional swb(r=-.05, p<.05), the existence of mother was not related to any of swb measures. Similarly existence of brothers was related positively to overall emotional swb, but existence of sisters was not. Though existence of son was not related to swb, daughter contributed negatively to swb(total swb -.12, p<.01; life satisfaction -.09, p<.05; emotional swb r=-.12, p<.01). We assumed that family member-in-Iaw also contributed to swb because the extended dose social networks were important in Korean culture. The results showed that the following family member-in-law variables were related to swb: Parents-in-law(total swb r=.11, p<.01; life satisfaction r=.10, p<.01; emotional swb r=.10, p<.01), father-in-law(total swb r=.11, p<.01; life satisfaction r=.11, p<.01; emotional swb r=.06, n.s). The result suggested that especially father-in-law contributed to swb through financial and social support. Correlations between emotional experiences in everyday life and swb were also presented. The range of correlation coefficients between the positive emotion measures and swb were r=.30~.48(p<.001) when the above two measures obtained at same time. But the range decreased to r=.19~32(p<.001) when the swb measure was obtained 9 month later longitudinally. Intercorrelations between positive emotional experience; and life satisfaction were r=.37~58(p<.001) when two measures were obtained at same time. We also examined the effects of the intrapersonal cognitive responses to the most stressful life event upon swb. The results of nationwide survey(n=1,021) showed that self-disclosure(total swb r=.09, p<.010; life satisfaction r=.10, p<.01; emotional swb r=.07, p<.01), rumination(total swb r=-.17, p<.001), thought avoidance(total swb r=.12, p<.001; life satisfaction r=-.08; emotional swb r=-.12, p<.001) and suppression(total swb r=-.13, p<.001; life satisfaction r=-.08, p<.05: emotional swb r=-.13, p<.001) contributed to swb. It was also suggested that mismatch between self-guide and regulatory focus contributed negatively to emotional swb. It was also found that social comparison motives and fulfillment of the motives contributed to swb. The results of a survey research(n=363 college students) revealed that the higher the general social comparison motive, the lower the swb(total swb r=-.15, P<.01: life satisfaction r=-.17. p<.01; emotional swb r=-.10, p<.05). It was also found that satisfaction level of self-evalution motive contributed positively to swb(total swb r=-.14. p<.01: life satisfaction r=-.12, p<.05; emotional swb r=.15, p<.001). Both of self-improvement motive(r=.13, p<.05) and satisfaction level of self-improvement motive(r=.12, p<.05) contributed positively to emotional swb, respectively. The above results suggested that swb was depended upon the interaction effect of social comparison motive; and level of fulfillment of the motives. We also reported the significant multiple predictors of swb in a sample of age from 60years to 89years olds. The results of multiple regression analysis showed that the significant multiple predictors of swb were past illness(β=.174, p<.001), economic status(β=.418, p<.001), marital satisfaction(β=.0841, p<.001), satisfaction of offsprins(β=.065, p<.01), expectation level of social support from offsprings(β=-.049, p<.001), and negative emotions(β=-.454. p<.001) among 16 social psychological factors. It was also found that swb was an important multiple predictors of physical health. This finding was replicated in a longitudinal study. Both of positive and negative emotional experiences were significant multiple predictors of physical health one year later. The results of the discriminant analysis showed both of total swb and positive emotional experiences contributed to discriminate the happy and healthy olds from unhappy and unhealthy olds. We paper also examined the effects of the nonnative social behaviors upon swb in Korean culture. The main hypotheses of the study(Hahn, 2006, in press) was that the important nonnative behaviors would influence on swb through both of the mediation processes of adjustment to social relationships and psychological stress. The survey data were collected from 2,129 adults age of 19 to 75, from 7 regional areas in Korea. The results of the study revealed that almost all of correlation coefficients between 15 normative social behaviors and the above three criteria w-ere significant. The fitness test results of the covariance structural equation model showed that all of the fitness indices were satisfactory (GFI=.974, AGFI=.909, NNFI=.922, NFI=.973, CFI=.974. RMR=.049, RMSEA=.073). The results of the analysis revealed that the following five path coeffi6ents from behaviors to social adjustment were significant; behavior tor family and family members(t=5.87, p<.001), courteous behavior(t=4.39, p<.001), faithful behavior (t=2.15. p<.05). collectivistic behavior(t=8.31, p<.001). Seven path coefficients from the normative behaviors to psychological stress were significant; behavior for family and family members (t=-4.63, p<.001), faithful behavior(t=-3.86, p<.001). suppression of emotional expression(t=3.99, p<.001), trustworthy and dependable behavior(t=-2.21, p<.05), collectivistic behavior(t=3.72, p<.001), effortful and diligent behavior(t=2.94, p<.001), husbandry and saving behavior(t=3.40, p<.001). The above results suggested that four normative behaviors among seven behaviors contributed negatively to psychological stress in current Korean society. The results abo confirmed the hypothesized paths from social adjustment (t=10.40, p<.001) to swb and from psychological stress(t=-19.74, p<.001) to swb. The important results of the study were discussed in terms of the Confucian traditions and recent social changes in Korean culture. Finally limitations of this review paper were discussed and the suggestions for the future study were also proposed.