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Unsupervised feature selection based on generalized regression model with linear discriminant constraints

COMPLEX & INTELLIGENT SYSTEMS 2025年第6期11卷 1-11页

作者： Dai, Xiangguang Guan, Mingyu Dai, Facheng Zhang, Wei Zhang, Tingji Che, Hangjun Dai, Xiangqin Chongqing Three Gorges Univ Chongqing Engn Res Ctr Internet Things & Intellige Wanzhou 404100 Peoples R China Coll Elect & Informat Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

Unsupervised feature selection (UFS) methods play a crucial role in improving the efficiency of extracting relevant information and reducing computational complexity in the context of big data analysis. Despite notable advancements in the field of unsupervised feature selection for large-scale datasets, many UFS methods still remain redundant and irrelevant features during the feature selection process. To tackle these challenges, we present a novel unsupervised feature selection method that leverages the generalized regression model with linear discriminant constraints to learn discriminant and effective features from the data. Benefited from this, the relationships and patterns within the high-dimensional data are retained in the reduced-dimensional feature space. We reformulate our proposed method as a multi-variable optimization problem that incorporates equality constraints. To efficiently solve this problem, we develop an algorithm that updates each variable alternately. Extensive experiments on six datasets among nine state-of-the-art methods on the clustering task are conducted to demonstrate the effectiveness of the proposed method.

关键词： Unsupervised feature selection generalized regression model Linear discriminant constraints

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generalized regression model for sequence matching and clustering

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KNOWLEDGE AND INFORMATION SYSTEMS 2007年第1期12卷 77-94页

作者： Lei, Hansheng Govindaraju, Venu Univ Texas Dept Comp Sci & Comp Informat Syst Brownsville TX 78520 USA SUNY Buffalo Dept Comp Sci & Engn Amherst NY USA

Linear relation has been found to be valuable in rule discovery of stocks, such as if stock X goes up a, stock Y will go down b. The traditional linear regression models the linear relation of two sequences faithfully. However, if a user requires clustering of stocks into groups where sequences have high linearity or similarity with each other, it is prohibitively expensive to compare sequences one by one. In this paper, we present generalized regression model (GRM) to match the linearity of multiple sequences at a time. GRM also gives strong heuristic support for graceful and efficient clustering. The experiments on the stocks in the NASDAQ market mined interesting clusters of stock trends efficiently.

关键词： similarity measure sequence matching sequence clustering generalized regression model eigenvalue and eigenvector

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Adaptive graph-based generalized regression model for unsupervised feature selection

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KNOWLEDGE-BASED SYSTEMS 2021年 227卷 107156-107156页

作者： Huang, Yanyong Shen, Zongxin Cai, Fuxu Li, Tianrui Lv, Fengmao SouthWestern Univ Finance & Econ Sch Stat Chengdu 611130 Peoples R China Affiliated Hosp Putian Coll Eye Inst Putian 351100 Peoples R China Southwest Jiaotong Univ Sch Comp & Artificial Intelligence Chengdu 611756 Peoples R China

Unsupervised feature selection is an important method to reduce dimensions of high-dimensional data without labels, which is beneficial to avoid "curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like clustering and retrieval. A lot of methods have been developed in recent years. However, most of them only focus on selecting discriminative features but ignore the redundancy of features. Besides, these methods construct the similarity structure of data in the original input space and remain fixed during feature selection. The similarity structure is easily affected by the noises and outliers. Then the reliability of the similarity structure will be reduced in the procedure of feature selection. In order to address these issues, we present a novel generalized regression model equipped with an uncorrelated constraint and the l(2,1)-norm regularization. It can simultaneously select the uncorrelated and discriminative features as well as reduce the variance of these data points belonging to the same neighborhood, which is helpful for the clustering task. Furthermore, to obtain the similarity structure of data and alleviate the influence of noises and outliers, we propose to adaptively learn a similarity-induced graph matrix in the reduced space and integrate it into the generalized regression model. An alternative iterative optimization algorithm is developed to solve the final objective function. A series of experiments are carried out on nine real-world data sets to demonstrate the effectiveness of the proposed method in comparison with other competing approaches. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Unsupervised feature selection generalized regression model Adaptive graph learning

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A general structural model for decomposing time series and its analysis as a generalized regression model

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Statistical Papers 1989年第1期30卷 245-261页

作者： Pauly, Ralf Institut für Empirische Wirtschaftsforschung Universität Osnabrück Osnabrück D-4500 Rolandstr. 8 Germany

The model of Harrison and Stevens (1976) for decomposing economic time series is reformulated and, following Harvey (1984), the reformulation is proposed as a general structural model. The discussion of this general model shows that it contains many recently discussed time series models as special cases. For structural models, the Kalman filter technique is usually used to decompose economic data. An alternative for the unifying description is the well-known regression analysis, which has some desirable properties. It is whown that in a first step classical estimation procedure such as the ML method, and test procedures such as the likelihood ratio test can be applied in the generalized regression model without increasing the low computational complexity reached by the Kalman filter algorithm. In a second step, the unobserved components such as trend, cycle and season can be determined in a generalized regression form. This form can also be used in a descriptive exploratory procedure for decomposing time series. © 1989 Springer-Verlag.

关键词： Exploratory Data Analysis generalized regression model Information Matrix Kalman Filter Smoothing Minimum Mean Squares Decomposition ML Estimator Seasonal Adjustment Wald Statistic

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Rank estimation of a generalized fixed-effects regression model

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JOURNAL OF ECONOMETRICS 2000年第1期95卷 1-23页

作者： Abrevaya, J Univ Chicago Grad Sch Business Chicago IL 60637 USA

This paper considers estimation of a fixed-effects version of the generalized regression model of Han (1987, Journal of Econometrics 35, 303-316). The model allows for censoring, places no parametric assumptions on the error disturbances, and allows the fixed effects to be correlated with the covariates. We introduce a class of rank estimators that consistently estimate the coefficients in the generalized! fixed-effects regression model. The maximum score estimator for the binary choice fixed-effects model is part of this class. Like the maximum score estimator, the class of rank estimators converge at less than the root n rate. Smoothed versions of these estimators, however, converge at rates approaching the root n rate. In a version of the model that allows for truncated data, a sufficient condition for consistency of the estimators is that the error disturbances have an increasing hazard function. (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification: C23;C14.

关键词： fixed-effects models generalized regression model panel data rank estimators maximum score estimator

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A Robust State Estimation Framework Considering Measurement Correlations and Imperfect Synchronization

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第4期33卷 4604-4613页

作者： Zhao, Junbo Wang, Shaobu Mili, Lamine Amidan, Brett Huang, Renke Huang, Zhenyu Virginia Polytech Inst & State Univ Bradley Dept Elect Comp Engn Northern Virginia Ctr Falls Church VA 22043 USA Pacific Northwest Natl Lab Richland WA 99352 USA

This paper develops a robust power system state estimation framework that accounts for correlations and imperfect time synchronization of the measurements. In this framework, correlations of the measurements obtained from the supervisory control and data acquisition (SCADA) system and the phasor measurement units (PMUs) are separately calculated through the unscented transformation and a vector auto-regression (VAR) model. Specifically, the PMU measurements during the waiting period of two successive SCADA measurement scans are buffered via a VAR model whose parameters are robustly estimated using the projection statistics. The latter take into account their temporal and spatial correlations and provide the needed measurement redundancy to suppress bad data and mitigate imperfect time synchronization. In the case where the SCADA and the PMU measurements do not arrive simultaneously at the control center, yielding imperfect measurement time synchronization, either the forecasted PMU measurements or the prior SCADA measurements from the latest state estimation run are leveraged to restore system observability. Finally, a robust generalized maximum-likelihood (GM)-estimator is extended to integrate the measurement error correlations and to handle the outliers, also known as bad data. Simulation results that stem from a comprehensive comparison with other alternatives under various conditions demonstrate the benefits of the proposed framework.

关键词： Power system state estimation measurement correlations robust estimation phasor measurement units vector auto-regression model bad data generalized regression model imperfect time synchronization

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Nowcasting fatal COVID-19 infections on a regional level in Germany

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BIOMETRICAL JOURNAL 2021年第3期63卷 471-489页

作者： Schneble, Marc De Nicola, Giacomo Kauermann, Goeran Berger, Ursula Ludwig Maximilians Univ Munchen Dept Stat Ludwigstr 33 D-80539 Munich Germany Ludwig Maximilians Univ Munchen Inst Med Informat Proc Biometry & Epidemiol Munich Germany

We analyse the temporal and regional structure in mortality rates related to COVID-19 infections, making use of the openly available data on registered cases in Germany published by the Robert Koch Institute on a daily basis. Estimates for the number of present-day infections that will, at a later date, prove to be fatal are derived through a nowcasting model, which relates the day of death of each deceased patient to the corresponding day of registration of the infection. Our district-level modelling approach for fatal infections disentangles spatial variation into a global pattern for Germany, district-specific long-term effects and short-term dynamics, while also taking the age and gender structure of the regional population into account. This enables to highlight areas with unexpectedly high disease activity. The analysis of death counts contributes to a better understanding of the spread of the disease while being, to some extent, less dependent on testing strategy and capacity in comparison to infection counts. The proposed approach and the presented results thus provide reliable insight into the state and the dynamics of the pandemic during the early phases of the infection wave in spring 2020 in Germany, when little was known about the disease and limited data were available.

关键词： COVID-19 disease mapping generalized regression model nowcasting

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ON A LIKELIHOOD-BASED APPROACH IN NONPARAMETRIC SMOOTHING AND CROSS-VALIDATION

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STATISTICS & PROBABILITY LETTERS 1995年第1期22卷 7-15页

作者： CHAUDHURI, P DEWANJI, A INDIAN STAT INST DIV THEORET STAT & MATHCALCUTTA 700035W BENGALINDIA INDIAN STAT INST DIV SURVEYS & COMPCALCUTTA 700035W BENGALINDIA

A likelihood-based generalization of usual kernel and nearest-neighbor-type smoothing techniques and a related extension of the least-squares leave-one-out cross-validation are explored in a generalized regression set up. Several attractive features of the procedure are discussed and asymptotic properties of the resulting nonparametric function estimate are derived under suitable regularity conditions. Large sample performance of likelihood-based leave-one-out cross validation is investigated by means of certain asymptotic expansions.

关键词： CONSISTENCY FISHER INFORMATION generalized regression model MAXIMUM LIKELIHOOD CROSS-VALIDATION WEIGHTED MAXIMUM LIKELIHOOD

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The Impact of Selected Parameters on Visibility: First Results from a Long-Term Campaign in Warsaw, Poland

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ATMOSPHERE 2015年第8期6卷 1154-1174页

作者： Majewski, Grzegorz Rogula-Kozlowska, Wioletta Czechowski, Piotr O. Badyda, Artur Brandyk, Andrzej Warsaw Univ Life Sci Fac Civil & Environm Engn Div Meteorol & Climatol PL-02776 Warsaw Poland Polish Acad Sci Inst Environm Engn PL-41819 Zabrze Poland Gdynia Maritime Univ Dept Informat Syst PL-81225 Gdynia Poland Warsaw Univ Technol Fac Environm Engn PL-00653 Warsaw Poland Warsaw Univ Life Sci Fac Civil & Environm Engn Water Ctr Lab PL-02776 Warsaw Poland

The aim of this study was to investigate how atmospheric air pollutants and meteorological conditions affected atmospheric visibility in the largest Polish agglomeration. The correlation analysis, principal component analysis (PCA) and generalized regression models (GRMs) were used to accomplish this objective. The meteorological parameters (temperature, relative humidity, precipitation, wind speed and insolation) and concentrations of the air pollutants (PM10, SO2, NO2, CO and O-3) were recorded in 2004-2013. The data came from the Ursynow-SGGW, MzWarszUrsynow and Okcie monitoring stations, located in the south of Warsaw (Poland). It was shown that the PM10 concentration was the most important parameter affecting the visibility in Warsaw. The concentration, and indirectly the visibility, was mainly affected by the pollutant emission from the flat/building heating (combustion of various fuels). It changed intensively during the research period. There were also periods in which this emission type did not have a great influence on the pollutant concentrations (mainly PM10) and visibility. In such seasons, the research revealed the influence of the traffic emission and secondary aerosol formation processes on the visibility.

关键词： visibility air pollutants meteorological parameters principal component analysis generalized regression model

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A stochastic evaluation method on the elimination of background sound noises with aid of vibration information and its experiment

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1999年第4期E82A卷 597-604页

作者： Nishimura, K Ohta, M Kinki Univ Fac Engn Kure 7370112 Japan Kinki Univ Fac Engn Higashihiroshima 7291715 Japan

Under a contamination of background sound noises, it seems difficult especially in a real working situation to evaluate various type statistics of only an objective sound signal fluctuation. In many cases of the noise evaluation, some signal processing method have been employed to eliminate the effect of background sound noises by first measuring emitted sound levels. In this study, a new evaluation method of sound level fluctuation is proposed in principle on the basis of the measurement of heterogeneous physical quantity other than sound pressures or sound levels to eliminate the effect of background sound noises. Though the theoretical analysis on acoustical emission caused by a mechanical vibration seems very difficult in a working situation, the sound noise fluctuation emitted only from an objective sound source can be effectively evaluated through its related vibration measurement by employing a fairly unified stochastic method proposed on the basis of a generalized regression analysis between sound and vibration. Here, the regression coefficients are determined by employing the least squares error method to minimize the mean square of estimation error to illustrate well the sound data by means of vibration data. Finally, the effectiveness of proposed method has been experimentally applied to the sound noise evaluation of a jigsaw.

关键词： vibration measurement probabilistic evaluation environmental noise generalized regression model prediction of noise distribution

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