Hamza Erol

Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression

Abstract Consider the linear regression model in the usual notation. In the presence of multicollinearity certain biased estimators like the ordinary ridge regression estimator and the Liu estimator introduced by Liu (Liu, Ke Jian. (1993). A new class of biased estimate in linear regression. Communications in Statistics-Theory and Methods 22(2):393–402) or improved ridge and Liu estimators are used to outperform the ordinary least squares estimates in the linear regression model. In this article we compare the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean square error sense.

A per‐field classification method based on mixture distribution models and an application to Landsat Thematic Mapper data

This study has three aims: firstly, to define an efficient and accurate supervised classification method to classify land use/land cover on per‐field basis using mixture distribution models. The second aim was to demonstrate the working principle of the per‐field classification method based on mixture distribution models by classifying a Landsat Thematic Mapper selected test image of an agricultural area. The third aim was to compare the overall classification accuracy and performance of the per‐field classification method based on mixture distribution models with those of three per‐pixel classification methods: minimum distance, nearest neighbour and maximum likelihood.

A multispectral classification algorithm for classifying parcels in an agricultural region

Abstract A multispectral classification algorithm is developed for classifying remotely-sensed data extracted from parcels in an agricultural region. The developed multispectral classification algorithm is based on the comparison of the probability density function of the mixture of three normal distributions constructed for a test parcel (test class) with the probability density functions of the mixture of three normal distributions constructed for control parcels (control or information classes) one by one according to the distances between them. A discriminant function is defined and a decision rule is established for the developed multispectral classification algorithm. The discriminant functions for the developed multispectral classification algorithm take values between 0 and 2, end points are included. The discriminant function values give extra information which can be used in decisions about the comparisons in the developed multispectral classification algorithm. The extra information includes si...

A practical method for constructing the mixture model for a spectral class

Remotely sensed multispectral image data are found in grouped form with (say) s spectral components (bands). In this study, a practical method for constructing a mixture model or the probability density function of the mixture of k (3 =< k =< s) normal distributions for a spectral class is given. A new method for estimation of the mixing proportions of spectral components (bands) in the remotely sensed multispectral image data is proposed with the assumption that the spectral component (band) means are different from each other.

Modeling Heterogeneous Survival Data Using Mixture of Extended Exponential-Geometric Distributions

In this article, we propose a mixture of extended exponential-geometric distributions to model heterogeneous survival data. Various properties of the proposed mixture of extended exponential-geometric distributions are discussed. Maximum likelihood estimations of the parameters are obtained by using the EM algorithm. Illustrative examples based on real data are also given.

A new supervised classification method for quantitative analysis of remotely-sensed multi-spectral data

Abstract A new supervised classification method is developed for quantitative analysis of remotely-sensed multi-spectral data. It is based on the comparisons of the probability density function of the mixture of three normal distributions for a pixel and the probability density functions of the mixture of three normal distributions for spectral classes. The comparisons are made according to the distances between them. The discriminant function, which takes values on the interval \[0, 2], is defined as Hellinger distance. The decision rule is established according to the values of Hellinger distances. The values of the discriminant functions give extra information including spectral similarity and difference percentages in the comparisons. This clarifies the classification results and could help researchers interpret better the classification results of remotely-sensed multi-spectral data.

A data mining method for refining groups in data using dynamic model based clustering

A new data mining method is proposed for determining the number and structure of clusters, and refining groups in multivariate heterogeneous data set including groups, partly and completely overlapped group structures by using dynamic model based clustering. It is called dynamic model based clustering since the structure of model changes at each stage of refinement process dynamically. The proposed data mining method works without data reduction for high dimensional data in which some of variables including completely overlapped situations.

A model selection algorithm for mixture model clustering of heterogeneous multivariate data

A model selection algorithm is developed for finding the best model among a set of mixture of normal densities fitted to heterogeneous multivariate data. Model selection algorithm proposed first finds total number of mixture of normal densities then selects possible number of mixture of normal densities and finally searches the best model among them in mixture model clustering of heterogeneous multivariate data. Log-likelihood function, Akaikes information criteria and Bayesian information criteria values are computed and graphically ploted for each mixture of normal densities. The best model is chosen according to the values of these information criterions.

A statistical approach for ground cover modelling according to the spectral brightness

Abstract The mixture of three normal distributions is proposed as a model for an area that we call a ‘class’ in a region according to the spectral brightness of three different band (pixel) values in remote sensing. The parameters in a mixture of three normal distributions arc estimated by the method of moments for grouped data. Newton-Raphson iteration method is used for estimating the parameters where all parameters are unconstrained. The method of finding suitable starting values for Newton-Raphson iterations is also given. A computer program is developed for this purpose.

Logical circuit design using orientations of clusters in multivariate data for decision making predictions: A data mining and artificial intelligence algorithm approach

A new artificial intelligence algorithm for logical circuit design using orientation of clusters in multivariate data is developed for decision making in robotic studies. The reliability and risk of decision making based on logical circuit design can be predicted. Clusters in multivariate data is obtained by the method of mixture model clustering based on model selection using the segmentations of heterogeneous variables. The segments of heterogeneous variables forms the number and determines the structures of clusters. The orientations of clusters is used to construct the logical circuit design. The number of all cases for cluster centers determined according to the segmentations of heterogeneous variables. Some of all cases which the assumptions are not satisfied eliminated. The rest cases gives the number of possible cluster centers which the assumptions satisfied. Candidate mixture models are established to determine the number and structures of clusters for possible cluster centers using the partitions of heterogeneous variables. Logical circuit designs are established for possible cluster centers using the orientations of partitions of heterogeneous variables. The best mixture model is chosen among candidate mixture models for data clustering using information criterions. The best mixture model determines the number and the structure of clusters in data. The number of components in the best mixture model corresponds to the number of clusters in data. The components of the best mixture model corresponds to the structure of clusters in multivariate data. Logical circuit design of the best mixture model is used in computations of reliability and risk prediction for decision making in robotic studies.