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Article Citation - WoS: 2Citation - Scopus: 2Enhancing Classification Modeling Through Feature Selection and Smoothness: a Conic-Fused Lasso Approach Integrated With Mean Shift Outlier Modelling(Amer inst Mathematical Sciences-aims, 2025) Yerlikaya-Ozkurt, Fatma; Taylan, PakizeOutlier detection and variable selection are among main objectives of statistical analysis. In our study, we address the outlier problem for classification by using the Mean Shift Outlier Model (CLMSOM). Since the MSOM has more coefficients than the linear regression model, the complexity of the model MSOM is high. Therefore, we consider feature selection for MSOM by using fused Lasso (FLasso), which is beneficial and helpful in the cases where the number of explanatory variables or features is greater than the sample size. FLasso is penalizing both the coefficients and their successive differences by the L-1-norm, and it allows sparsity for both of them, while Lasso only allows the coefficients by considering a nonsmooth optimization problem. In this study, we take into account Iterated Ridge approximation which enables us to use a smooth optimization for FLasso problem. Generated smooth optimization problem is solved by using one of continuous optimization techniques called Conic Quadratic Programming (CQP), which is enabling the utilization of interior point methods. The newly developed method is called Conic FLasso for classification by MSOM (C-FLasso-CLMSOM) and is applied to real world data set to show its performance.Article Citation - WoS: 1Citation - Scopus: 1Spline Based Sparseness and Smoothness for Partially Nonlinear Model Via C-Fused Lasso(American Institute of Mathematical Sciences, 2025) Taylan, P.; Yerlikaya-¨Ozkurt, F.; Tez, M.; Yerlikaya-Ozkurt, FatmaOne of the most beneficial and widely used models for data analysis are partially nonlinear models (PNLRM), which consists of parametric and nonparametric components. Since the model includes the coefficients of both the parametric and nonparametric parts, the complexity of the model will be high and its interpretation will be very difficult. In this study, we propose a procedure that not only achieves sparseness, but also smoothness for PNLRM to obtain a simpler model that better explains the relationship between the response and covariates. Thus, the fused Lasso problem is taken into account where nonparametric components are expressed as a spline basis function, and then the Fused Lasso estimation problem is built and expressed in terms of conic quadratic programming. Applications are conducted to evaluate the performance of the proposed method by considering commonly utilized measures. Promising results are obtained, especially in the data with nonlinearly correlated variables. © (2025), (American Institute of Mathematical Sciences). All rights reserved.