Data mining and knowledge discovery are important technologies for business and research. Despite their benefits in various areas such as marketing, business and medical analysis, the use of data mining techniques can also result in new threats to privacy and information security. Therefore, a new class of data mining methods called privacy preserving data mining (PPDM) has been developed. The aim of researches in this field is to develop techniques those could be applied to databases without violating the privacy of individuals. In this work we introduce a new approach to preserve sensitive information in databases with both numerical and categorical attributes using fuzzy logic. We map a database into a new one that conceals private information while preserving mining benefits. In our proposed method, we use fuzzy membership functions (MFs) such as Gaussian, P-shaped, Sigmoid, S-shaped and Z-shaped for private data. Then we cluster modified datasets by Expectation Maximization (EM) algorithm. Our experimental results show that using fuzzy logic for preserving data privacy guarantees valid data clustering results while protecting sensitive information. The accuracy of the clustering algorithm using fuzzy data is approximately equivalent to original data and is better than the state of the art methods in this field.

Multilevel image thresholding is essential for segmenting images. Expectation Maximization (EM) is effective for finding thresholds; but, it is sensitive to starting points. The Grey Wolf Optimizer (GWO) is fast at finding thresholds but can get stuck in local optima. This paper presents a new algorithm, EM+GWO, combining both methods to improve segmentation. EM estimates Gaussian Mixture Model (GMM) coefficients, while GWO finds better solutions when EM is stuck. GWO adjusts GMM parameters using Root Mean Square Error (RMSE) for the best fit. The algorithm was tested on nine standard images, evaluating global fitness, PSNR, SSIM, FSIM, and computational time. The results show that EM+GWO significantly enhances image segmentation effectiveness. Statistical tools indicate that RCG achieves the best RMSE and PSNR in 7 out of 9 test images, and it holds the highest rank in both SSIM and FSIM. The average execution time of each algorithm was calculated, showing that EM+GWO has an acceptable running time compared to EM and GWO. This balance between computational efficiency and improved segmentation performance makes the proposed EM+GWO algorithm a robust and effective solution for image segmentation tasks. Overall, the combination of EM and GWO methods provides a more reliable and accurate approach to optimizing image segmentation, avoiding local optima, and enhancing overall performance.

The aim of this study is to introduce a parametric mixture model to analysis the competing-risks data with two types of failure. In mixture context, ith type of failure is i th component. The baseline failure time for the first and second types of failure are modeled as proportional hazard models according to Weibull and Gompertz distributions, respectively. The covariates affect on both the probability of occurrence and the hazards of the failure types. The probability of occurrence is modeled to depend on covariates through the logistic model. The parameters can be estimated by application of the Expectation-conditional Maximization and Newton-Raphson algorithms. The simulation studies are performed to compare the proposed model with parametric cause-specific and Fine and Gray models. The results show that the proposed parametric mixture method compared with other models provides consistently less biased estimates for low, mildly, moderately, and heavily censored samples. The analysis of post-kidney transplant malignancy data showed that the conclusions obtained from the mixture and other approaches have some different interpretations.

In this paper, we discuss the calibration of the geometric Brownian motion model equipped with Markov-switching factor. Since the motivation for this research comes from a recent stream of literature in stock economics, we propose an efficient estimation method to sample a series of stock prices based on the Expectation-Maximization algorithm. We also implement an empirical application to evaluate the performance of the suggested model. Numerical results through the classification of the data set show that the proposed Markov-switching model fits the actual stock prices and reflects the main stylized facts of market dynamics. Since the motivation for this research comes from a recent stream of literature in stock economics, we propose an efficient estimation method to sample a series of stock prices based on the Expectation-Maximization algorithm. Numerical results through the classification of the data set show that the proposed Markov-switching model fits the actual stock prices and reflects the main stylized facts of market dynamics. Since the motivation for this research comes from a recent stream of literature in stock economics, we propose an efficient estimation method to sample a series of stock prices based on the Expectation-Maximization algorithm.