The purpose of the theoretical considerations and research conducted was to indicate the instruments with which the quality of a dataset can be verified for the segmentation of observations occurring in the dataset. The paper proposes a novel way to deal with mixed datasets containing categorical and continuous attributes in a customer segmentation task. The categorical variables were embedded using an innovative unsupervised model based on an autoencoder. The customers were then divided into groups using different clustering algorithms, based on similarity matrices. In addition to the classic k-means method and the more modern DBSCAN, three graph algorithms were used: the Louvain algorithm, the greedy algorithm and the label propagation algorithm. The research was conducted on two datasets: one containing on retail customers and the other containing wholesale customers. The Calinski–Harabasz index, Davies–Bouldins index, NMI index, Fowlkes–Mallows index and silhouette score were used to assess the quality of the clustering. It was noted that the modularity parameter for graph methods was a good indicator of whether a given set could be meaningfully divided into groups.

This paper presents a novel approach to federated learning based on the Smooth Ordered Weighted Averaging (OWA) operator which enables flexible and context-sensitive weighting of local models during the aggregation process. To enhance the precision of the aggregated weight computations, we...

Ordered Weighted Averaging (OWA) operators are widely used as flexible rank-based aggregation mechanisms, including in ensemble classification where class-membership degrees produced by multiple models must be fused into a single decision score. This paper proposes an interpolated OWA framework that replaces the discrete summation by a numerical integration of a continuous surrogate constructed from the rank-wise products wix(i). The surrogate is obtained via interpolation on a normalized rank grid, and the integral is approximated using the composite trapezoidal rule. The proposed operators are evaluated in application to probability fusion in ensemble classification. Three interpolation schemes are investigated: Barycentric polynomial interpolation, cubic splines, and the shape-preserving Piecewise Cubic Hermite Interpolating Polynomial (PCHIP). In addition, a trapezoidally smoothed baseline (Smooth OWA) and its interpolated extension are evaluated to separate the effect of local smoothing from interpolation. Experiments were conducted on a heterogeneous benchmark suite including binary and multiclass datasets ranging from 2 to 26 classes, with substantial variation in size and class imbalance. The proposed interpolated OWA yields consistent and frequently statistically significant accuracy improvements over the baseline OWA, increasing the benchmark-level mean accuracy, with the largest dataset-level gains reaching approximately 1.56 percentage point. The interpolated Smooth OWA variants provide additional, smaller yet stable improvements on top of quadrature-inspired smoothing. These results indicate that interpolation-based integration is a simple, modular, and robust refinement of rank-based aggregation for ensemble learning.

This paper introduces a procedure that transforms multiple evaluation metrics into a single aggregated score, providing a comprehensive and interpretable summary of machine learning performance. The approach is demonstrated on a set of metrics obtained from various anomaly detection algorithms...