Density-aware Hierarchical Clustering Based on Element-Categorized Connection Subgraphs

Clustering is a fundamental data mining technique for pattern recognition through unsupervised learning. Among various clustering methods, hierarchical clustering, density-based clustering, and graph clustering stand out as representative approaches. For hierarchical clustering, it can be categorized into agglomerative and divisive modes to construct clusters in a recursive manner. The key aspect of both modes is the calculation of inter-cluster similarity, which determines whether to merge the sub-clusters into one cluster or divide a current cluster into sub-clusters. Traditionally, the similarity is derived from pairwise distances, often overlooking density variations and structural connectivity in graphs. To address this, we propose a density-aware hierarchical clustering method based on element-categorized connection subgraphs (DHC-ECS), which effectively integrates the hierarchical clustering, density-based clustering, and graph clustering. Particularly, a novel inter-cluster similarity metric is introduced that considers not only distances but also the element categorization in the KNN connection subgraphs, kernel density estimation, and local connectivity within sub-clusters. Extensive evaluations on heterogeneous benchmark datasets demonstrate that DHC-ECS exhibits superior overall performance in terms of clustering accuracy and parameter robustness compared with the baseline methods (including AChameleon, RNN-DBSCAN, McDPC, and G-RMS). The work indicates the great potential of the proposed clustering algorithm for low-dimensional datasets by leveraging local density and graph-structured connectivity (i.e., the duality of vertices and edges), as well as the possibility to determine an intrinsic threshold, reducing the reliance on manual parameter tuning.

Bit error probability and capacity bound of OFDM systems in deterministic doubly-selective channels

Doubly-selective channels, such as those that occur when the transmitter and the receiver move relative to each other at high speeds, are a key scenario for fifth generation (5G) cellular systems, which are mostly based in the use of the orthogonal frequency-division multiplexing (OFDM) modulation. In this paper, we consider an OFDM system using quadrature amplitude modulation (QAM) symbols and we show that, when transmitting over deterministic doubly-selective channels, the inter-carrier interference (ICI) affecting a symbol can be well approximated by a complex-valued normal distribution. Based on this, we derive a lower bound for the link capacity using the Shannon-Hartley theorem. Finally, we provide an approximation of the bit error probability (BEP) using the well-known BEP expressions for Gray-coded QAM constellations over additive white Gaussian noise (AWGN) channels, and show numerical results that confirm that the proposed BEP expression approximates accurately the bit error ratio (BER) of the OFDM system for standardized channel models. The proposed closed-form analytical expressions for the capacity and the BEP do not only allow for discarding the need of computationally-costly Monte-Carlo system simulations, but also provide a theoretical framework to optimize the system parameters directly impacting on the achievable performance.