Hybrid Hard–Soft Clustering For Outlier Detection: Development of the HS-COS Framework

Abstract

Outlier detection is essential for maintaining the robustness of data-driven models in fields such as healthcare and ecommerce. However, existing clustering-based techniques, such as K-Means, Fuzzy C-Means (FCM), and Possibilistic C-Means (PCM), only capture an aspect of anomaly behavior, such as global structural deviation, membership uncertainty, and representational characteristic. This provides fragmented and uneven detection findings. To solve these limitations, this paper presents a new hybrid framework called the Hybrid Hard-Soft Clustering Outlier Score (HS-COS), which combines distance-based and membership-based anomalous indicators into a single scoring system. The proposed method uses a weighted formulation to combine normalized distance from cluster centroids (hard clustering component) with membership ambiguity (soft clustering component). An adaptive weighting technique is also added to help the model match dataset-specific structural characteristics. The algorithm has been evaluated on a variety of real-world datasets, including Diabetes, Heart Disease, Online Retail, and RetailRocket. The experimental results show that HS-COS has reliable and interpretable performance, with improved anomaly concentration (Lift = 1.57) and competitive detection capacity across heterogeneous datasets. The findings show that incorporating structural deviation and uncertainty improves adaptability, decreases false positives, and offers a generalized approach for detecting anomalies in complicated data settings.