It is widely acknowledged that real-world data tend to complex and heterogeneous, often consisting of multimodal, unstructured, and noisy components. Estimating the posterior probability \(\:P\left(\mathcal{C}=c|X=\mathbf{x}\right)\) is a fundamental aspect of statistical classification. Unlike conventional approaches that model this global probability directly with a single complex function, we propose the more principled approach based on probabilistic decomposition. Specifically, we factorize the posterior probability \(\:P\left(\mathcal{C}|X=\mathbf{x}\right)\) as \(\:P\left(\mathcal{C}=c|X=\mathbf{x}\right)={\sum\:}_{k}P\left({\Gamma\:}=k|X=\mathbf{x}\right)\cdot\:P\left(\mathcal{C}=c|{\Gamma\:}=k,\:X=\mathbf{x}\right)\) , where \(\:{\Gamma\:}\) denotes a latent variable that captures local structure or context. This decomposition enables modular learning and provides a flexible framework for modeling complex distributions. In this framework, the Fuzzy C-Means clustering algorithm models the gating probability \(\:P\left({\Gamma\:}=k|X=\mathbf{x}\right)\) , representing the membership degree of the input data \(\:\mathbf{x}\) to a fuzzy sub-region \(\:k\) . To model the local posterior distribution \(\:P\left(\mathcal{C}=c|{\Gamma\:}=k,\:X=\mathbf{x}\right)\) , we assign an independent Multi-Layer Perceptron (MLP) to each sub-region, where each MLP estimates the local class distribution through an output layer activated by softmax function. To evaluate the performance of the proposed model, we conduct extensive experiments using diverse machine learning datasets from the UCI Machine Learning Repository and a real-world dataset. The experimental results demonstrate that the proposed model consistently outperforms conventional global models in terms of the classification accuracy by effectively capturing the local characteristics of the data.
