Enhanced Image Clustering with Random-Bond Ising Models Using LDPC Graph Representations and Nishimori Temperature

This paper addresses the challenge of improving clustering accuracy of image data, particularly focusing on feature representations extracted from convolutional deep neural networks (CNNs). Traditional spectral clustering methods often struggle with high dimension features tensors generated by CNNs like the VGG model. To overcome these limitations, this work proposes a novel approach that enhances spectral clustering by utilizing sparse graph representations (hyperbolic embedding) based on quasi-cyclic low-density parity check (QC-LDPC) and multiedge type (MET) QC-LDPC codes. These graphs are constructed using progressive edge growth (PEG), simulated annealing methods. The paper tackles the specific problem of effectively clustering high-dimensional, sparse image features by modeling their interactions with a random-bond Ising model (RBIM). The optimization process leverages Nishimori temperature estimation to assign weights to graph edges based on image features, leading to more accurate grouping of images into distinct clusters. This approach can be applied to various tasks, including classification. The proposed method not only improves clustering accuracy but also reduces the number of required parameters. It achieves a 17.39 $$\%$$ improvement in accuracy (90.60 $$\%$$ ) compared to state-of-the-art Erdõs–Rényi graphs (73.21 $$\%$$ ), which lack the hardware-efficient structure of QC-LDPC graphs. By utilizing sparse feature parameters, an efficient MET QC-LDPC multigraph is created that outperforms conventional techniques such as mean-field approximation and Laplacian methods in graph clustering, binary classification. These findings highlight the potential of this approach for a wide range of applications, including image clustering, neural network pruning, data representation, and neuron activation pattern prediction.