# A Spectral Clustering Algorithm for Non-Linear Graph Embedding in Information Networks
###### Abstract
Their method combines feature embedding and linear encoding and was implemented through a deep hierarchical architecture. [PERSON] et al. [18] proposed the DNGR model for learning graph representations. The model utilizes pointwise mutual information (PMI) to represent the original graph. It then projects this low-dimensional representation using stacked denoising autoencoders. The authors theoretically and empirically demonstrate the effectiveness of the model in clustering and classification processes. [PERSON] et al. [13] indicated in their study that the computational complexity of autoencoders, \(O(n)\), is considerably lower than the characteristic decomposition time, \(O(n^{3})\), of spectral clustering. They proposed a non-linear spectral clustering algorithm based on deep learning. In this method, the graph is embedded in deep learning through autoencoders, followed by clustering using the K-means algorithm. This study on non-linear mapping spectral clustering algorithms made significant contributions to the field; however, the study presented the following issues: (1) for large-scale data, directly representing graph structures with high-dimensional similarity matrices does not reflect the essential features of graph structures; and (2) the authors simply propose a framework for non-linear spectral clustering algorithms without providing theoretical proof. In our study, we utilized sparse representation for the graph similarity matrix, which typically enhances clustering accuracy by eliminating noise information that can impact clustering results. In representation learning, deep structures are used to construct features. Deep structures can benefit from hierarchical training for fine-tuning, which helps in finding improved local solutions to meet the expectation maximization objectives. The method proposed in this paper is called sparse encoder graph spectral clustering (\(SEG\_SC\)). The \(SEG\_SC\) algorithm proposed in this paper makes the following contributions:  
1. In this study, we study the manifold learning similarity matrix and linear low-dimensional mapping of semantic information networks. We define a model structure using the K-means clustering algorithm, similar to spectral algorithms. 2. Theoretically, the results presented in this paper prove that the model adopts a clustering method consistent with the spectral clustering objective function and captures the non-linear features of semantic information networks. 3. Empirically, our results demonstrate that the model can enhance the clustering performance of semantic information networks by capturing meaningful semantic, relational, and structural information. Our experimental results show that the model can effectively complete clustering tasks. The remainder of this paper is arranged as follows: in Section 2, we review related works; in Section 3, we describe the proposed framework, its theoretical analysis, computation complexity analysis, and the optimization algorithm; in Section 4, we report the experimental results; and finally, we conclude the paper in Section 5.