Spectral clustering with linear embedding: A discrete clustering method for large-scale data

In recent decades, spectral clustering has found widespread applications in various real-world scenarios, showcasing its effectiveness. Traditional spectral clustering typically follows a two-step procedure to address the optimization problem. However, this approach may result in substantial information loss and performance decline. Furthermore, the eigenvalue decomposition, a key step in spectral clustering, entails cubic computational complexity. This paper incorporates linear embedding into the objective function of spectral clustering and proposes a direct method to solve the indicator matrix. Moreover, our method achieves a linear time complexity with respect to the input data size. Our method, referred to as Spectral Clustering with Linear Embedding (SCLE), achieves a direct and efficient solution and naturally handles out-of-sample data. SCLE initiates the process with balanced and hierarchical K-means, effectively partitioning the input data into balanced clusters. After generating anchors, we compute a similarity matrix based on the distances between the input data points and the generated anchors. In contrast to the conventional two-step spectral clustering approach, we directly solve the cluster indicator matrix at a linear time complexity. Extensive experiments across multiple datasets underscore the efficiency and effectiveness of our proposed SCLE method.