<p>Recent methods that utilize data neighborhood graph Laplacians have gained significant attention due to their ability to capture the underlying structure of data across diverse manifolds. In this paper, a novel method is introduced for constructing a normalized graph Laplacian, called Soft Laplacian Eigenmap (SLE). This method not only preserves the local geometry of the original data points but also incorporates their local correlations. Traditional graph Laplacians, which rely on Euclidean distance, may not fully capture the inherent distribution of the data. To address this limitation, a distance metric is employed, which considers the importance of features and effectively eliminates irrelevant ones. This metric is then used as a regularization term based on sample constraints. The learned graph Laplacian is then applied for dimensionality reduction, and the reduced-dimensional data is used for clustering through reinforcement learning (RL). The SLE-based representation enhances the clustering performance of the RL method by improving its convergence speed and ensuring more accurate cluster assignments in high-dimensional spaces. The proposed method has been evaluated on various real-world datasets, and the experimental results demonstrate that it achieves superior within-cluster consistency and outperforms k-means, spectral clustering, and several other techniques in clustering performance.</p>