Dimensionality reduction is a crucial preprocessing step for clustering. While nonlinear dimensionality reduction methods effectively capture complex data structures, linear dimensionality reduction methods are often preferred in applications requiring interpretability. However, existing linear approaches, while preserving local or global data characteristics, often struggle to effectively preserve cluster structures. In this paper, we propose a novel linear dimensionality reduction method based on modularity maximization, which is widely used in community detection. The proposed method is formulated as an extension of Locality Preserving Projection (LPP), controlled by a single parameter. More precisely, our method preserves local structural information based on the principle of LPP, while incorporating a distinctive regularization term designed to promote inter-cluster separation. We further show that this parameter serves to control the inter-cluster separation. Experimental results demonstrate that our method can robustly obtain a low-dimensional space that preserves cluster structures, particularly for datasets with high-variance clusters, compared to conventional methods.