Science Density Peaks Clustering Algorithm Source Code

Density Peaks Clustering (DPC) is an unsupervised learning algorithm based on local density and relative distance of data points, originally published in the 2014 Science journal. The core concept of this algorithm is that cluster centers typically exhibit two characteristics: high local density and relatively large distance from points with higher density.

The algorithm implementation primarily consists of three key steps: Local Density Calculation: For each data point, count the number of neighboring points within its surrounding area, commonly using Gaussian kernel function or cutoff distance method for smoothing. In code implementation, this involves vectorized matrix operations to efficiently compute pairwise distances and apply density estimation functions. Relative Distance Calculation: For each point, find the minimum distance among all points with higher density, while the point with highest density selects the global maximum distance. This step typically requires sorting density values and implementing a search mechanism to identify nearest higher-density neighbors. Decision Graph Selection: By plotting a two-dimensional scatter plot (decision graph) of density versus distance, manually select outliers in the upper-right corner as cluster centers. The MATLAB implementation provides visualization tools to assist in this interactive center selection process.

The original paper's accompanying MATLAB implementation includes two important components: the core clustering algorithm module and the S1 standard test dataset. This dataset contains artificially generated 2D distribution data with 15 Gaussian clusters, frequently used to validate clustering algorithms' capability to handle non-spherical distribution data. In implementation details, the source code employs vectorized computation to optimize density matrix operations and utilizes KD-tree structures to accelerate nearest neighbor searches, significantly improving computational efficiency for large datasets.

Compared to traditional K-Means, DPC's advantages include automatic determination of cluster numbers and ability to identify arbitrarily shaped clusters. However, two parameter selections require attention: the cutoff distance dc value affects density calculation sensitivity, while the quality of the visual decision graph directly impacts center point selection accuracy. Subsequent improved algorithms like FKNN-DPC enhance stability in noisy environments by introducing fuzzy K-nearest neighbor mechanisms, which can be implemented through weighted density calculations and probabilistic assignment functions.