Abstract
Using 74 players from the NBA 75th Anniversary Team list with available official standard portraits as samples, this paper establishes a complete research workflow consisting of "pixel features - geodesic distance - 2D projection - distance clustering - six-phase mapping." All images were converted to grayscale, normalized to 1040x760, further downsampled to 80x80, and then vectorized into 6400-dimensional representations. Based on Euclidean distance, a k-nearest neighbor graph was constructed, and shortest paths were calculated to obtain the geodesic distance matrix. Classical MDS was employed to project the data onto a 2D destiny-potential plane, where k-medoids clustering was applied to the corresponding distance structure. The six physiognomy labels (Wealthy, Noble, Longevity, Destitute, Solitary, and Premature Death) were generated based on the descending order of the cluster-level separation ratio R_c=inter_c/intra_c . The results indicate that Cluster 2 has the highest separation ratio (2.2665), while Cluster 4 has the lowest (1.3367). The closest sample pair is Kobe Bryant–Tim Duncan (28.5800), and the farthest sample pair is Clyde Drexler–James Worthy (227.6564). Furthermore, this paper conducts a thematic combined analysis of 14 graph maps, constructing a "six-phase destiny narrative" from five dimensions: global geometry, local diffusion, network skeleton, texture statistics, and directional distribution, thereby forming a logically closed conclusion system.