Browsing by Author "Hajij, Mustafa"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Generalized K-means for Metric Space Clustering Using PageRank
    (The Eurographics Association, 2020) Hajij, Mustafa; Said, Eyad; Todd, Robert; Ritsos, Panagiotis D. and Xu, Kai
    We utilize the PageRank vector to generalize the k-means clustering algorithm to directed and undirected graphs. We demonstrate that PageRank and other centrality measures can be used in our setting to robustly compute centrality of nodes in a given graph. Furthermore, we show how our method can be generalized to metric spaces and apply it to other domains such as point clouds and triangulated meshes.
  • No Thumbnail Available
    Item
    Persistent Homology and the Discrete Laplace Operator For Mesh Similarity
    (The Eurographics Association, 2020) Hajij, Mustafa; Zhang, Yunhao; Liu, Haowen; Rosen, Paul; Ritsos, Panagiotis D. and Xu, Kai
    We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst geometric and combinatorial objects. Our method relies on studying the lower-star filtration induced by the eigenfunctions of the Laplacian. This gives us a shape descriptor that inherits the rich information encoded in the eigenfunctions of the Laplacian. Moreover, the similarity between these descriptors can be easily computed using tools that are readily available in Topological Data Analysis. We provide experiments to illustrate the effectiveness of the proposed method.