Heat Kernel Embeddings, Differential Geometry and Graph Structure

Heat Kernel Signature Discrete Differential Geometry - Project Writeup

Labeling Subgraph Embeddings and Cordiality of Graphs

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...

Partitioning Well-Clustered Graphs with k-Means and Heat Kernel

We study a suitable class of well-clustered graphs that admit good k-way partitions and present the first almost-linear time algorithm for with almost-optimal approximation guarantees partitioning such graphs. A good k-way partition is a partition of the vertices of a graph into disjoint clusters (subsets) {Si}i=1, such that each cluster is better connected on the inside than towards the outsid...

Representation, Segmentation and Matching of 3D Visual Shapes using Graph Laplacian and Heat-Kernel

3D shape analysis is an extremely active research topic in both computer graphics and computer vision. In computer vision, 3D shape acquisition and modeling are generally the result of complex data processing and data analysis methods. There are many practical situations where a visual shape is modeled by a point cloud observed with a variety of 2D and 3D sensors. Unlike the graphical data, the...

Matching of 3 D Visual Shapes using Graph Laplacian and Heat - Kernel

3D shape analysis is an extremely active research topic in both computer graphics and computer vision. In computer vision, 3D shape acquisition and modeling are generally the result of complex data processing and data analysis methods. There are many practical situations where a visual shape is modeled by a point cloud observed with a variety of 2D and 3D sensors. Unlike the graphical data, the...