arXiv subjects
Publications and source records attributed to Mark Kozdoba.
We present a new online algorithm for detecting overlapping communities. The main ingredients are a modification of an online k-means algorithm and a new approach to modelling overlap in communities. An evaluation on large benchmark graphs shows that the quality of discovered communities compares favorably to several methods in the recent literature, while the running time is significantly improved.
Let $X$ be a metric space and let $μ$ be a probability measure on it. Consider a Lipschitz map $T: X \rightarrow \Rn$, with Lipschitz constant $\leq 1$. Then one can ask whether the image $TX$ can have large projections on many directions. For a large class of spaces $X$, we show that there are directions $ϕ\in \nsphere$ on which the projection of the image $TX$ is small on the average, with bounds depending on the dimension $n$ and the eigenvalues of the Laplacian on $X$.
For a curve T:[0,1] -> R^n, we consider the directions theta in R^n which T "misses" the most and quantify this, as a function of the L_2 norm of T's differential.