We study the random composition of a small family of O(n) simple permutations on {0, 1}n. Specifically we ask how many randomly selected simple permutations need be composed to yield a permutation that is close to k-wise independent. We improve on the results of Gowers [12] and Hoory et al. [13] and show that up to a polylogarithmic factor, nk compositions of random permutations from this famil...

This work focuses on incorporating pairwise constraints into a spectral clustering algorithm. A new constrained spectral clustering method is proposed, as well as an active constraint acquisition technique and a heuristic for parameter selection. We demonstrate that our constrained spectral clustering method, CSC, works well when the data exhibits what we term local proximity structure. Empiric...

Clustering has recently enjoyed progress via spectral methods which group data using only pairwise affinities and avoid parametric assumptions. While spectral clustering of vector inputs is straightforward, extensions to structured data or time-series data remain less explored. This paper proposes a clustering method for time-series data that couples non-parametric spectral clustering with para...

We present a hybrid clustering algorithm of multiple information sources via tensor decomposition, which can be regarded an extension of the spectral clustering based on modularity maximization. This hybrid clustering can be solved by the truncated higher-order singular value decomposition (HOSVD). Experimental results conducted on the synthetic data have demonstrated the effectiveness. keyword...

Abstract Anchor-based techniques reduce the computational complexity of spectral clustering algorithms. Although empirical tests have shown promising results, there is currently a lack theoretical support for anchoring approach. We define specific anchor-based algorithm and show that it amenable to rigorous analysis, as well being effective in practice. establish consistency method an asymptoti...

The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is widely used method for graph partitioning. It can be seen as natural relaxation to NP-hard minimum ratio cut problem. In this paper, we study following central question: When able find global solution problem? First, provide condition that naturally depends on intra- intercluster connectivi...