A recent result of Moshkovitz [Mos14] presented an ingenious method to provide a completely elementary proof of the Parallel Repetition Theorem for certain projection games via a construction called fortification. However, the construction used in [Mos14] to fortify arbitrary label cover instances using an arbitrary extractor is insufficient to prove parallel repetition. In this paper, we provi...

Current state-of-the-art fish monitoring systems are lack of intelligent in interpreting fishes behaviors automatically. To tackle these problems, we propose a vision-based method that automatically analyze behaviors of a group of fishes in an aquarium and detect abnormality precisely. Here we consider the problem in two steps. First, we propose a new incremental spectral clustering method to e...

We present a method for bounding, and in some cases computing, the spectral gap for systems of many particles evolving under the influence a random collision mechanism. In particular, the method yields the exact spectral gap in a model due to Mark Kac of energy conserving collisions with one dimensional velocities. It is also sufficiently robust to provide qualitatively sharp bounds also in the...

We study Schrödinger operators on Rn formally given by Hμ = −∆− μ, where μ is a positive, compactly supported measure from the Kato class. Under the assumption that a certain condition on the μ-volume of balls is satisfied and that Hμ has at least two eigenvalues below the essential spectrum σess(Hμ) = [0,∞), we derive a lower bound on the first spectral gap of Hμ. The assumption on the μ-volum...

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the “raw coordinates” encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow data, properly conditioned, illustrate the procedure as well as visualization...

Spectral clustering is a method of subspace clustering which is suitable for the data of any shape and converges to global optimal solution. By combining concepts of shared nearest neighbors and geodesic distance with spectral clustering, a self-adaptive spectral clustering based on geodesic distance and shared nearest neighbors was proposed. Experiments show that the improved spectral clusteri...