We show that averaging eigenvectors of randomly sampled submatrices efficiently approximates the true eigenvectors of the original matrix under certain conditions on the incoherence of the spectral decomposition. This incoherence assumption is typically milder than those made in matrix completion and allows eigenvectors to be sparse. We discuss applications to spectral methods in dimensionality...

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

In “Epistemic Relativism,” Mark Kalderon defends a view that has become increasingly popular across various academic disciplines. He wrote his article in response to Paul Boghossian’s book Fear of Knowledge, in which epistemic relativism is criticized and dismissed as incoherent. Kalderon argues that Boghossian does not accurately characterize epistemic relativism resulting in a hasty dismissal...

Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.

Eliminating Incoherence from Subjective Estimates of Chance