Isomap is a well-known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its complexity mainly arises two stages; a) embedding full graph on the data in ambient space, and b) complete eigenvalue decomposition. Although of graphing stage has been investigated by processing methods, decomposition remains bottleneck problem. In this paper, we propose Low-...

In this paper, we propose and solve low phase-rank approximation problems, which serve as a counterpart to the well-known low-rank problem Schmidt-Mirsky theorem. It is well known that nonzero complex number can be specified by its gain phase, while it generally accepted gains of matrix may defined singular values, there no widely definition for phases. work, consider sectorial matrices, whose ...

Several recent empirical studies demonstrate that important machine learning tasks such as training deep neural networks, exhibit a low-rank structure, where most of the variation in loss function occurs only few directions input space. In this paper, we leverage structure to reduce high computational cost canonical gradient-based methods gradient descent (GD). Our proposed Low-Rank Gradient De...

In this paper we prove Vaught's conjecture for superstable theories in which each complete type has nite U? rank. The general idea is to associate with the theory an V ? deenable group G (called the structure group) which controls the isomorphism types of the models. We use module theory to show that when the theory has few countable models and M is a countable model there is a nice decompositi...

We present a multi-scale version of low rank matrix decomposition. Our motivation comes from imaging applications, in which image sequences are correlated locally on several scales in space and time rather than globally. We model our data matrix as a sum of matrices, where each matrix has increasing scales of locally low-rank matrices. Using this multi-scale modeling, we can capture different s...

We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We describe the relation between this rank and the notion of strong regularity in max-min algebra, which is traditionally defined in terms of unique solvabi...

In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the Kendall Tau distance. In other words, the problem consists of finding a robust cyclic r...