Matrix and Stimulus Sample Sizes in the Weighted MDS Model: Empirical Metric Recovery Functions

MDS-Tree and MDS-Matrix for High Dimensional Data Visualization

In this work, we propose MDS-Tree and MDS-Matrix as novel high dimensional data visualization methods to gain insight in both the data aspect and dimension aspect of the data. Dimension metrics of the high dimensional dataset are first computed to create a hierarchy. In an MDS-Tree, each node is an MDS projection of the original data items on a specific subset of dimensions associated with the ...

On The Ranking Fuzzy Numbers Using Weighted Metric

Weighted Matrix Completion and Recovery with Prior Subspace Information

A low-rank matrix with “diffuse” entries can beefficiently reconstructed after observing a few of its entries,at random, and then solving a convex program. In manyapplications, in addition to these measurements, potentiallyvaluable prior knowledge about the column and row spaces ofthe matrix is also available to the practitioner. In this paper,we incorporate this prior k...

Two-Sample Covariance Matrix Testing And Support Recovery

This paper proposes a new test for testing the equality of two covariance matrices Σ1 and Σ2 in the high-dimensional setting and investigates its theoretical and numerical properties. The limiting null distribution of the test statistic is derived. The test is shown to enjoy certain optimality and to be especially powerful against sparse alternatives. The simulation results show that the test s...

Ghodsi 1 Metric Multidimensional Scaling ( MDS )

An alternative perspective on dimensionality reduction is offered by Multidimensional scaling (MDS). MDS is another classical approach that maps the original high dimensional space to a lower dimensional space, but does so in an attempt to preserve pairwise distances. That is MDS addresses the problem of constructing a configuration of t points in Euclidean space by using information about the ...