For closed linear operators or relations A and B acting between Hilbert spaces H and K the concepts of compact and finite rank perturbations are defined with the help of the orthogonal projections PA and PB in H⊕K onto the graphs of A and B. Various equivalent characterizations for such perturbations are proved and it is shown that these notions are a natural generalization of the usual concept...

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the literature to partition such highdimensional data into clusters corresponding to...

Two linear ordering are equimorphic if they can be embedded in each other. We define invariants for scattered linear orderings which classify them up to equimorphism. Essentially, these invariants are finite sequences of finite trees with ordinal labels. Also, for each ordinal α, we explicitly describe the finite set of minimal scattered equimorphism types of Hausdorff rank α. We compute the in...

the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

We give two applications of the recent classification of locally finite simple finitary skew linear groups. We show that certain irreducible finitary skew linear groups of infinite dimension, generate the variety of all groups and have infinite Prüfer rank.

This work introduces a transformation-based learner model for classification forests. The weak learner at each split node plays a crucial role in a classification tree. We propose to optimize the splitting objective by learning a linear transformation on subspaces using nuclear norm as the optimization criteria. The learned linear transformation restores a low-rank structure for data from the s...