2013 Academic Year Seminars
I will report recent results on two rather different problems:
1) Least squares contour alignment 2) Microarray data analysis using low rank matrix factorization
The common tread underlying them is numerical linear algebra.
The considered contour alignment problem is a constrained nonlinear least squares problem with respect to the translation, rotation and scaling parameters. A nonlinear change of variables, however, renders this problem an ordinary linear least squares problem. Therefore, a global solution of the considered contour alignment problem can be computed efficiently. A normalized minimum value of the cost function is invariant to ordering and affine transformation of the contours and can be used as a measure for the distance between the contours. This is joint work with Sasan Mahmoodi.
The second problem is approximate rank revealing factorization with structure constraint on the normalized factors. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing factorization problem is nonconvex. An alternating projections algorithm is developed, which is globally convergent to a locally optimal solution. This is joint work with Mahesan Niranjan.