Abstract:
The ℓp-constrained least squares, which is denoted by (Pc), for 0 <; p <; 1 is addressed. A maximal continuous curve of its critical solutions β(c) for different bounds c...Show MoreMetadata
Abstract:
The ℓp-constrained least squares, which is denoted by (Pc), for 0 <; p <; 1 is addressed. A maximal continuous curve of its critical solutions β(c) for different bounds c forms a critical path which can be constructed with the variational method. The path is a piecewise smooth single-valued function of c, containing non-optimal points such as saddle points and local maxima in general as well as global minima. The path of global minima may coincide with a critical path but may jump from a critical path to another one. The breakpoints of the greedy path (a critical path constructed with a certain greedy selection criterion) coincide with the step-by-step solutions generated by the orthogonal matching pursuit (OMP). A critical point of (Pc) is also a critical point of the ℓp-penalized least squares (Qλ) which reformulates (Pc) with the Lagrangian multiplier. The greedy path is a multi-valued function of λ and is formed by a collection of multiple critical paths of (Qλ).
Date of Conference: 01-06 July 2012
Date Added to IEEE Xplore: 27 August 2012
ISBN Information: