Sparse Bilinear Logistic Regression

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces, style/content factorization, and parallel factor analysis. The underlying optimization problem is bi-convex; we study its solution and develop an efficient algorithm based on block coordinate descent. We provide a theoretical guarantee for global convergence and estimate the asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.Comment: 27 pages, 5 figure

From Elastic Deformation to Terminal Flow of a Monodisperse Entangled Melt in Uniaxial Extension

Using a well-entangled monodisperse styrene-butadiene random-copolymer (SBR) melt as a model system, we illustrate generic features of uniaxial extension behavior that may be shared by all well-entangled thermoplastic and elastomeric materials. Depending on the imposed extensional rate, the same sample may behave like a viscous liquid or an elastic solid. Analogous to the recently revealed shear inhomogeneity, the SBR melt inevitably undergoes cohesive failure in the form of sample breakage whenever the Weissenberg number is much greater than unity, making it challenging to reach steady state. In the elastic deformation regime where the external deformation rate is faster than Rouse relaxation rate, the sample undergoes a finite amount of uniform stretching before yielding occurs in a period much shorter than the terminal relaxation time. Steady flow can be achieved only in the terminal regime where entangled chains utilize directed molecular diffusion to achieve rearrangement and enable uniform flow

Exploring Stress Overshoot Phenomenon Upon Startup Deformation of Entangled Linear Polymeric Liquids

This work explores the picture associated with stress overshoot during sudden continual (i.e., startup) external deformation of entangled polymeric liquids and proposes a specific scaling form to depict the intermolecular interactions responsible for chain deformation. Following a previously proposed idea that the stress overshoot in startup deformation is a signature of yielding, we search for ingredients that should go into the description of the force imbalance at the yield point and show that the expression for the intermolecular locking force f(iml), derived from the characteristics associated with the yield point, can be tested against experiment. New rate-switching experiments support the proposed formula for fiml. (C) 2009 The Society of Rheology. [DOI: 10.1122/1.3208063