The structure representation of data distribution plays an important role in understanding the underlying mechanism of generating data. In this paper, we propose nearest prime simplicial complex approaches (NSC) by utilizing persistent homology to capture such structures. Assuming that each class is represented with a prime simplicial complex, we classify unlabeled samples based on the nearest ...

In this paper, a precise and robust algorithm is presented to automatically model the 3D face with only single frontal face image. For shape and projection parameters estimation, an energy function is built to represent the difference between the approximate observed face 3D shape and estimated face 3D shape. To achieve more robust results, shape constraint is added to the energy function. For ...

Projection of a Markov process with constant rates of transition to a small number of observable aggregated states can result in complex kinetics with memory. Here, we define the entropy production along a single sequence of aggregated states and show that it obeys detailed and integral fluctuation theorems. More importantly, we prove that projection shifts the distribution of entropy productio...

The gradient projection algorithm for function minimization is often implemented using an approximate local minimization along the projected negative gradient. On the other hand, for some difficult combinational optimization problems, where a starting guess may be far from a solution, it may be advantageous to perform a nonlocal (exact) line search. In this paper we show how to evaluate the pie...

In this paper, a new affine projection sign algorithm with a variable step-size, robust in impulsive noise environments, is proposed. For that purpose, l1-norm of the a posteriori error vector is minimized under a box constraint on the step-size. Since the proposed l1-norm minimization problem is non-differentiable convex one, an efficient numerical procedure is developed for the affine project...

This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry, radiometry, kinematics and dynamics. Specific topics include perspective projection transformation, persp...

This paper presents a improved POCS-based deblocking technique, based on the theory of the projection onto convex sets (POCS) to reduce the blocking artifacts in decoded images. We propose a new smoothness constraint set (SCS) and its projection operator in the wavelet transform (WT) domain to remove unnecessary high-frequency components caused by blocking artifacts. In order to eliminate the b...

In this paper, a novel discriminant analysis named two-dimensional Heteroscedastic Discriminant Analysis (2DHDA) is presented, and used for gender classification. In 2DHDA, equal within-class covariance constraint is removed. Firstly, the criterion of 2DHDA is defined according to that of 2DLDA. Secondly, the criterion of 2DHDA, log and rearranging terms are taken, and then the optimal projecti...

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected N...

We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, cl...