Solving constrained Procrustes problems: a conic optimization approach

Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision, multidimensional scaling or finance. The known methods for solving Procrustes problems have been designed to handle specific sub-classes, where the set of feasible solutions has a special structure (e.g. a Stiefel manifold), and the objective function is defined using a specific matrix norm (typically the Frobenius norm). We show that a wide class of Procrustes problems can be formulated and solved as a (rank-constrained) semi-definite program. This includes balanced and unbalanced (weighted) Procrustes problems, possibly to a partially specified target, but also oblique, projection or two-sided Procrustes problems. The proposed approach can handle additional linear, quadratic, or semi-definite constraints and the objective function defined using the Frobenius norm but also standard operator norms. The results are demonstrated on a set of numerical experiments and also on real applications

In-the-wild Facial Expression Recognition in Extreme Poses

In the computer research area, facial expression recognition is a hot research problem. Recent years, the research has moved from the lab environment to in-the-wild circumstances. It is challenging, especially under extreme poses. But current expression detection systems are trying to avoid the pose effects and gain the general applicable ability. In this work, we solve the problem in the opposite approach. We consider the head poses and detect the expressions within special head poses. Our work includes two parts: detect the head pose and group it into one pre-defined head pose class; do facial expression recognize within each pose class. Our experiments show that the recognition results with pose class grouping are much better than that of direct recognition without considering poses. We combine the hand-crafted features, SIFT, LBP and geometric feature, with deep learning feature as the representation of the expressions. The handcrafted features are added into the deep learning framework along with the high level deep learning features. As a comparison, we implement SVM and random forest to as the prediction models. To train and test our methodology, we labeled the face dataset with 6 basic expressions.Comment: Published on ICGIP201

Rotated canonical correlation analysis for multilingual corpora

This paper aims at proposing the joint use of Canonical Correlation Analysis and Procrustes Rotations (RCA), when we deal with a text and its translation into another language. The basic idea is representing words in the two different natural languages on a common reference space. The main characteristic of this space is to be lan-guage independent, although Procrustes Rotation is performed transforming the lexical table derived from trans-lation by minimizing its distance from the lexical table belonging to the original corpus, while the subsequent Canonical Correlation Analysis treats symmetrically the two word sets. The most interesting RCA feature is building a unique reference space for representing the correlation structure in the data, inducing the two systems of canonical factors to lie on the same space. These graphical representations enables us to read distances be-tween corresponding points in terms of different way of translating the same word in relation with the general context defined by the canonical variates. Trying to understand the distances between matched points could rep-resent an useful tool for enriching lexical resources in a translation procedure. In this paper we propose the com-parison of the most frequent content bearing words in the two languages, analyzing one year (2003) of Le Monde Diplomatique and its Italian edition

Bayesian matching of unlabelled point sets using Procrustes and configuration models

The problem of matching unlabelled point sets using Bayesian inference is considered. Two recently proposed models for the likelihood are compared, based on the Procrustes size-and-shape and the full configuration. Bayesian inference is carried out for matching point sets using Markov chain Monte Carlo simulation. An improvement to the existing Procrustes algorithm is proposed which improves convergence rates, using occasional large jumps in the burn-in period. The Procrustes and configuration methods are compared in a simulation study and using real data, where it is of interest to estimate the strengths of matches between protein binding sites. The performance of both methods is generally quite similar, and a connection between the two models is made using a Laplace approximation

On the Procrustean analogue of individual differences scaling (INDSCAL)

In this paper, individual differences scaling (INDSCAL) is revisited, considering INDSCAL as being embedded within a hierarchy of individual difference scaling models. We explore the members of this family, distinguishing (i) models, (ii) the role of identification and substantive constraints, (iii) criteria for fitting models and (iv) algorithms to optimise the criteria. Model formulations may be based either on data that are in the form of proximities or on configurational matrices. In its configurational version, individual difference scaling may be formulated as a form of generalized Procrustes analysis. Algorithms are introduced for fitting the new models. An application from sensory evaluation illustrates the performance of the methods and their solutions