Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspace $U$ that ensures any positive semidefinite matrix $L$ with column space $U$ can be recovered from $D+L$ for any diagonal matrix $D$ using a convex optimization-based heuristic known as minimum trace factor analysis. This result leads to a new understanding of the structure of rank-deficient correlation matrices and a simple condition on a set of points that ensures there is a centered ellipsoid passing through them.Comment: 20 page

Representations of integers by the form x2 + xy + y2 + z2 + zt + t2

Electronic version of an article published in International Journal of Number Theory Volume 04, Issue 05, October 2008, pp. 709-714. DOI: 10.1142/S1793042108001638. Copyright © 2008 World Scientific Publishing Company: http://www.worldscientific.com/worldscinet/ijntWe give an elementary proof of the number of representations of an integer by the quaternary quadratic form x2 + xy + y2 + z2 + zt + t2

Distance-based decision tree algorithms for label ranking

The problem of Label Ranking is receiving increasing attention from several research communities. The algorithms that have developed/adapted to treat rankings as the target object follow two different approaches: distribution-based (e.g., using Mallows model) or correlation-based (e.g., using Spearman’s rank correlation coefficient). Decision trees have been adapted for label ranking following both approaches. In this paper we evaluate an existing correlation-based approach and propose a new one, Entropy-based Ranking trees. We then compare and discuss the results with a distribution-based approach. The results clearly indicate that both approaches are competitive

Materials flow control in hybrid make-to-stock/make-to-order manufacturing

Today’s company competiveness is favoured by product customisation and fast delivery. A strategy to meet this challenge is to manufacture standard items to stock for product customisation. This configures a hybrid environment of make-to-stock and make-to-order. To explore the advantages of this requires good understanding of production control. Thus, we study production under hybrid MTS-MTO, organising the system in two stages. The 1 st manufactures items to inventory, which are then customised in the 2 nd . We analyse how the percentage of tardy orders is affected by the inventory of items required to achieve a given fill rate. The impact of two mechanisms for releasing orders to both stages is also analysed. Results of a simulation study indicate that most of the reduction on the percentage of tardy orders is achieved by a moderate increase in the stock level of semi-finished products. Moreover the percentage of tardy orders decreases if suitable controlled release of orders is exerted.This study had the financial support of FCT-Fundação para a Ciência e Tecnologia of Portugal under the project PEst2015-2020: UID/CEC/ 00319/2013.info:eu-repo/semantics/publishedVersio

Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast

The Assessment of Reliability Under Range Restriction: A Comparison of α, ω, and Test–Retest Reliability for Dichotomous Data

Though much research and attention has been directed at assessing the correlation coefficient under range restriction, the assessment of reliability under range restriction has been largely ignored. This article uses item response theory to simulate dichotomous item-level data to assess the robustness of KR-20 (α), ω, and test–retest under varying selection ratios. These estimators, both corrected and uncorrected for range restriction, were compared in terms of both bias and precision. Test–retest reliability was usually the best estimator of reliability across a variety of conditions. Only under indirect range restriction did KR-20 and ω performed well. All estimators suffered imprecision as a function of range restriction, above and beyond the reduction in sample size. Based on the results, a set of recommendations are proposed.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Unblind Your Apps: Predicting Natural-Language Labels for Mobile GUI Components by Deep Learning

According to the World Health Organization(WHO), it is estimated that approximately 1.3 billion people live with some forms of vision impairment globally, of whom 36 million are blind. Due to their disability, engaging these minority into the society is a challenging problem. The recent rise of smart mobile phones provides a new solution by enabling blind users' convenient access to the information and service for understanding the world. Users with vision impairment can adopt the screen reader embedded in the mobile operating systems to read the content of each screen within the app, and use gestures to interact with the phone. However, the prerequisite of using screen readers is that developers have to add natural-language labels to the image-based components when they are developing the app. Unfortunately, more than 77% apps have issues of missing labels, according to our analysis of 10,408 Android apps. Most of these issues are caused by developers' lack of awareness and knowledge in considering the minority. And even if developers want to add the labels to UI components, they may not come up with concise and clear description as most of them are of no visual issues. To overcome these challenges, we develop a deep-learning based model, called LabelDroid, to automatically predict the labels of image-based buttons by learning from large-scale commercial apps in Google Play. The experimental results show that our model can make accurate predictions and the generated labels are of higher quality than that from real Android developers.Comment: Accepted to 42nd International Conference on Software Engineerin