Quadratic Optimization

Generalized Structured Component Analysis Accommodating Convex Components: A Knowledge-Based Multivariate Method with Interpretable Composite Indexes

Generalized structured component analysis (GSCA) is a multivariate method for examining theory-driven relationships between variables including components. GSCA can provide the deterministic component score for each individual once model parameters are estimated. As the traditional GSCA always standardizes all indicators and components, however, it could not utilize information on the indicators' scale in parameter estimation. Consequently, its component scores could just show the relative standing of each individual for a component, rather than the individual's absolute standing in terms of the original indicators' measurement scales. In the paper, we propose a new version of GSCA, named convex GSCA, which can produce a new type of unstandardized components, termed convex components, which can be intuitively interpreted in terms of the original indicators' scales. We investigate the empirical performance of the proposed method through the analyses of simulated and real data.

Support Vector Machines Trained with Evolutionary Algorithms Employing Kernel Adatron for Large Scale Classification of Protein Structures

With the increasing power of computers, the amount of data that can be processed in small periods of time has grown exponentially, as has the importance of classifying large-scale data efficiently. Support vector machines have shown good results classifying large amounts of high-dimensional data, such as data generated by protein structure prediction, spam recognition, medical diagnosis, optical character recognition and text classification, etc. Most state of the art approaches for large-scale learning use traditional optimization methods, such as quadratic programming or gradient descent, which makes the use of evolutionary algorithms for training support vector machines an area to be explored. The present paper proposes an approach that is simple to implement based on evolutionary algorithms and Kernel-Adatron for solving large-scale classification problems, focusing on protein structure prediction. The functional properties of proteins depend upon their three-dimensional structures. Knowing the structures of proteins is crucial for biology and can lead to improvements in areas such as medicine, agriculture and biofuels.

On the uncertainty of interdisciplinarity measurements due to incomplete bibliographic data

The accuracy of interdisciplinarity measurements is directly related to the quality of the underlying bibliographic data. Existing indicators of interdisciplinarity are not capable of reflecting the inaccuracies introduced by incorrect and incomplete records because correct and complete bibliographic data can rarely be obtained. This is the case for the Rao–Stirling index, which cannot handle references that are not categorized into disciplinary fields. We introduce a method that addresses this problem. It extends the Rao–Stirling index to acknowledge missing data by calculating its interval of uncertainty using computational optimization. The evaluation of our method indicates that the uncertainty interval is not only useful for estimating the inaccuracy of interdisciplinarity measurements, but it also delivers slightly more accurate aggregated interdisciplinarity measurements than the Rao–Stirling index.