The alternating least-squares algorithm for CDPCA

Clustering and Disjoint Principal Component Analysis (CDP CA) is a constrained principal component analysis recently proposed for clustering of objects and partitioning of variables, simultaneously, which we have implemented in R language. In this paper, we deal in detail with the alternating least-squares algorithm for CDPCA and highlight its algebraic features for constructing both interpretable principal components and clusters of objects. Two applications are given to illustrate the capabilities of this new methodology.

An efficient parallel implementation of a least squares problem

Least squares solutions are a very important problem, which appear in a broad range of disciplines (for instance, control systems, statistics, signal processing). Our interest in this kind of problems lies in their use of training neural network controllers.

An efficient parallel implementation of a least squares problem

Least squares solutions are a very important problem, which appear in a broad range of disciplines (for instance, control systems, statistics, signal processing). Our interest in this kind of problems lies in their use of training neural network controllers.

Face recogniton based on the optimal combination of neural networks, eigenfaces and least squares matching methods

Report of a research project of the Fachhochschule Hannover, University of Applied Sciences and Arts, Department of Information Technologies. Automatic face recognition increases the security standards at public places and border checkpoints. The picture inside the identification documents could widely differ from the face, that is scanned under random lighting conditions and for unknown poses. The paper describes an optimal combination of three key algorithms of object recognition, that are able to perform in real time. The camera scan is processed by a recurrent neural network, by a Eigenfaces (PCA) method and by a least squares matching algorithm. Several examples demonstrate the achieved robustness and high recognition rate.

Modernism and Magic: Experiments with Spiritualism, Philosophy and the Occult, paperback

The book explores the aesthetic and political implications of the relationship between magic and mimesis in the work of those early twentieth-century writers, artists and filmmakers who were most self-consciously experimental, including James Joyce, Ezra Pound, Dziga Vertov and Sergei Eisenstein.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Priming psychic and conjuring abilities of a magic demonstration influences event interpretation and random number generation biases

Magical ideation and belief in the paranormal is considered to represent a trait-like character; people either believe in it or not. Yet, anecdotes indicate that exposure to an anomalous event can turn skeptics into believers. This transformation is likely to be accompanied by altered cognitive functioning such as impaired judgments of event likelihood. Here, we investigated whether the exposure to an anomalous event changes individuals' explicit traditional (religious) and non-traditional (e.g., paranormal) beliefs as well as cognitive biases that have previously been associated with non-traditional beliefs, e.g., repetition avoidance when producing random numbers in a mental dice task. In a classroom, 91 students saw a magic demonstration after their psychology lecture. Before the demonstration, half of the students were told that the performance was done respectively by a conjuror (magician group) or a psychic (psychic group). The instruction influenced participants' explanations of the anomalous event. Participants in the magician, as compared to the psychic group, were more likely to explain the event through conjuring abilities while the reverse was true for psychic abilities. Moreover, these explanations correlated positively with their prior traditional and non-traditional beliefs. Finally, we observed that the psychic group showed more repetition avoidance than the magician group, and this effect remained the same regardless of whether assessed before or after the magic demonstration. We conclude that pre-existing beliefs and contextual suggestions both influence people's interpretations of anomalous events and associated cognitive biases. Beliefs and associated cognitive biases are likely flexible well into adulthood and change with actual life events.

Quaterninic Kähler manifolds, constrained instantons, and the magic square

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Of Eureka Moments and Magic Barometers: Freedom of Religion as the “First” Freedom in the Canadian Constitutional Context

"La liberté de religion, souvent reconnue comme étant la « première liberté » dans de nombreuses traditions juridiques, reflète également les différentes conceptions de la place de l'individu et de la communauté dans la société. Cet article examinera la liberté de religion dans le contexte constitutionnel canadien. Nous avons choisi d'étudier la liberté de religion dans trois vagues successives : avant l'entrée en vigueur de la Déclaration canadienne des droits, sous la Déclaration canadienne des droits; et enfin, après l'entrée en vigueur de la Charte canadienne des droits et libertés. De plus, l'accommodement ainsi que de la proportionnalité de la liberté de religion d'un individu sera également traité. Ainsi que nous le démontrerons, la liberté de religion a engendré un repositionnement de l'individu face aux intérêts de la communauté ainsi qu'une réinterprétation des justifications menant à la sauvegarde de ces croyances."

Non invasive classification system of scoliosis curve types using least-squares support vector machines

Objective To determine scoliosis curve types using non invasive surface acquisition, without prior knowledge from X-ray data. Methods Classification of scoliosis deformities according to curve type is used in the clinical management of scoliotic patients. In this work, we propose a robust system that can determine the scoliosis curve type from non invasive acquisition of the 3D back surface of the patients. The 3D image of the surface of the trunk is divided into patches and local geometric descriptors characterizing the back surface are computed from each patch and constitute the features. We reduce the dimensionality by using principal component analysis and retain 53 components using an overlap criterion combined with the total variance in the observed variables. In this work, a multi-class classifier is built with least-squares support vector machines (LS-SVM). The original LS-SVM formulation was modified by weighting the positive and negative samples differently and a new kernel was designed in order to achieve a robust classifier. The proposed system is validated using data from 165 patients with different scoliosis curve types. The results of our non invasive classification were compared with those obtained by an expert using X-ray images. Results The average rate of successful classification was computed using a leave-one-out cross-validation procedure. The overall accuracy of the system was 95%. As for the correct classification rates per class, we obtained 96%, 84% and 97% for the thoracic, double major and lumbar/thoracolumbar curve types, respectively. Conclusion This study shows that it is possible to find a relationship between the internal deformity and the back surface deformity in scoliosis with machine learning methods. The proposed system uses non invasive surface acquisition, which is safe for the patient as it involves no radiation. Also, the design of a specific kernel improved classification performance.

On the relationship between the Method of Least Squares and Gram-Schmidt orthogonalization

The method of Least Squares is due to Carl Friedrich Gauss. The Gram-Schmidt orthogonalization method is of much younger date. A method for solving Least Squares Problems is developed which automatically results in the appearance of the Gram-Schmidt orthogonalizers. Given these orthogonalizers an induction-proof is available for solving Least Squares Problems.

Cooperative squares

An exercise described in detail to use with groups to enable them to understand how different approaches within a group can have different outcomes. This was sent to Debra Morris in 2007 by David Jaques, an educationist with long experience in working with groups.