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The Effects of Pupil Grouping: Literature Review
, 2005
"... This extended review of the literature on pupil grouping includes an analysis and synthesis
of current and yet to be published research to identify types of grouping suited to particular
pupils, the range of organisational policies regarding pupil grouping within schools that are
related to differen ..."
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This extended review of the literature on pupil grouping includes an analysis and synthesis
of current and yet to be published research to identify types of grouping suited to particular
pupils, the range of organisational policies regarding pupil grouping within schools that are
related to different levels of performance and subjects suited to particular types of
grouping. The review also considers how type of grouping may affect pupil learning and
how the transition from primary to secondary school may be affected by various pupil
groupings. This review of the literature draws upon studies undertaken in primary and
secondary schools.
The literature review draws together schoolbased information on âorganisationalâ and
âwithinclassâ grouping of pupils, as well as theoretical background and practical
implementation issues. The methodology adopted used systematic procedures that include
electronic and hand searching, mapping the research territory and qualityassuring the
studies. This review identifies issues in the study of grouping, theories underlying grouping
initiatives, the role of grouping practices in school transfer and the importance of teaching
pupils to work in groups.
A novel FrankWolfe algorithm. analysis and applications to largescale SVM training. Information Sciences (in press
, 2014
"... Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as the FrankWolfe (FW) method. In particular, this procedure has been successfully applied to train largescale instances of nonline ..."
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Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as the FrankWolfe (FW) method. In particular, this procedure has been successfully applied to train largescale instances of nonlinear Support Vector Machines (SVMs). Specializing FW to SVM training has allowed to obtain efficient algorithms but also important theoretical results, including convergence analysis of training algorithms and new characterizations of model sparsity. In this paper, we present and analyze a novel variant of the FWmethod based on a new way to perform away steps, a classic strategy used to accelerate the convergence of the basic FW procedure. Our formulation and analysis is focused on a general concave maximization problem on the simplex. However, the specialization of our algorithm to quadratic forms is strongly related to some classic methods in computational geometry, namely the Gilbert and MDM algorithms. On the theoretical side, we demonstrate that the method matches the guarantees in terms of convergence rate and number of iterations obtained by using classic away steps. In particular, the method enjoys a linear rate of convergence, a result that has been recently proved for MDM on quadratic forms. On the practical side, we provide experiments on several classification datasets, and evaluate the results using statistical tests. Experiments show that our method is faster than the FW method with classic away steps, and works well even in the cases in which classic away steps slow down the algorithm. Furthermore, these improvements are obtained without sacrificing the predictive accuracy of the obtained SVM model. 1 ar
New Approximation Algorithms for Minimum Enclosing Convex Shapes
"... Given n points in a d dimensional Euclidean space, the Minimum Enclosing Ball (MEB) problem is to find the ball with the smallest radius which contains all n points. We give two approximation algorithms for producing an enclosing ball whose radius is at most ɛ away from the optimum. The first requir ..."
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Given n points in a d dimensional Euclidean space, the Minimum Enclosing Ball (MEB) problem is to find the ball with the smallest radius which contains all n points. We give two approximation algorithms for producing an enclosing ball whose radius is at most ɛ away from the optimum. The first requires O(ndL / √ ɛ) effort, where L is a constant that depends on the scaling of the data. The second is a O ∗ (ndQ / √ ɛ) approximation algorithm, where Q is an upper bound on the norm of the points. This is in contrast with coresets based algorithms which yield a O(nd/ɛ) greedy algorithm. Finding the Minimum Enclosing Convex Polytope (MECP) is a related problem wherein a convex polytope of a fixed shape is given and the aim is to find the smallest magnification of the polytope which encloses the given points. For this problem we present O(mndL/ɛ) and O ∗ (mndQ/ɛ) approximation algorithms, where m is the number of faces of the polytope. Our algorithms borrow heavily from convex duality and recently developed techniques in nonsmooth optimization, and are in contrast with existing methods which rely on geometric arguments. In particular, we specialize the excessive gap framework of Nesterov [19] to obtain our results. 1
ISCA Archive
"... In the last few years, Support Vector Machine classifiers have been shown to give results comparable, or better, than Hidden Markov Models for a variety of tasks involving variable length sequential data. This type of data arises naturally in the fields of bioinformatics, text categorization and aut ..."
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In the last few years, Support Vector Machine classifiers have been shown to give results comparable, or better, than Hidden Markov Models for a variety of tasks involving variable length sequential data. This type of data arises naturally in the fields of bioinformatics, text categorization and automatic speech recognition. In particular, in a previous work it was shown that certain string kernels gave a classification performance comparable to discrete Hidden Markov Models on an isolated Spanish digit recognition task. It is known that speech recognition degrades, often quite severely, when noise is present, and it is interesting to ask whether Support Vector Machines with string kernels continue to give a similar proficiency to discrete Hidden Markov Models in this context. In the present paper, this question is explored by considering the performance of Support Vector Machines with string kernels on the same isolated Spanish digit recognition task in which the speech data has been corrupted with different types of noise. Specifically, white noise and speech babble from the NOISEX92 database. Results of these experiments are given. 1.
SUPPORT VECTOR MACHINE (SVM) CLASSIFICATION THROUGH GEOMETRY
"... Support Vector Machines is a very attractive and useful tool for classification and regression; however, since they rely on subtle and complex algebraic notions of optimization theory, lose their elegance and simplicity when implementation is concerned. It has been shown that the SVM solution, for t ..."
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Support Vector Machines is a very attractive and useful tool for classification and regression; however, since they rely on subtle and complex algebraic notions of optimization theory, lose their elegance and simplicity when implementation is concerned. It has been shown that the SVM solution, for the case of separate classes, corresponds to the minimum distance between the respective convex hulls. For the nonseparable case, this is true for the Reduced Convex Hulls (RCH). In this paper a new geometric algorithm is presented, applied and compared with other nongeometric algorithms for the nonseparable case. 1.
Acknowledgements
"... We extend our gratitude to the children who were at the heart of this study and who willingly consented to participate. Their candour and unselfconsciousness was most encouraging. Parents/caregivers, principals, and school boards of trustees provided their support and gave us the necessary freedom t ..."
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We extend our gratitude to the children who were at the heart of this study and who willingly consented to participate. Their candour and unselfconsciousness was most encouraging. Parents/caregivers, principals, and school boards of trustees provided their support and gave us the necessary freedom to explore learning and teaching in the Arts in a range of primary classrooms. We also thank our colleagues in schools and at the University of Waikato who provided both challenge and support in equal measure. Noteworthy in this regard were Dr Viv Aitken (consultant in drama) and Sue Cheesman (consultant in dance) who provided invaluable expertise from their respective disciplines. In addition, we appreciate the willing involvement of