Unfolding kernel embeddings of graphs:enhancing class separation through manifold learning

In this paper, we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels. The idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels, the resulting data tends to be clustered along a curve that wraps around the embedding space, a behavior that suggests that long range distances are not estimated accurately, resulting in an increased curvature of the embedding space. Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation. We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path (Borgwardt and Kriegel, 2005), graphlet (Shervashidze et al., 2009), random walk (Kashima et al., 2003) and Weisfeiler-Lehman (Shervashidze et al., 2011) kernels. We observe the most significant improvement in the case of the graphlet kernel, which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold. On the other hand, the Weisfeiler-Lehman kernel partially mitigates the locality problem by using the node labels information, and thus does not clearly benefit from the manifold learning. Interestingly, our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels.

Transitive state alignment for the quantum jensen-shannon kernel

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks. © 2014 Springer-Verlag Berlin Heidelberg.

Manifold learning and the quantum Jensen-Shannon divergence kernel

The quantum Jensen-Shannon divergence kernel [1] was recently introduced in the context of unattributed graphs where it was shown to outperform several commonly used alternatives. In this paper, we study the separability properties of this kernel and we propose a way to compute a low-dimensional kernel embedding where the separation of the different classes is enhanced. The idea stems from the observation that the multidimensional scaling embeddings on this kernel show a strong horseshoe shape distribution, a pattern which is known to arise when long range distances are not estimated accurately. Here we propose to use Isomap to embed the graphs using only local distance information onto a new vectorial space with a higher class separability. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

EXAMINING SECONDARY MATHEMATICS TEACHER CANDIDATES’ LEARNING AND ENACTMENT OF MATHEMATICS TEACHING PRACTICES: A MULTIPLE CASE STUDY

This qualitative case study explored three teacher candidates’ learning and enactment of discourse-focused mathematics teaching practices. Using audio and video recordings of their teaching practice this study aimed to identify the shifts in the way in which the teacher candidates enacted the following discourse practices: elicited and used evidence of student thinking, posed purposeful questions, and facilitated meaningful mathematical discourse. The teacher candidates’ written reflections from their practice-based coursework as well as interviews were examined to see how two mathematics methods courses influenced their learning and enactment of the three discourse focused mathematics teaching practices. These data sources were also used to identify tensions the teacher candidates encountered. All three candidates in the study were able to successfully enact and reflect on these discourse-focused mathematics teaching practices at various time points in their preparation programs. Consistency of use and areas of improvement differed, however, depending on various tensions experienced by each candidate. Access to quality curriculum materials as well as time to formulate and enact thoughtful lesson plans that supported classroom discourse were tensions for these teacher candidates. This study shows that teacher candidates are capable of enacting discourse-focused teaching practices early in their field placements and with the support of practice-based coursework they can analyze and reflect on their practice for improvement. This study also reveals the importance of assisting teacher candidates in accessing rich mathematical tasks and collaborating during lesson planning. More research needs to be explored to identify how specific aspects of the learning cycle impact individual teachers and how this can be used to improve practice-based teacher education courses.

Kernel machines for epilepsy diagnosis via EEG signal classification: A comparative study

Objective: We carry out a systematic assessment on a suite of kernel-based learning machines while coping with the task of epilepsy diagnosis through automatic electroencephalogram (EEG) signal classification. Methods and materials: The kernel machines investigated include the standard support vector machine (SVM), the least squares SVM, the Lagrangian SVM, the smooth SVM, the proximal SVM, and the relevance vector machine. An extensive series of experiments was conducted on publicly available data, whose clinical EEG recordings were obtained from five normal subjects and five epileptic patients. The performance levels delivered by the different kernel machines are contrasted in terms of the criteria of predictive accuracy, sensitivity to the kernel function/parameter value, and sensitivity to the type of features extracted from the signal. For this purpose, 26 values for the kernel parameter (radius) of two well-known kernel functions (namely. Gaussian and exponential radial basis functions) were considered as well as 21 types of features extracted from the EEG signal, including statistical values derived from the discrete wavelet transform, Lyapunov exponents, and combinations thereof. Results: We first quantitatively assess the impact of the choice of the wavelet basis on the quality of the features extracted. Four wavelet basis functions were considered in this study. Then, we provide the average accuracy (i.e., cross-validation error) values delivered by 252 kernel machine configurations; in particular, 40%/35% of the best-calibrated models of the standard and least squares SVMs reached 100% accuracy rate for the two kernel functions considered. Moreover, we show the sensitivity profiles exhibited by a large sample of the configurations whereby one can visually inspect their levels of sensitiveness to the type of feature and to the kernel function/parameter value. Conclusions: Overall, the results evidence that all kernel machines are competitive in terms of accuracy, with the standard and least squares SVMs prevailing more consistently. Moreover, the choice of the kernel function and parameter value as well as the choice of the feature extractor are critical decisions to be taken, albeit the choice of the wavelet family seems not to be so relevant. Also, the statistical values calculated over the Lyapunov exponents were good sources of signal representation, but not as informative as their wavelet counterparts. Finally, a typical sensitivity profile has emerged among all types of machines, involving some regions of stability separated by zones of sharp variation, with some kernel parameter values clearly associated with better accuracy rates (zones of optimality). (C) 2011 Elsevier B.V. All rights reserved.

Host selection in phytophagous insects: a new explanation for learning in adults

Insect learning can change the preferences an egg laying female displays towards different host plant species. Current hypotheses propose that learning may be advantageous in adult host selection behaviour through improved recognition, accuracy or selectivity in foraging. In this paper, we present a hypothesis for when learning can be advantageous without such improvements in adult host foraging. Specifically, that learning can be an advantageous strategy for egg laying females when larvae must feed on more than one plant in order to complete development, if the fitness of larvae is reduced when they switch to a different host species. Here, larvae benefit from developing on the most abundant host species, which is the most likely choice of host for an adult insect which increases its preference for a host species through learning. The hypothesis is formalised with a mathematical model and we provide evidence from studies on the behavioural ecology, of a number of insect species which demonstrate that the assumptions of this hypothesis may frequently be fulfilled in nature. We discuss how multiple mechanisms may convey advantages in insect learning and that benefits to larval development, which have so far been overlooked, should be considered in explanations for the widespread occurrence of learning.

Engaging with theories of dialogue and voice: Using Bakhtin as a framework to understand teaching and learning Indigenous Australian women's performance

In this paper I explore the Indigenous Australian women's performance classroom (hereafter ANTH2120) as a dialectic and discursive space where the location of possibility is opened for female Indigenous performers to enter into a dialogue from and between both non-Indigenous and Indigenous voices. The work of Bakhtin on dialogue serves as a useful standpoint for understanding the multiple speaking positions and texts in the ANTH2120 context. Bakhtin emphasizes performance, history, actuality and the openness of dialogue to provide an important framework for analysing multiple speaking positions and ways of making meaning through dialogue between shifting and differing subjectivities. I begin by briefly critiquing Bakhtin's "dialogic imagination" and consider the application and usefulness of concepts such as dialogism, heteroglossia and the utterance to understanding the ANTH2120 classroom as a polyphonic and discursive space. I then turn to an analysis of dialogue in the ANTH2120 classroom and primarily situate my gaze on an examination of the interactions that took place between the voices of myself as family/teacher/student and senior Yanyuwa women from the r e m o t e N o r t h e r n T e r r i t o r y A b o r i g i n a l c o m m u n i t y o f B o r r o l o o l a as family/performers/teachers. The 2000 and 2001 Yanyuwa women's performance workshops will be used as examples of the way power is constantly shifting in this dialogue to allow particular voices to speak with authority, and for others to remain silent as roles and relationships between myself and the Yanyuwa women change. Conclusions will be drawn regarding how my subject positions and white race privilege affect who speaks, who listens and on whose terms, and further, the efficacy of this pedagogical platform for opening up the location of possibility for Indigenous Australian women to play a powerful part in the construction of knowledges about women's performance traditions.

Use of web-based formative assessment to support student learning in metabolism/nutrition unit

In 2002, an integrated basic science course was introduced into the Bachelor of Dental Sciences programme at the University of Queensland, Australia. Learning activities for the Metabolism and Nutrition unit within this integrated course included lectures, problem-based learning tutorials, computer-based self-directed learning exercises and practicals. To support student learning and assist students to develop the skills necessary to become lifelong learners, an extensive bank of formative assessment questions was set up using the commercially available package, WebCT®. Questions included short-answer, multiple-choice and extended matching questions. As significant staff time was involved in setting up the question database, the extent to which students used the formative assessment and their perceptions of its usefulness to their learning were evaluated to determine whether formative assessment should be extended to other units within the course. More than 90% of the class completed formative assessment tasks associated with learning activities scheduled in the first two weeks of the block, but this declined to less than 50% by the fourth and final week of the block. Patterns of usage of the formative assessment were also compared in students who scored in the top 10% for all assessment for the semester with those who scored in the lowest 10%. High-performing students accessed the Web-based formative assessment about twice as often as those who scored in the lowest band. However, marks for the formative assessment tests did not differ significantly between the two groups. In a questionnaire that was administered at the completion of the block, students rated the formative assessment highly, with 80% regarding it as being helpful for their learning. In conclusion, although substantial staff time was required to set up the question database, this appeared to be justified by the positive responses of the students.

Moodle and multiple-choice tests

Multiple-Choice items are used in many different kinds of tests in several areas of knowledge. They can be considered an interesting tool to the self-assessing or as an alternative or complementary instrument to the traditional methods for assessing knowledge. The objectivity and accuracy of the multiple-choice tests is an important reason to think about. They are especially useful when the number of students to evaluate is too large. Moodle (Modular Object-Oriented Dynamic Learning Environment) is an Open Source course management system centered around learners' needs and designed to support collaborative approaches to teaching and learning. Moodle offers to the users a rich interface, context-specific help buttons, and a wide variety of tools such as discussion forums, wikis, chat, surveys, quizzes, glossaries, journals, grade books and more, that allow them to learn and collaborate in a truly interactive space. Come together the interactivity of the Moodle platform and the objectivity of this kind of tests one can easily build manifold random tests. The proposal of this paper is to relate our journey in the construction of these tests and share our experience in the use of the Moodle platform to create, take advantage and improve the multiple-choices tests in the Mathematic area.

Reasserting curriculum design through virtual learning environments : The case of MAPE

II European Conference on Curriculum Studies. "Curriculum studies: Policies, perspectives and practices”. Porto, FPCEUP, October 16th - 17th.

Work in progress - learning through role play games

It is commonly accepted that the educational environment has been undergoing considerable change due to the use of the Information and Communication tools. But learning depends upon actions such as experimenting, visualizing and demonstrating through which the learner succeeds in constructing his own knowledge. Although it is not easy to achieve these actions through current ICT supported learning approaches, Role Playing Games (RPG) may well develop such capacities. The creation of an interactive computer game with RPG characteristics, about the 500th anniversary of the city of Funchal, the capital of Madeira Island, is invested with compelling educational/pedagogical implications, aiming clearly at teaching history and social relations through playing. Players interpret different characters in different settings/scenarios, experiencing adventures, meeting challenges and trying to reach multiple and simultaneous goals in the areas of education, entertainment and social integration along the first 150 years of the history of Funchal. Through this process they will live and understand all the social and historical factors of that epoch.

A distributed system for learning programming on-line

Several Web-based on-line judges or on-line programming trainers have been developed in order to allow students to train their programming skills. However, their pedagogical functionalities in the learning of programming have not been clearly defined. EduJudge is a project which aims to integrate the “UVA On-line Judge”, an existing on-line programming trainer with an important number of problems and users, into an effective educational environment consisting of the e-learning platform Moodle and the competitive learning tool QUESTOURnament. The result is the EduJudge system which allows teachers to apply different pedagogical approaches using a proven e-learning platform, makes problems easy to search through an effective search engine, and provides an automated evaluation of the solutions submitted to these problems. The final objective is to provide new learning strategies to motivate students and present programming as an easy and attractive challenge. EduJudge has been tried and tested in three algorithms and programming courses in three different Engineering degrees. The students’ motivation and satisfaction levels were analysed alongside the effects of the EduJudge system on students’ academic outcomes. Results indicate that both students and teachers found that among other multiple benefits the EduJudge system facilitates the learning process. Furthermore, the experi- ment also showed an improvement in students’ academic outcomes. It must be noted that the students’ level of satisfaction did not depend on their computer skills or their gender.

Integrating the LMS in service oriented e-learning systems

Learning management systems are routinely used for presenting, solving and grading exercises with large classes. However, teachers are constrained to use questions with pre-defined answers, such as multiple-choice, to automatically correct the exercises of their students. Complex exercises cannot be evaluated automatically by the LMS and require the coordination of a set of heterogeneous systems. For instance, programming exercises require a specialized exercise resolution environment and automatic evaluation features, each provided by a different type of system. In this paper, the authors discuss an approach for the coordination of a network of eLearning systems supporting the resolution of exercises. The proposed approach is based on a pivot component embedded in the LMS and has two main roles: 1) provide an exercise resolution environment, and 2) coordinate communication between the LMS and other systems, exposing their functions as web services. The integration of the pivot component in the LMS relies on Learning Tools Interoperability (LTI). This paper presents an architecture to coordinate a network of eLearning systems and validate the proposed approach by creating such a network integrated with LMS from two different vendors.