Artefactual structure from least squares multidimensional scaling

We consider the problem of illusory or artefactual structure from the visualisation of high-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SSTRESs measure) gives rise to an annular structure when the input data is drawn from a high-dimensional isotropic distribution, and we provide a theoretical justification for this observation.

Topographic mappings and feed-forward neural networks

This thesis is a study of the generation of topographic mappings - dimension reducing transformations of data that preserve some element of geometric structure - with feed-forward neural networks. As an alternative to established methods, a transformational variant of Sammon's method is proposed, where the projection is effected by a radial basis function neural network. This approach is related to the statistical field of multidimensional scaling, and from that the concept of a 'subjective metric' is defined, which permits the exploitation of additional prior knowledge concerning the data in the mapping process. This then enables the generation of more appropriate feature spaces for the purposes of enhanced visualisation or subsequent classification. A comparison with established methods for feature extraction is given for data taken from the 1992 Research Assessment Exercise for higher educational institutions in the United Kingdom. This is a difficult high-dimensional dataset, and illustrates well the benefit of the new topographic technique. A generalisation of the proposed model is considered for implementation of the classical multidimensional scaling (¸mds}) routine. This is related to Oja's principal subspace neural network, whose learning rule is shown to descend the error surface of the proposed ¸mds model. Some of the technical issues concerning the design and training of topographic neural networks are investigated. It is shown that neural network models can be less sensitive to entrapment in the sub-optimal global minima that badly affect the standard Sammon algorithm, and tend to exhibit good generalisation as a result of implicit weight decay in the training process. It is further argued that for ideal structure retention, the network transformation should be perfectly smooth for all inter-data directions in input space. Finally, there is a critique of optimisation techniques for topographic mappings, and a new training algorithm is proposed. A convergence proof is given, and the method is shown to produce lower-error mappings more rapidly than previous algorithms.

A study of cluster analysis techniques and their applications

This thesis seeks to describe the development of an inexpensive and efficient clustering technique for multivariate data analysis. The technique starts from a multivariate data matrix and ends with graphical representation of the data and pattern recognition discriminant function. The technique also results in distances frequency distribution that might be useful in detecting clustering in the data or for the estimation of parameters useful in the discrimination between the different populations in the data. The technique can also be used in feature selection. The technique is essentially for the discovery of data structure by revealing the component parts of the data. lhe thesis offers three distinct contributions for cluster analysis and pattern recognition techniques. The first contribution is the introduction of transformation function in the technique of nonlinear mapping. The second contribution is the us~ of distances frequency distribution instead of distances time-sequence in nonlinear mapping, The third contribution is the formulation of a new generalised and normalised error function together with its optimal step size formula for gradient method minimisation. The thesis consists of five chapters. The first chapter is the introduction. The second chapter describes multidimensional scaling as an origin of nonlinear mapping technique. The third chapter describes the first developing step in the technique of nonlinear mapping that is the introduction of "transformation function". The fourth chapter describes the second developing step of the nonlinear mapping technique. This is the use of distances frequency distribution instead of distances time-sequence. The chapter also includes the new generalised and normalised error function formulation. Finally, the fifth chapter, the conclusion, evaluates all developments and proposes a new program. for cluster analysis and pattern recognition by integrating all the new features.

Individual differences in occupational perceptions: a developmental study

This thesis presents an investigation of the structure of people's occupational perceptions. The questionnaires used In this study collected both descriptive information about people's perceptions of occupations and also pair comparison similarities data. The data were collected both in the United States of America and England from samples of subjects who differed in terms of age and sex. This provided, therefore, both cross-cultural and developmental dimensions to the study. A cognitive orientation to the study of vocational behaviour is developed and multidimensional scaling procedures are used to analyze the data. A prime concern of the thesis is to examine the appropriateness of this approach and these techniques to this subject area. The results of this study show that a considerable range of individuaI differences exist in occupational perceptions.0lder subjects have a more complex structure to their perceptions and showed greater consensus as to how they perceived occupations to relate to each other. Younger subjects exhibited a greater range of individual differences in occupational perceptions but had, on average, a simpler subjective occupational structure. The multidimensional scaling procedures used in this study were able to reveal how occupational perceptions were structured, to relate these occupational perceptions to occupational preferences and other evaluative data, and to show that the groupings and structure of occupational perceptions ore similar to the dimensions used in occupational classification schemes. ImpIications of these resultts to vocationaI guidance theory and practice are discussed. The resuIts reported here strongly support both the use of the cognitive approach adopted here and demonstrate the potential of multidimensional scaling techniques for further:research in the field of vocational psychology.

Individual differences in the sensory perception of fats

Excessive consumption of dietary fat is acknowledged to be a widespread problem linked to a range of medical conditions. Despite this, little is known about the specific sensory appeal held by fats and no previous published research exists concerning human perception of non-textural taste qualities in fats. This research aimed to address whether a taste component can be found in sensory perception of pure fats. It also examined whether individual differences existed in human taste responses to fat, using both aggregated data analysis methods and multidimensional scaling. Results indicated that individuals were able to detect both the primary taste qualities of sweet, salty, sour and bitter in pure processed oils and reliably ascribe their own individually-generated taste labels, suggested that a taste component may be present in human responses to fat. Individual variation appeared to exist, both in the perception of given taste qualities and in perceived intensity and preferences. A number of factors were examined in relation to such individual differences in taste perception, including age, gender, genetic sensitivity to 6-n-propylthiouracil, body mass, dietary preferences and intake, dieting behaviours and restraint. Results revealed that, to varying extents, gender, age, sensitivity to 6-n-propylthiouracil, dietary preferences, habitual dietary intake and restraint all appeared to be related to individual variation in taste responses to fat. However, in general, these differences appeared to exist in the form of differing preferences and levels of intensity with which taste qualities detected in fat were perceived, as opposed to the perception of specific taste qualities being associated with given traits or states. Equally, each of these factors appeared to exert only a limited influence upon variation in sensory responses and thus the potential for using taste responses to fats as a marker for issues such as over-consumption, obesity or eating disorder is at present limited.

Feed-forward neural networks and topographic mappings for exploratory data analysis

A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feed-forward neural network is utilised to effect a topographic, structure-preserving, dimension-reducing transformation of the data, with an additional facility to incorporate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established techniques for feature extraction, and related to topographic mappings, the Sammon projection and the statistical field of multidimensional scaling.

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.

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.

Improved data visualisation through multiple dissimilarity modelling

Popular dimension reduction and visualisation algorithms rely on the assumption that input dissimilarities are typically Euclidean, for instance Metric Multidimensional Scaling, t-distributed Stochastic Neighbour Embedding and the Gaussian Process Latent Variable Model. It is well known that this assumption does not hold for most datasets and often high-dimensional data sits upon a manifold of unknown global geometry. We present a method for improving the manifold charting process, coupled with Elastic MDS, such that we no longer assume that the manifold is Euclidean, or of any particular structure. We draw on the benefits of different dissimilarity measures allowing for the relative responsibilities, under a linear combination, to drive the visualisation process.

Q parameter scaling in scalar and vector models with dominant signal-noise and noise-noise beating terms

The Q parameter scales differently with the noise power for the signal-noise and the noise-noise beating terms in scalar and vector models. Some procedures for including noise in the scalar model largely under-estimate the Q parameter.

MILVA:An interactive tool for the exploration of multidimensional microarray data

Clustering techniques such as k-means and hierarchical clustering are commonly used to analyze DNA microarray derived gene expression data. However, the interactions between processes underlying the cell activity suggest that the complexity of the microarray data structure may not be fully represented with discrete clustering methods.

Spatial scaling in human peripheral vision

The observation that performance in many visual tasks can be made independent of eccentricity by increasing the size of peripheral stimuli according to the cortical magnification factor has dominated studies of peripheral vision for many years. However, it has become evident that the cortical magnification factor cannot be successfully applied to all tasks. To find out why, several tasks were studied using spatial scaling, a method which requires no pre-determined scaling factors (such as those predicted from cortical magnification) to magnify the stimulus at any eccentricity. Instead, thresholds are measured at the fovea and in the periphery using a series of stimuli, all of which are simply magnified versions of one another. Analysis of the data obtained in this way reveals the value of the parameter E2, the eccentricity at which foveal stimulus size must double in order to maintain performance equivalent to that at the fovea. The tasks investigated include hyperacuities (vernier acuity, bisection acuity, spatial interval discrimination, referenced displacement detection, and orientation discrimination), unreferenced instantaneous and gradual movement, flicker sensitivity, and face discrimination. In all cases tasks obeyed the principle of spatial scaling since performance in the periphery could be equated to that at the fovea by appropriate magnification. However, E2 values found for different spatial tasks varied over a 200-fold range. In spatial tasks (e.g. bisection acuity and spatial interval discrimination) E2 values were low, reaching about 0.075 deg, whereas in movement tasks the values could be as high as 16 deg. Using a method of spatial scaling it has been possible to equate foveal and peripheral perfonnance in many diverse visual tasks. The rate at which peripheral stimulus size had to be increased as a function of eccentricity was dependent upon the stimulus conditions and the task itself. Possible reasons for these findings are discussed.

Peer mentoring in higher education:a multidimensional approach to conceptualising the role of peer mentoring programmes in enhancing the first year undergraduate experience

Across the literature researchers agree that the concept of mentoring results in positive outcomes for both mentors and mentees alike (Enrich et al, 2004). From a pedagogical perspective, student focused mentoring activities in Higher Education are generally perceived to comprise dyadic or triadic relationships that encapsulate a diverse range of learning strategies and/or support mechanisms. Whilst there exists a significant amount of literature regarding the wider value of Peer Mentoring in Higher Education, there remains a notable gap in knowledge about the value of such programmes in enhancing the first year undergraduate experience and thus promoting a smooth transition to University. Using the emergent study findings of a large international project, a multidimensional conceptual framework bringing together the theoretical, conceptual and contextual determinants of Peer Mentoring is proposed. This framework makes a distinctive contribution to current pedagogical theory and practice – particularly in relation to the first year experience.