A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

Hierarchical GTM: Constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 19-dimensional data sets.

Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Semi-supervised learning of hierarchical latent trait models for data visualisation

An interactive hierarchical Generative Topographic Mapping (HGTM) ¸iteH_GTM has been developed to visualise complex data sets. In this paper, we build a more general visualisation system by extending the HGTM visualisation system in 3 directions: bf (1) We generalize HGTM to noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM) developed in ¸iteKaban_pami. bf (2) We give the user a choice of initializing the child plots of the current plot in either em interactive, or em automatic mode. In the interactive mode the user interactively selects ``regions of interest'' as in ¸iteH_GTM, whereas in the automatic mode an unsupervised minimum message length (MML)-driven construction of a mixture of LTMs is employed. bf (3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualisation plots, since they can highlight the boundaries between data clusters. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. We illustrate our approach on a toy example and apply our system to three more complex real data sets.

Clustering of Pick bodies in the dentate gyrus in Pick's disease

In patients with Pick's disease (PD), high densities of tau positive Pick bodies (PB) have been observed within the granule cell layer of the dentate gyrus. This study investigated the spatial patterns of PB along the granule cell layer in coronal sections of the hippocampus in eight patients with PD. In all patients, there was evidence of clustering of PB within the granule cell layer; however, there was considerable variation in the pattern of clustering. In five patients, the clusters of PB were regularly distributed along the dentate gyms, and in two of these patients, the smaller clusters were aggregated into larger superclusters. In three patients, a single large cluster of PB, more than 1200 μm in diameter, was present. Clustering of PB may reflect a primary degenerative process within the granule cells or the degeneration of pathways that project to the dentate gyrus.

Clustering and spatial correlations of the neuronal cytoplasmic inclusions, astrocytic plaques and ballooned neurons in corticobasal degeneration

This study tested three hypotheses: (1) that there is clustering of the neuronal cytoplasmic inclusions (NCI), astrocytic plaques (AP) and ballooned neurons (BN) in corticobasal degeneration (CBD), (2) that the clusters of NCI and BN are not spatially correlated, and (3) that the lesions are correlated with disease ‘stage’. In 50% of the regions, clusters of lesions were 400–800 µm in diameter and regularly distributed parallel to the tissue boundary. Clusters of NCI and BN were larger in laminae II/III and V/VI, respectively. In a third of regions, the clusters of BN and NCI were negatively spatially correlated. Cluster size of the BN in the parahippocampal gyrus (PHG) was positively correlated with disease ‘stage’. The data suggest the following: (1) degeneration of the cortico-cortical pathways in CBD, (2) clusters of NCI and BN may affect different anatomical pathways and (3) BN may develop after the NCI in the PHG.

Clustering and periodicity of neurofibrillary tangles in the upper and lower cortical laminae in Alzheimer's disease

In Alzheimer's disease (AD), neurofibrillary tangles (NFT) occur within neurons in both the upper and lower cortical laminae. Using a statistical method that estimates the size and spacing of NFT clusters along the cortex parallel to the pia mater, two hypotheses were tested: 1) that the cluster size and distribution of the NFT in gyri of the temporal lobe reflect degeneration of the feedforward (FF) and feedback (FB) cortico-cortical pathways, and 2) that there is a spatial relationship between the clusters of NFT in the upper and lower laminae. In 16 temporal lobe gyri from 10 cases of sporadic AD, NFT were present in both the upper and lower laminae in 11/16 (69%) gyri and in either the upper or lower laminae in 5/16 (31%) gyri. Clustering of the NFT was observed in all gyri. A significant peak-to-peak distance was observed in the upper laminae in 13/15 (87%) gyri and in the lower laminae in 8/ 12 (67%) gyri, suggesting a regularly repeating pattern of NFT clusters along the cortex. The regularly distributed clusters of NFT were between 500 and 800 μm in size, the estimated size of the cells of origin of the FF and FB cortico-cortical projections, in the upper laminae of 6/13 (46%) gyri and in the lower laminae of 2/8 (25%) gyri. Clusters of NFT in the upper laminae were spatially correlated (in phase) with those in the lower laminae in 5/16 (31%) gyri. The clustering patterns of the NFT are consistent with their formation in relation to the FF and FB cortico-cortical pathways. In most gyri, NFT clusters appeared to develop independently in the upper and lower laminae.

Clustering of neuronal inclusions in "dementia with neurofilament inclusions"

Dementia with neurofilament inclusions (DNI) is a new disorder characterized clinically by early-onset dementia and histologically by the presence of intraneural inclusions immunopositive for neurofilament antigens but lacking tau and α-synuclein reactivity. We studied the clustering patterns of the neurofilament inclusions (NI) in regions of the temporal lobe in three cases of DNI to determine whether they have the same spatial patterns as inclusions in the tauopathies and α-synucleinopathies. The NI exhibited a clustered distribution (mean size of clusters 400 μm, range 50-800 μm, SD 687.8) in 24/28 of the areas studied. In 22 of these areas, the clusters exhibited a regular distribution along the tissue parallel to the pia mater or alveus. In 3 cortical areas, there was evidence of a more complex pattern in which the NI clusters were aggregated into larger superclusters. In 6 cortical areas, the size of the clusters approximated to those of the cells of origin of the cortico-cortical pathways but in the remaining areas cluster size was smaller than 400 μm. Despite the unique molecular profile of the NI, their spatial patterns are similar to those shown by filamentous neuronal inclusions in the tauopathies and α-synucleinopathies.

Correlations between the clustering patterns of the pathological changes in sporadic Creutzfeldt-Jakob disease

Correlations between the clustering patterns of the vacuolation ('spongiform change'), prion protein (PrP) deposits, and surviving neurons were studied in the cerebral cortex, hippocampus, and cerebellum in 11 cases of sporadic Creutzfeldt-Jakob disease (sCJD). Differences in the sizes of the clusters of vacuoles were observed between brain regions and in the cerebral cortex, between the upper and lower laminae. With the exception of the parietal cortex, mean cluster size of the vacuoles was similar to that of the PrP deposits in each brain area. Clusters of the vacuoles were spatially correlated with the density of surviving neurons and with the clusters of PrP deposits in 47% and 53% of cortical areas analysed respectively but there were few spatial correlation between the PrP deposits and the density of surviving neurons. The data suggest that the pathology of sCJD may spread through the brain via specific anatomical pathways. Development of the clusters of vacuoles is spatially related to surviving neurons while the appearance of clusters of PrP deposits is related to the development of the vacuolation.

GPCRTree:online hierarchical classification of GPCR function

G protein-coupled receptors (GPCRs) play important physiological roles transducing extracellular signals into intracellular responses. Approximately 50% of all marketed drugs target a GPCR. There remains considerable interest in effectively predicting the function of a GPCR from its primary sequence.

Constructing localized non-linear projection manifolds in a principled way:hierarchical generative topographic mapping

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis (Bishop98a) in several directions: 1. We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. 2. We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. 3. Using tools from differential geometry we derive expressions for local directionalcurvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model.We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set andapply our system to two more complex 12- and 19-dimensional data sets.

'Girls who do Boys like they’re girls'? Exploring the role of gender in the junior management of contemporary service work

This article attempts to explain the clustering of women managers at junior managerial grades in the service sector by focusing on the structuring and organization of work in a call centre. The article is based on an ethnography of an organization and seeks to contribute to the ongoing debate in gender research by exploring and documenting the requirement for the enactment of masculinities at work for successful managers. Central to our account is the role of team leader which, as a junior management position, occupies a key role in understanding and accounting for the gendered hierarchical terrain of contemporary service-based organizations. In exploring the role of team leader, a position that tends overwhelmingly to be held by female staff, we draw attention to the perception of the gendered nature of the role by subordinate members of the organization, the team-leaders themselves and more senior managers. The position is also brought into sharp relief in comparison with the subordinate role of the ‘problem manager’, a position overwhelmingly held by men.