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.

Using directional curvatures to visualize folding patterns of the GTM projection manifolds

In data visualization, characterizing local geometric properties of non-linear projection manifolds provides the user with valuable additional information that can influence further steps in the data analysis. We take advantage of the smooth character of GTM projection manifold and analytically calculate its local directional curvatures. Curvature plots are useful for detecting regions where geometry is distorted, for changing the amount of regularization in non-linear projection manifolds, and for choosing regions of interest when constructing detailed lower-level visualization plots.

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.

Hebbian and homeostatic plasticity mechanisms in regular spiking and intrinsic bursting cells of cortical layer 5

Layer 5 contains the major projection neurons of the neocortex and is composed of two major cell types: regular spiking (RS) cells, which have cortico-cortical projections, and intrinsic bursting cells (IB), which have subcortical projections. Little is known about the plasticity processes and specifically the molecular mechanisms by which these two cell classes develop and maintain their unique integrative properties. In this study, we find that RS and IB cells show fundementally different experience-dependent plasticity processes and integrate Hebbian and homeostatic components of plasticity differently. Both RS and IB cells showed TNFα-dependent homeostatic plasticity in response to sensory deprivation, but IB cells were capable of a much faster synaptic depression and homeostatic rebound than RS cells. Only IB cells showed input-specific potentiation that depended on CaMKII autophosphorylation. Our findings demonstrate that plasticity mechanisms are not uniform within the neocortex, even within a cortical layer, but are specialized within subcircuits.

'They cooperate with us, so they are like me': perceived intergroup relationship moderates projection from self to outgroups

Whereas projection of self-attributes to ingroups is ubiquitous, projection of self-attributes to outgroups (outgroup projection) is an elusive phenomenon. Two experiments examined the moderating effect of perceived intergroup relationship on outgroup projection and explored underlying mechanisms. Perceived cooperation versus competition between ingroup and outgroup was manipulated using fictitious (Experiment 1) or natural groups (Experiment 2). In both experiments, participants judged the outgroup as more similar to the self in the cooperation condition than in the competition condition. This effect was independent of recategorization, perceived intergroup similarity, and ingroup-to-outgroup projection. These studies demonstrate the very existence of outgroup projection and extend previous work on moderators of projection from self to groups.

Topography of α-internexin-positive neuronal aggregates in 10 patients with neuronal intermediate filament inclusion disease

Abnormal neuronal intermediate filament (IF) inclusions immunopositive for the type IV IF α-internexin have been identified as the pathological hallmark of neuronal intermediate filament inclusion disease (NIFID). We studied the topography of these inclusions in the frontal and temporal lobe in 68 areas from 10 cases of NIFID. In the cerebral cortex, CA sectors of the hippocampus, and dentate gyrus granule cell layer, the inclusions were distributed mainly in regularly distributed clusters, 50-800 μm in diameter. In seven cortical areas, there was a more complex pattern in which the clusters of inclusions were aggregated into larger superclusters. In 11 cortical areas, the size of the clusters approximated to those of the cells of origin of the cortico-cortical pathways but in the majority of the remaining areas, cluster size was smaller than 400 μm. The topography of the lesions suggests that there is degeneration of the cortico-cortical projections in NIFID with the formation of α-internexin-positive aggregates within vertical columns of cells. Initially, only a subset of cells within a vertical column develops inclusions but as the disease progresses, the whole of the column becomes affected. The corticostriate projection appears to have little effect on the cortical topography of the inclusions. © 2006 EFNS.

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.

Rapid heuristic projection on simplicial cones

A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.

Is the clustering of neurofibrillary tangles in Alzheimer's patients related to the cells of origin of specific cortico-cortical projections?

The spatial pattern of cellular neurofibrillary tangles (NFT) was studied in the supra- and infragranular layers of various cortical regions in cases of Alzheimer's disease (AD). The objective was to test the hypothesis that NFT formation was associated with the cells of origin of specific cortico-cortical projections. The novel feature of the study was that pattern analysis enabled the dimension and spacing of NFT clusters along the cortical ribbon to be estimated. In the majority of brain regions studied, NFT occurred in clusters of neurons which were regularly spaced along the cortical strip. This pattern is consistent with the predicted distribution of the cells of origin of specific cortico-cortico projections. Mean NFT cluster size varied from 250 to > 12800 microns in different cortical tissues suggesting either variation in the size of the cell clusters or a dynamic process in the development of NFT in relation to these cell clusters. The formation of NFT in cell clusters which may give rise to the feed-forward and feed-back cortico-cortical projections suggests a possible route of spread of NFT pathology in AD between cortical regions and from the cortex to subcortical areas.

Does the neurodegeneration of Alzheimer’s disease spread between visual cortical regions B17 and B18 via the feedforward or feedback short cortico-cortical projections?

The laminar distribution of senile plaques (SP) and neurofibrillary tangles (NFT) was studied in areas B17 and B18 of the visual cortex in 18 cases of Alzheimer’s disease which varied in disease onset and duration. The objective was to test the hypothesis that SP and NFT could spread via either the feedforward or feedback short cortico-cortical projections. In area B17, the mean density of SP and NFT reached a maximum in lamina III and in laminae II and III respectively. In B18, mean SP density was maximal in laminae III and IV and NFT density in laminae II and III. No significant correlations were observed in any cortical lamina between the density of SP and patient age. However, the density of NFT in laminae III, IV and VI in B18 was negatively correlated with patient age. In addition, in B18, the density of SP in lamina II and lamina V was negatively correlated with disease duration and disease onset respectively. Although these results suggest that SP and NFT might spread between B17 and B18 via the feedforward short cortico-cortical projections, it is also possible that the longer cortico-cortical and cortico-subcortical connections may be involved.

Alzheimer's disease: Are cellular neurofibrillary tangles linked to beta/A4 formation at the projection sites?

The density of senile plaques (SP) and cellular neurofibrillary tabgles (NFT) revealed by the Glees and Gallyas stains; and beta/A4 deposits revealed by immunocytochemical staining, was estimated in the hippocampus and adjacent gyri in Alzheimer's disease (AD). Stepwise multiple regression was used to detemine whether the density of cellular NFT was related to the density of SP or beta/A4 deposits totalled over the projection sites. Cellular NFT density was only weakly correlated with the density of Glees SP and beta/A4 deposits at some of the projection sites. However, beta/A4 deposit density in a tissue was strongly correlated with the density of beta/A4 deposits at the projection sites suggesting that the lesions could spread through the brain. Hence, although there is a strong correlation between the density of beta/A4 deposits in different parts of the hippocampal formation there is little association between SP or beta/A4 and cellular NFT. These results do not provide strong evidence that beta/A4 protein is the cause of the neuritc changes in AD.

Projection and interpolation based techniques for structured and impulsive noise filtering

In this chapter we present the relevant mathematical background to address two well defined signal and image processing problems. Namely, the problem of structured noise filtering and the problem of interpolation of missing data. The former is addressed by recourse to oblique projection based techniques whilst the latter, which can be considered equivalent to impulsive noise filtering, is tackled by appropriate interpolation methods.

Visual data mining using principled projection algorithms and information visualization techniques

We introduce a flexible visual data mining framework which combines advanced projection algorithms from the machine learning domain and visual techniques developed in the information visualization domain. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection algorithms, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates and billboarding, to provide a visual data mining framework. Results on a real-life chemoinformatics dataset using GTM are promising and have been analytically compared with the results from the traditional projection methods. It is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework. Copyright 2006 ACM.

2D-3D registration of CT vertebra volume to fluoroscopy projection:a calibration model assessment

This study extends a previous research concerning intervertebral motion registration by means of 2D dynamic fluoroscopy to obtain a more comprehensive 3D description of vertebral kinematics. The problem of estimating the 3D rigid pose of a CT volume of a vertebra from its 2D X-ray fluoroscopy projection is addressed. 2D-3D registration is obtained maximising a measure of similarity between Digitally Reconstructed Radiographs (obtained from the CT volume) and real fluoroscopic projection. X-ray energy correction was performed. To assess the method a calibration model was realised a sheep dry vertebra was rigidly fixed to a frame of reference including metallic markers. Accurate measurement of 3D orientation was obtained via single-camera calibration of the markers and held as true 3D vertebra position; then, vertebra 3D pose was estimated and results compared. Error analysis revealed accuracy of the order of 0.1 degree for the rotation angles of about 1mm for displacements parallel to the fluoroscopic plane, and of order of 10mm for the orthogonal displacement. © 2010 P. Bifulco et al.