Reliability measures for local nodes assessment in classification trees

Most of the modem developments with classification trees are aimed at improving their predictive capacity. This article considers a curiously neglected aspect of classification trees, namely the reliability of predictions that come from a given classification tree. In the sense that a node of a tree represents a point in the predictor space in the limit, the aim of this article is the development of localized assessment of the reliability of prediction rules. A classification tree may be used either to provide a probability forecast, where for each node the membership probabilities for each class constitutes the prediction, or a true classification where each new observation is predictively assigned to a unique class. Correspondingly, two types of reliability measure will be derived-namely, prediction reliability and classification reliability. We use bootstrapping methods as the main tool to construct these measures. We also provide a suite of graphical displays by which they may be easily appreciated. In addition to providing some estimate of the reliability of specific forecasts of each type, these measures can also be used to guide future data collection to improve the effectiveness of the tree model. The motivating example we give has a binary response, namely the presence or absence of a species of Eucalypt, Eucalyptus cloeziana, at a given sampling location in response to a suite of environmental covariates, (although the methods are not restricted to binary response data).

Using the EM Algorithm to Train Neural Networks: Misconceptions and a New Algorithm for Multiclass Classification

The expectation-maximization (EM) algorithm has been of considerable interest in recent years as the basis for various algorithms in application areas of neural networks such as pattern recognition. However, there exists some misconceptions concerning its application to neural networks. In this paper, we clarify these misconceptions and consider how the EM algorithm can be adopted to train multilayer perceptron (MLP) and mixture of experts (ME) networks in applications to multiclass classification. We identify some situations where the application of the EM algorithm to train MLP networks may be of limited value and discuss some ways of handling the difficulties. For ME networks, it is reported in the literature that networks trained by the EM algorithm using iteratively reweighted least squares (IRLS) algorithm in the inner loop of the M-step, often performed poorly in multiclass classification. However, we found that the convergence of the IRLS algorithm is stable and that the log likelihood is monotonic increasing when a learning rate smaller than one is adopted. Also, we propose the use of an expectation-conditional maximization (ECM) algorithm to train ME networks. Its performance is demonstrated to be superior to the IRLS algorithm on some simulated and real data sets.

Hierarchical organisation of neuro-anatomical constraints in interlimb coordination

Based on the observation that bimanual finger tapping movements tend toward mirror symmetry with respect to the body midline, despite the synchronous activation of non-homologous muscles, F. Mechsner, D. Kerzel, G. Knoblich, and W. Prinz (2001) [Perceptual basis of bimanual coordination. Nature, 414, 69-73] suggested that the basis of rhythmic coordination is purely spatial/perceptual in nature, and independent of the neuro-anatomical constraints of the motor system. To investigate this issue further, we employed a four finger tapping task similar to that used by F. Mechsner and G. Knoblich (2004) [Do muscle matter in bimanual coordination? Journal of Experimental Psychology: Human Perception and Performance, 30, 490-503] in which six male participants were required to alternately tap combinations of adjacent pairs of index (1), middle (M) and ring (R) fingers of each hand in time with an auditory metronome. The metronome pace increased continuously from 1 Hz to 3 Hz over the course of a 30-s trial. Each participant performed three blocks of trials in which finger combination for each hand (IM or MR) and mode of coordination (mirror or parallel) were presented in random order. Within each block, the right hand was placed in one of three orientations; prone, neutral and supine. The order of blocks was counterbalanced across the six participants. The left hand maintained a prone position throughout the experiment. On the basis of discrete relative phase analyses between synchronised taps, the time at which the initial mode of coordination was lost was determined for each trial. When the right hand was prone, transitions occurred only from parallel symmetry to mirror symmetry, regardless of finger combination. In contrast, when the right hand was supine, transitions occurred only from mirror symmetry to parallel but no transitions were observed in the opposite direction. In the right hand neutral condition, mirror and parallel symmetry are insufficient to describe the modes of coordination since the hands are oriented orthogonally. When defined anatomically, however, the results in each of the three right hand orientations are consistent. That is, synchronisation of finger tapping is deter-mined by a hierarchy of control of individual fingers based on their intrinsic neuro-mechanical properties rather than on the basis of their spatial orientation. (c) 2005 Elsevier B.V. All rights reserved.

Linking riparian vegetation spatial structure in Australian tropical savannas to ecosystem health indicators: semi-variogram analysis of high spatial resolution satellite imagery

Government agencies responsible for riparian environments are assessing the combined utility of field survey and remote sensing for mapping and monitoring indicators of riparian zone health. The objective of this work was to determine if the structural attributes of savanna riparian zones in northern Australia can be detected from commercially available remotely sensed image data. Two QuickBird images and coincident field data covering sections of the Daly River and the South Alligator River - Barramundie Creek in the Northern Territory were used. Semi-variograms were calculated to determine the characteristic spatial scales of riparian zone features, both vegetative and landform. Interpretation of semi-variograms showed that structural dimensions of riparian environments could be detected and estimated from the QuickBird image data. The results also show that selecting the correct spatial resolution and spectral bands is essential to maximize the accuracy of mapping spatial characteristics of savanna riparian features. The distribution of foliage projective cover of riparian vegetation affected spectral reflectance variations in individual spectral bands differently. Pan-sharpened image data enabled small-scale information extraction (< 6 m) on riparian zone structural parameters. The semi-variogram analysis results provide the basis for an inversion approach using high spatial resolution satellite image data to map indicators of savanna riparian zone health.

Ecoregion classification using a bayesian approach and centre-focused clusters

Ecological regions are increasingly used as a spatial unit for planning and environmental management. It is important to define these regions in a scientifically defensible way to justify any decisions made on the basis that they are representative of broad environmental assets. The paper describes a methodology and tool to identify cohesive bioregions. The methodology applies an elicitation process to obtain geographical descriptions for bioregions, each of these is transformed into a Normal density estimate on environmental variables within that region. This prior information is balanced with data classification of environmental datasets using a Bayesian statistical modelling approach to objectively map ecological regions. The method is called model-based clustering as it fits a Normal mixture model to the clusters associated with regions, and it addresses issues of uncertainty in environmental datasets due to overlapping clusters.

Monitoring the condition of savanna riparian zones in Northern Australia using high spatial resolution imagery and a field based rapid assessment method

Government agencies responsible for riparian environments are assessing the combined utility of field survey and remote sensing for mapping and monitoring indicators of riparian zone condition. The objective of this work was to compare the Tropical Rapid Appraisal of Riparian Condition (TRARC) method to a satellite image based approach. TRARC was developed for rapid assessment of the environmental condition of savanna riparian zones. The comparison assessed mapping accuracy, representativeness of TRARC assessment, cost-effectiveness, and suitability for multi-temporal analysis. Two multi-spectral QuickBird images captured in 2004 and 2005 and coincident field data covering sections of the Daly River in the Northern Territory, Australia were used in this work. Both field and image data were processed to map riparian health indicators (RHIs) including percentage canopy cover, organic litter, canopy continuity, stream bank stability, and extent of tree clearing. Spectral vegetation indices, image segmentation and supervised classification were used to produce RHI maps. QuickBird image data were used to examine if the spatial distribution of TRARC transects provided a representative sample of ground based RHI measurements. Results showed that TRARC transects were required to cover at least 3% of the study area to obtain a representative sample. The mapping accuracy and costs of the image based approach were compared to those of the ground based TRARC approach. Results proved that TRARC was more cost-effective at smaller scales (1-100km), while image based assessment becomes more feasible at regional scales (100-1000km). Finally, the ability to use both the image and field based approaches for multi-temporal analysis of RHIs was assessed. Change detection analysis demonstrated that image data can provide detailed information on gradual change, while the TRARC method was only able to identify more gross scale changes. In conclusion, results from both methods were considered to complement each other if used at appropriate spatial scales.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Spatially orthogonal chemical functionalization of a hierarchical pore network for catalytic cascade reactions

The chemical functionality within porous architectures dictates their performance as heterogeneous catalysts; however, synthetic routes to control the spatial distribution of individual functions within porous solids are limited. Here we report the fabrication of spatially orthogonal bifunctional porous catalysts, through the stepwise template removal and chemical functionalization of an interconnected silica framework. Selective removal of polystyrene nanosphere templates from a lyotropic liquid crystal-templated silica sol–gel matrix, followed by extraction of the liquid crystal template, affords a hierarchical macroporous–mesoporous architecture. Decoupling of the individual template extractions allows independent functionalization of macropore and mesopore networks on the basis of chemical and/or size specificity. Spatial compartmentalization of, and directed molecular transport between, chemical functionalities affords control over the reaction sequence in catalytic cascades; herein illustrated by the Pd/Pt-catalysed oxidation of cinnamyl alcohol to cinnamic acid. We anticipate that our methodology will prompt further design of multifunctional materials comprising spatially compartmentalized functions.

Present perspectives on the automated classification of the G-protein coupled receptors (GPCRs) at the protein sequence level

The G-protein coupled receptors--or GPCRs--comprise simultaneously one of the largest and one of the most multi-functional protein families known to modern-day molecular bioscience. From a drug discovery and pharmaceutical industry perspective, the GPCRs constitute one of the most commercially and economically important groups of proteins known. The GPCRs undertake numerous vital metabolic functions and interact with a hugely diverse range of small and large ligands. Many different methodologies have been developed to efficiently and accurately classify the GPCRs. These range from motif-based techniques to machine learning as well as a variety of alignment-free techniques based on the physiochemical properties of sequences. We review here the available methodologies for the classification of GPCRs. Part of this work focuses on how we have tried to build the intrinsically hierarchical nature of sequence relations, implicit within the family, into an adaptive approach to classification. Importantly, we also allude to some of the key innate problems in developing an effective approach to classifying the GPCRs: the lack of sequence similarity between the six classes that comprise the GPCR family and the low sequence similarity to other family members evinced by many newly revealed members of the family.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

The integration of multi-source data to improve the classification of remotely sensed images

The number of remote sensing platforms and sensors rises almost every year, yet much work on the interpretation of land cover is still carried out using either single images or images from the same source taken at different dates. Two questions could be asked of this proliferation of images: can the information contained in different scenes be used to improve the classification accuracy and, what is the best way to combine the different imagery? Two of these multiple image sources are MODIS on the Terra platform and ETM+ on board Landsat7, which are suitably complementary. Daily MODIS images with 36 spectral bands in 250-1000 m spatial resolution and seven spectral bands of ETM+ with 30m and 16 days spatial and temporal resolution respectively are available. In the UK, cloud cover may mean that only a few ETM+ scenes may be available for any particular year and these may not be at the time of year of most interest. The MODIS data may provide information on land cover over the growing season, such as harvest dates, that is not present in the ETM+ data. Therefore, the primary objective of this work is to develop a methodology for the integration of medium spatial resolution Landsat ETM+ image, with multi-temporal, multi-spectral, low-resolution MODIS \Terra images, with the aim of improving the classification of agricultural land. Additionally other data may also be incorporated such as field boundaries from existing maps. When classifying agricultural land cover of the type seen in the UK, where crops are largely sown in homogenous fields with clear and often mapped boundaries, the classification is greatly improved using the mapped polygons and utilising the classification of the polygon as a whole as an apriori probability in classifying each individual pixel using a Bayesian approach. When dealing with multiple images from different platforms and dates it is highly unlikely that the pixels will be exactly co-registered and these pixels will contain a mixture of different real world land covers. Similarly the different atmospheric conditions prevailing during the different days will mean that the same emission from the ground will give rise to different sensor reception. Therefore, a method is presented with a model of the instantaneous field of view and atmospheric effects to enable different remote sensed data sources to be integrated.

Contrast integration over area is extensive: a three-stage model of spatial summation

Classical studies of area summation measure contrast detection thresholds as a function of grating diameter. Unfortunately, (i) this approach is compromised by retinal inhomogeneity and (ii) it potentially confounds summation of signal with summation of internal noise. The Swiss cheese stimulus of T. S. Meese and R. J. Summers (2007) and the closely related Battenberg stimulus of T. S. Meese (2010) were designed to avoid these problems by keeping target diameter constant and modulating interdigitated checks of first-order carrier contrast within the stimulus region. This approach has revealed a contrast integration process with greater potency than the classical model of spatial probability summation. Here, we used Swiss cheese stimuli to investigate the spatial limits of contrast integration over a range of carrier frequencies (1–16 c/deg) and raised plaid modulator frequencies (0.25–32 cycles/check). Subthreshold summation for interdigitated carrier pairs remained strong (~4 to 6 dB) up to 4 to 8 cycles/check. Our computational analysis of these results implied linear signal combination (following square-law transduction) over either (i) 12 carrier cycles or more or (ii) 1.27 deg or more. Our model has three stages of summation: short-range summation within linear receptive fields, medium-range integration to compute contrast energy for multiple patches of the image, and long-range pooling of the contrast integrators by probability summation. Our analysis legitimizes the inclusion of widespread integration of signal (and noise) within hierarchical image processing models. It also confirms the individual differences in the spatial extent of integration that emerge from our approach.

Interactions between landcover pattern and geospatial processing methods:effects on landscape metrics and classification accuracy

Remote sensing data is routinely used in ecology to investigate the relationship between landscape pattern as characterised by land use and land cover maps, and ecological processes. Multiple factors related to the representation of geographic phenomenon have been shown to affect characterisation of landscape pattern resulting in spatial uncertainty. This study investigated the effect of the interaction between landscape spatial pattern and geospatial processing methods statistically; unlike most papers which consider the effect of each factor in isolation only. This is important since data used to calculate landscape metrics typically undergo a series of data abstraction processing tasks and are rarely performed in isolation. The geospatial processing methods tested were the aggregation method and the choice of pixel size used to aggregate data. These were compared to two components of landscape pattern, spatial heterogeneity and the proportion of landcover class area. The interactions and their effect on the final landcover map were described using landscape metrics to measure landscape pattern and classification accuracy (response variables). All landscape metrics and classification accuracy were shown to be affected by both landscape pattern and by processing methods. Large variability in the response of those variables and interactions between the explanatory variables were observed. However, even though interactions occurred, this only affected the magnitude of the difference in landscape metric values. Thus, provided that the same processing methods are used, landscapes should retain their ranking when their landscape metrics are compared. For example, highly fragmented landscapes will always have larger values for the landscape metric "number of patches" than less fragmented landscapes. But the magnitude of difference between the landscapes may change and therefore absolute values of landscape metrics may need to be interpreted with caution. The explanatory variables which had the largest effects were spatial heterogeneity and pixel size. These explanatory variables tended to result in large main effects and large interactions. The high variability in the response variables and the interaction of the explanatory variables indicate it would be difficult to make generalisations about the impact of processing on landscape pattern as only two processing methods were tested and it is likely that untested processing methods will potentially result in even greater spatial uncertainty. © 2013 Elsevier B.V.

Ontology-based Classification of News in an Electronic Newspaper

This paper deals with the classification of news items in ePaper, a prototype system of a future personalized newspaper service on a mobile reading device. The ePaper system aggregates news items from various news providers and delivers to each subscribed user (reader) a personalized electronic newspaper, utilizing content-based and collaborative filtering methods. The ePaper can also provide users "standard" (i.e., not personalized) editions of selected newspapers, as well as browsing capabilities in the repository of news items. This paper concentrates on the automatic classification of incoming news using hierarchical news ontology. Based on this classification on one hand, and on the users' profiles on the other hand, the personalization engine of the system is able to provide a personalized paper to each user onto her mobile reading device.

Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version

Mathematics Subject Classification: 26D10.