A forward-constrained regression algorithm for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward-constrained regression (FCR) manner. The proposed algorithm selects significant kernels one at a time, while the leave-one-out (LOO) test score is minimized subject to a simple positivity constraint in each forward stage. The model parameter estimation in each forward stage is simply the solution of jackknife parameter estimator for a single parameter, subject to the same positivity constraint check. For each selected kernels, the associated kernel width is updated via the Gauss-Newton method with the model parameter estimate fixed. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

3D surface point and wireframe reconstruction from multiview photographic images

This paper describes a new method for reconstructing 3D surface points and a wireframe on the surface of a freeform object using a small number, e.g. 10, of 2D photographic images. The images are taken at different viewing directions by a perspective camera with full prior knowledge of the camera configurations. The reconstructed surface points are frontier points and the wireframe is a network of contour generators. Both of them are reconstructed by pairing apparent contours in the 2D images. Unlike previous works, we empirically demonstrate that if the viewing directions are uniformly distributed around the object's viewing sphere, then the reconstructed 3D points automatically cluster closely on a highly curved part of the surface and are widely spread on smooth or flat parts. The advantage of this property is that the reconstructed points along a surface or a contour generator are not under-sampled or under-represented because surfaces or contours should be sampled or represented with more densely points where their curvatures are high. The more complex the contour's shape, the greater is the number of points required, but the greater the number of points is automatically generated by the proposed method. Given that the viewing directions are uniformly distributed, the number and distribution of the reconstructed points depend on the shape or the curvature of the surface regardless of the size of the surface or the size of the object. The unique pattern of the reconstructed points and contours may be used in 31) object recognition and measurement without computationally intensive full surface reconstruction. The results are obtained from both computer-generated and real objects. (C) 2007 Elsevier B.V. All rights reserved.

Optimal 3D surface reconstruction from a small number of conventional 2D X-ray images

This paper describes a method for reconstructing 3D frontier points, contour generators and surfaces of anatomical objects or smooth surfaces from a small number, e. g. 10, of conventional 2D X-ray images. The X-ray images are taken at different viewing directions with full prior knowledge of the X-ray source and sensor configurations. Unlike previous works, we empirically demonstrate that if the viewing directions are uniformly distributed around the object's viewing sphere, then the reconstructed 3D points automatically cluster closely on a highly curved part of the surface and are widely spread on smooth or flat parts. The advantage of this property is that the reconstructed points along a surface or a contour generator are not under-sampled or under-represented because surfaces or contours should be sampled or represented with more densely points where their curvatures are high. The more complex the contour's shape, the greater is the number of points required, but the greater the number of points is automatically generated by the proposed method. Given that the number of viewing directions is fixed and the viewing directions are uniformly distributed, the number and distribution of the reconstructed points depend on the shape or the curvature of the surface regardless of the size of the surface or the size of the object. The technique may be used not only in medicine but also in industrial applications.

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance.

Regression based D-optimality experimental design for sparse kernel density estimation

This paper derives an efficient algorithm for constructing sparse kernel density (SKD) estimates. The algorithm first selects a very small subset of significant kernels using an orthogonal forward regression (OFR) procedure based on the D-optimality experimental design criterion. The weights of the resulting sparse kernel model are then calculated using a modified multiplicative nonnegative quadratic programming algorithm. Unlike most of the SKD estimators, the proposed D-optimality regression approach is an unsupervised construction algorithm and it does not require an empirical desired response for the kernel selection task. The strength of the D-optimality OFR is owing to the fact that the algorithm automatically selects a small subset of the most significant kernels related to the largest eigenvalues of the kernel design matrix, which counts for the most energy of the kernel training data, and this also guarantees the most accurate kernel weight estimate. The proposed method is also computationally attractive, in comparison with many existing SKD construction algorithms. Extensive numerical investigation demonstrates the ability of this regression-based approach to efficiently construct a very sparse kernel density estimate with excellent test accuracy, and our results show that the proposed method compares favourably with other existing sparse methods, in terms of test accuracy, model sparsity and complexity, for constructing kernel density estimates.

Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Reconstruction of historical pollination rates reveals linked declines of pollinators and plants

Widespread reports of low pollination rates suggest a recent anthropogenic decline in pollination that could threaten natural and agricultural ecosystems. Nevertheless, unequivocal evidence for a decline in pollination over time has remained elusive because it was not possible to determine historical pollination rates. Here we demonstrate a widely applicable method for reconstructing historical pollination rates, thus allowing comparison with contemporary rates from the same sites. We focused on the relationship between the oil-collecting bee Rediviva peringueyi (Melittidae) and the guild of oil-secreting orchid species (Coryciinae) that depends on it for pollination. The guild is distributed across the highly transformed and fragmented lowlands of the Cape Region of South Africa. We show that rehydrated herbarium specimens of Pterygodium catholicum, the most abundant member of the guild, contain a record of past pollinator activity in the form of pollinarium removal rates. Analysis of a pollination time series showed a recent decline in pollination on Signal Hill, a small urban conservation area. The same herbaria contain historical species occurrence data. We analyzed this data and found that there has been a contemporaneous shift in orchid guild composition in urban areas due to the local extirpation of the non-clonal species, consistent with their greater dependence on seeds and pollination for population persistence.

Historicizing counterurbanization: in-migration and the reconstruction of rural space in Berkshire (UK), 1901-51

This article uses census data for Berkshire to argue that large-scale counterurbanization began much earlier than is generally recognized in some parts of southern England. This was not just movement down the urban hierarchy, which as Pooley and Turnbull have demonstrated was a long-term feature of England’s settlement system, but in some cases at least amenity-driven migration to rural areas of the kind increasingly recognized as a core component of recent counterurbanization. Despite a reduction of acreage Berkshire’s rural districts saw a 54% rise in population between 1901 and 1951. The sub-regional pattern of growth is assessed to gauge whether ‘clean break’ migration to the remote west of the county (which remained effectively out of commuting range from London throughout the period) was taking place, or whether counterurbanization was confined to the more accessible eastern districts. However, whilst population did increase in both west and east, it was in fact the central districts that grew most impressively. Three case study parishes are investigated in order to gauge the nature and consequences of counterurbanization at a local level. Professional and business migrants figure prominently, seeking to preserve and promote the rural attributes of their new communities, without however cutting their ties to urban centres. It is argued that migration to rural Berkshire in the first half of the twentieth century cannot adequately be described either as a form of extended suburbanization or an anti-metropolitan ‘clean break’. Rather, early counterurbanization marks the first stage on the long road to a post-productivist countryside, in which countryside becomes detached from agriculture, there is socio-economic convergence between town and country, and the ‘rural’ increasingly becomes defined by landscape and identity rather than economic function.

Reduced space optimal interpolation of daily rain gauge precipitation in Switzerland

The coarse spacing of automatic rain gauges complicates near-real- time spatial analyses of precipitation. We test the possibility of improving such analyses by considering, in addition to the in situ measurements, the spatial covariance structure inferred from past observations with a denser network. To this end, a statistical reconstruction technique, reduced space optimal interpolation (RSOI), is applied over Switzerland, a region of complex topography. RSOI consists of two main parts. First, principal component analysis (PCA) is applied to obtain a reduced space representation of gridded high- resolution precipitation fields available for a multiyear calibration period in the past. Second, sparse real-time rain gauge observations are used to estimate the principal component scores and to reconstruct the precipitation field. In this way, climatological information at higher resolution than the near-real-time measurements is incorporated into the spatial analysis. PCA is found to efficiently reduce the dimensionality of the calibration fields, and RSOI is successful despite the difficulties associated with the statistical distribution of daily precipitation (skewness, dry days). Examples and a systematic evaluation show substantial added value over a simple interpolation technique that uses near-real-time observations only. The benefit is particularly strong for larger- scale precipitation and prominent topographic effects. Small-scale precipitation features are reconstructed at a skill comparable to that of the simple technique. Stratifying the reconstruction method by the types of weather type classifications yields little added skill. Apart from application in near real time, RSOI may also be valuable for enhancing instrumental precipitation analyses for the historic past when direct observations were sparse.