Decentralised Data Fusion with Parzen Density Estimates

Decentralised sensor networks typically consist of multiple processing nodes supporting one or more sensors. These nodes are interconnected via wireless communication. Practical applications of Decentralised Data Fusion have generally been restricted to using Gaussian based approaches such as the Kalman or Information Filter This paper proposes the use of Parzen window estimates as an alternate representation to perform Decentralised Data Fusion. It is required that the common information between two nodes be removed from any received estimates before local data fusion may occur Otherwise, estimates may become overconfident due to data incest. A closed form approximation to the division of two estimates is described to enable conservative assimilation of incoming information to a node in a decentralised data fusion network. A simple example of tracking a moving particle with Parzen density estimates is shown to demonstrate how this algorithm allows conservative assimilation of network information.

DENSITY ESTIMATES of THE BLACK-FRONTED PIPING GUAN IN THE BRAZILIAN ATLANTIC RAINFOREST

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Standing stock density estimates (kg/hectare) for fish from 1969 through 70 UNDP/FAO and 1976 EAFFRO trawl surveys in the Kenya waters of Lake Victoria

A statistical comparison of standing stock density estimates (Kg/hectare) from 26 UNDP/FAO 1%9 thru 70 and 63 EAFFRO 1976 bottom trawl surveys revealed the following; 1) Statistically significant differences between mean density values at 4 of 7 depths {4-9 to 30-39 m}. 2) The 1969 thru 70 UNDP/FAO Values were higher at the 4 levels. 3) No statistically significant menn density value differences at 3 depths (40-49 to 60-69 m), but decreased values for the 1976 EAFFRO survey at 40-49 and 50-59 m depth. It was concluded from these comparisons that no capital investment should be made into a trawler industry for fish meal production in the Kenya waters of Lake Victoria until further bottom trawl surveys can be conducted to either substantiate or disapprove these differences over the six year time span.

The energy density of jellyfish: Estimates from bomb-calorimetry and proximate-composition

Two techniques are described to calculate energy densities for the bell, gonad and oral arm tissues of three scyphozoan jellyfish (Cyanea capillata, Rhizostoma octopus and Chrysaora hysoscella). First, bomb-calorimetry was used, a technique that is readily available and inexpensive. However, the reliability of this technique for gelatinous material is contentious. Second, further analysis involving the more labour intensive proximate-composition analysis (protein, fat and carbohydrate) was carried out on two species (C capillata and R. octopus). These proximate data were subsequently converted to energy densities. The two techniques (bomb-calorimetry and proximate-composition) gave very similar estimates of energy density. Differences in energy density were found both amongst different species and between different tissues of the same species. Mean ( +/- S.D.) energy density estimates for whole animals from bomb-calorimetry were 0.18 +/- 0.05, 0.11 +/- 0.04, and 0.10 +/- 0.03 kJ g wet mass(-1) for C. capillata, R. octopus, and C. hysoscella respectively. The implications of these low energy densities for species feeding on jellyfish are discussed. (c) 2007 Elsevier B.V. All rights reserved.

Probability density function estimation using orthogonal forward regression

Using the classical Parzen window estimate as the target function, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density estimates. The proposed algorithm incrementally minimises a leave-one-out test error score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights are finally updated using the multiplicative nonnegative quadratic programming algorithm, which has the ability to reduce the model size further. Except for the kernel width, the proposed algorithm has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Two examples are used to demonstrate the ability of this regression-based approach to effectively construct a sparse kernel density estimate with comparable accuracy to that of the full-sample optimised Parzen window density estimate.

Kernel density construction using orthogonal forward regression

An automatic algorithm is derived for constructing kernel density estimates based on a regression approach that directly optimizes generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. Local regularization is incorporated into the density construction process to further enforce sparsity. Examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample Parzen window density estimate.

Sparse kernel density construction using orthogonal forward regression with leave-one-out test score and local regularization

This paper presents an efficient construction algorithm for obtaining sparse kernel density estimates based on a regression approach that directly optimizes model generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. A local regularization method is incorporated naturally into the density construction process to further enforce sparsity. An additional advantage of the proposed algorithm is that it is fully automatic and the user is not required to specify any criterion to terminate the density construction procedure. This is in contrast to an existing state-of-art kernel density estimation method using the support vector machine (SVM), where the user is required to specify some critical algorithm parameter. Several examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample optimized Parzen window density estimate. Our experimental results also demonstrate that the proposed algorithm compares favorably with the SVM method, in terms of both test accuracy and sparsity, for constructing kernel density estimates.

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.

How to not inflate population estimates? Spatial density distribution of white-lipped peccaries in a continuous Atlantic forest

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation of methods to estimate foliage density in the understorey of a tropical evergreen forest

Foliage density and leaf area index are important vegetation structure variables. They can be measured by several methods but few have been tested in tropical forests which have high structural heterogeneity. In this study, foliage density estimates by two indirect methods, the point quadrat and photographic methods, were compared with those obtained by direct leaf counts in the understorey of a wet evergreen forest in southern India. The point quadrat method has a tendency to overestimate, whereas the photographic method consistently and ignificantly underestimates foliage density. There was stratification within the understorey, with areas close to the ground having higher foliage densities.

Evaluation of census techniques to estimate the density of slender Loris (Loris lydekkerianus) in Southern India

Reliable estimates of species density are fundamental to planning conservation strategies for any species; further, it is equally crucial to identify the most appropriate technique to estimate animal density. Nocturnal, small-sized animal species are notoriously difficult to census accurately and this issue critically affects their conservation status, We carried out a field study in southern India to estimate the density of slender loris, a small-sized nocturnal primate using line and strip transects. Actual counts of study individuals yielded a density estimate of 1.61 ha(-1); density estimate from line transects was 1.08 ha(-1); and density estimates varied from 1.06 ha(-1) to 0.59 ha(-1) in different fixed-width strip transects. We conclude that line and strip transects may typically underestimate densities of cryptic, nocturnal primates.

Sparse kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

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.