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.

Characterisation of soils containing naturally occurring radioactive material (NORM) using in situ and rapid laboratory techniques. Case study: South Terras, Cornwall

In situ analysis has become increasingly important for contaminated land investigation and remediation. At present, portable techniques are used mainly as scanning tools to assess the spread and magnitude of the contamination, and are an adjunct to conventional laboratory analyses. A site in Cornwall, containing naturally occurring radioactive material (NORM), provided an opportunity for Reading University PhD student Anna Kutner to compare analytical data collected in situ with data generated by laboratory-based methods. The preliminary results in this paper extend the author‟s poster presentation at last September‟s GeoSpec2010 conference held in Lancaster.

'The Elements' and Hobbesian moral thinking

It is easy to read Hobbes's moral thinking as a deviant contribution to 'modern' natural law, especially if Leviathan (1651) is read through a lens provided by De Cive (1642). But The Elements of Law (1640) encourages the view that Hobbes's argument is 'physicalist', that is, that it requires no premises beyond those required by his physics of matter in motion. The Elements included a draft De Homine and its argument is intimately connected with De Cive's; it shows how such concepts as 'reason', 'right', 'natural law' and 'obligation' can be understood in physicalist terms. But Hobbes's decision to print the latter work in isolation has led to serious misunderstandings

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.