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

The 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 favourably with the SVM method, in terms of both test accuracy and sparsity, for constructing kernel density estimates

Kernel Ellipsoidal Trimming

Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered information matrix. Although the method is very general and can be applied to many of the aforementioned problems, the main focus in this paper is the problem of novelty or outlier detection associated with fault detection. A simple iterative algorithm based on Titterington's minimum volume ellipsoid method is proposed for practical implementation. The KIMEE method demonstrates very good performance on a set of real-life and simulated datasets compared with support vector machine methods

The role of the loss function in the probabilistic function approximation

Generalising results on the time series estimation it is natural to consider function approximation with finite data observations in a probabilistic setting. The function is treated as a stochastic process where for each point in the functions domain the function is a random variable. Equivalently the function can be considered as a single random variable whose range is a space of functions. In this paper two results well known within the context of time series estimation and stochastic control are generalised to probabilistic function approximation problems. Under mild conditions on the space of functions it is shown that the optimal function estimate corresponds for all reasonable symmetrical loss functions to the pointwise conditioned expectation given the observed data. Further in the case where the space of functions belongs to the class of Gaussian process the optimal estimate is the conditional expectation even for asymmetric loss functions

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

Comparing Different Template Features for Recognizing People by Their Gait

To recognize people by their gait from a sequence of images, we have proposed a statistical approach which combined eigenspace transformation (EST) with canonical space transformation (CST) for feature transformation of spatial templates. This approach is used to reduce data dimensionality and to optimize the class separability of different gait sequences simultaneously. Good recognition rates have been achieved. Here, we incorporate temporal information from optical flows into three kinds of temporal templates and use them as features for gait recognition in addition to the spatial templates. The recognition performance for four kinds of template features has been evaluated in this paper. Experimental results show that spatial templates, horizontal-flow templates and the combined horizontal-flow and vertical-flow templates are better than vertical-flow templates for gait recognition

Nuclear Star Clusters across the Hubble Sequence

Over the last decade, HST imaging studies have revealed that the centers of most galaxies are occupied by compact, barely resolved sources. Based on their structural properties, position in the fundamental plane, and spectra, these sources clearly have a stellar origin. They are therefore called ``nuclear star clusters'' (NCs) or ``stellar nuclei''. NCs are found in galaxies of all Hubble types, suggesting that their formation is intricately linked to galaxy evolution. In this contribution, I briefly review the results from recent studies of NCs, touch on some ideas for their formation, and mention some open issues related to the possible connection between NCs and supermassive black holes.Comment: 6 page conference proceedings, to appear in "The impact of HST on European Astronomy" (41st ESLAB Symposium), pdflatex file, uses svmult.cls (included

Provenance history of detrital diamond deposits, West Coast of Namaqualand, South Africa

The West Coast of Namaqualand in South Africa hosts extensive detrital diamond deposits, but considerable debate exists as to the provenance of these diamonds. Some researchers have suggested derivation of the diamonds from Cretaceous-Jurassic kimberlites (also termed Group I kimberlites) and orangeites (also termed Group II kimberlites) located on the Kaapvaal Craton. However, others favour erosion of diamonds from the ca.300 Ma Dwyka Group sediments, with older, pre-Karoo kimberlites being the original source(s). Previous work has demonstrated that 40Ar/39Ar analyses of clinopyroxene inclusions, extracted from diamonds, yield ages approaching the time(s) of source kimberlite emplacement, which can be used to constrain the provenance of placer diamond deposits. In the current study, 40Ar/39Ar analyses were conducted on clinopyroxene inclusions from two similar batches of Namaqualand detrital diamonds, yielding (maximum) ages ranging from 117.5 ± 43.6 Ma to 3684 ± 191 Ma (2σ) and 120.6 ± 15.4 Ma to 688.8 ± 4.9 Ma (2σ), respectively. The vast majority of inclusions (88%) produced ages younger than 500 Ma, indicating that most Namaqualand diamonds originated from Cretaceous-Jurassic kimberlites/orangeites, with few, if any, derived from the Dwyka tillites. The provenance of the Namaqualand diamonds from ca.115–200 Ma orangeites is consistent with Late Cretaceous paleo-drainage reconstructions, as these localities could have been sampled by the ‘paleo-Karoo’ River and transported to the West Coast via an outlet close to the current Olifants River mouth. At ca.90 Ma, this drainage system appears to have been captured by the ‘paleo-Kalahari’ River, a precursor to the modern Orange River system. This latter drainage is considered to have transported diamonds eroded from both ca.80–90 Ma kimberlites and ca.115–200 Ma orangeites to the West Coast, which were subsequently reworked along the Namibian coast, forming additional placer deposits

Polariton Analysis of a Four-Level Atom Strongly Coupled to a Cavity Mode

We present a complete analytical solution for a single four-level atom strongly coupled to a cavity field mode and driven by external coherent laser fields. The four-level atomic system consists of a three-level subsystem in an EIT configuration, plus an additional atomic level; this system has been predicted to exhibit a photon blockade effect. The solution is presented in terms of polaritons. An effective Hamiltonian obtained by this procedure is analyzed from the viewpoint of an effective two-level system, and the dynamic Stark splitting of dressed states is discussed. The fluorescence spectrum of light exiting the cavity mode is analyzed and relevant transitions identified.Comment: 12 pages, 9 figure