Multiview point cloud kernels for semisupervised learning [Lecture Notes]

In semisupervised learning (SSL), a predictive model is learn from a collection of labeled data and a typically much larger collection of unlabeled data. These paper presented a framework called multi-view point cloud regularization (MVPCR), which unifies and generalizes several semisupervised kernel methods that are based on data-dependent regularization in reproducing kernel Hilbert spaces (RKHSs). Special cases of MVPCR include coregularized least squares (CoRLS), manifold regularization (MR), and graph-based SSL. An accompanying theorem shows how to reduce any MVPCR problem to standard supervised learning with a new multi-view kernel.

Calculation of dose kernels for radiotherapy applications using the GEANT 4 Monte Carlo toolkit

Dose kernels may be used to calculate dose distributions in radiotherapy (as described by Ahnesjo et al., 1999). Their calculation requires use of Monte Carlo methods, usually by forcing interactions to occur at a point. The Geant4 Monte Carlo toolkit provides a capability to force interactions to occur in a particular volume. We have modified this capability and created a Geant4 application to calculate dose kernels in cartesian, cylindrical, and spherical scoring systems. The simulation considers monoenergetic photons incident at the origin of a 3 m x 3 x 9 3 m water volume. Photons interact via compton, photo-electric, pair production, and rayleigh scattering. By default, Geant4 models photon interactions by sampling a physical interaction length (PIL) for each process. The process returning the smallest PIL is then considered to occur. In order to force the interaction to occur within a given length, L_FIL, we scale each PIL according to the formula: PIL_forced = L_FIL 9 (1 - exp(-PIL/PILo)) where PILo is a constant. This ensures that the process occurs within L_FIL, whilst correctly modelling the relative probability of each process. Dose kernels were produced for an incident photon energy of 0.1, 1.0, and 10.0 MeV. In order to benchmark the code, dose kernels were also calculated using the EGSnrc Edknrc user code. Identical scoring systems were used; namely, the collapsed cone approach of the Edknrc code. Relative dose difference images were then produced. Preliminary results demonstrate the ability of the Geant4 application to reproduce the shape of the dose kernels; median relative dose differences of 12.6, 5.75, and 12.6 % were found for an incident photon energy of 0.1, 1.0, and 10.0 MeV respectively.

Supplementary information : weighted tree kernels for sequence analysis

Genomic sequences are fundamentally text documents, admitting various representations according to need and tokenization. Gene expression depends crucially on binding of enzymes to the DNA sequence at small, poorly conserved binding sites, limiting the utility of standard pattern search. However, one may exploit the regular syntactic structure of the enzyme's component proteins and the corresponding binding sites, framing the problem as one of detecting grammatically correct genomic phrases. In this paper we propose new kernels based on weighted tree structures, traversing the paths within them to capture the features which underpin the task. Experimentally, we and that these kernels provide performance comparable with state of the art approaches for this problem, while offering significant computational advantages over earlier methods. The methods proposed may be applied to a broad range of sequence or tree-structured data in molecular biology and other domains.

Solution of singular integral equations with logarithmic and Cauchy kernels

A direct method of solution is presented for singular integral equations of the first kind, involving the combination of a logarithmic and a Cauchy type singularity. Two typical cages are considered, in one of which the range of integration is a Single finite interval and, in the other, the range of integration is a union of disjoint finite intervals. More such general equations associated with a finite number (greater than two) of finite, disjoint, intervals can also be handled by the technique employed here.

Assessment of quality defects in macadamia kernels using NIR spectroscopy

Spectral data were collected of intact and ground kernels using 3 instruments (using Si-PbS, Si, and InGaAs detectors), operating over different areas of the spectrum (between 400 and 2500 nm) and employing transmittance, interactance, and reflectance sample presentation strategies. Kernels were assessed on the basis of oil and water content, and with respect to the defect categories of insect damage, rancidity, discoloration, mould growth, germination, and decomposition. Predictive model performance statistics for oil content models were acceptable on all instruments (R2 > 0.98; RMSECV < 2.5%, which is similar to reference analysis error), although that for the instrument employing reflectance optics was inferior to models developed for the instruments employing transmission optics. The spectral positions for calibration coefficients were consistent with absorbance due to the third overtones of CH2 stretching. Calibration models for moisture content in ground samples were acceptable on all instruments (R2 > 0.97; RMSECV < 0.2%), whereas calibration models for intact kernels were relatively poor. Calibration coefficients were more highly weighted around 1360, 740 and 840 nm, consistent with absorbance due to overtones of O-H stretching and combination. Intact kernels with brown centres or rancidity could be discriminated from each other and from sound kernels using principal component analysis. Part kernels affected by insect damage, discoloration, mould growth, germination, and decomposition could be discriminated from sound kernels. However, discrimination among these defect categories was not distinct and could not be validated on an independent set. It is concluded that there is good potential for a low cost Si photodiode array instrument to be employed to identify some quality defects of intact macadamia kernels and to quantify oil and moisture content of kernels in the process laboratory and for oil content in-line. Further work is required to examine the robustness of predictive models across different populations, including growing districts, cultivars and times of harvest.

Hardness Methods for Testing Maize Kernels

Maize is a highly important crop to many countries around the world, through the sale of the maize crop to domestic processors and subsequent production of maize products and also provides a staple food to subsistance farms in undeveloped countries. In many countries, there have been long-term research efforts to develop a suitable hardness method that could assist the maize industry in improving efficiency in processing as well as possibly providing a quality specification for maize growers, which could attract a premium. This paper focuses specifically on hardness and reviews a number of methodologies as well as important biochemical aspects of maize that contribute to maize hardness used internationally. Numerous foods are produced from maize, and hardness has been described as having an impact on food quality. However, the basis of hardness and measurement of hardness are very general and would apply to any use of maize from any country. From the published literature, it would appear that one of the simpler methods used to measure hardness is a grinding step followed by a sieving step, using multiple sieve sizes. This would allow the range in hardness within a sample as well as average particle size and/or coarse/fine ratio to be calculated. Any of these parameters could easily be used as reference values for the development of near-infrared (NIR) spectroscopy calibrations. The development of precise NIR calibrations will provide an excellent tool for breeders, handlers, and processors to deliver specific cultivars in the case of growers and bulk loads in the case of handlers, thereby ensuring the most efficient use of maize by domestic and international processors. This paper also considers previous research describing the biochemical aspects of maize that have been related to maize hardness. Both starch and protein affect hardness, with most research focusing on the storage proteins (zeins). Both the content and composition of the zein fractions affect hardness. Genotypes and growing environment influence the final protein and starch content and. to a lesser extent, composition. However, hardness is a highly heritable trait and, hence, when a desirable level of hardness is finally agreed upon, the breeders will quickly be able to produce material with the hardness levels required by the industry.

Maintaining high moisture content of macadamia nuts-in-shell during storage induces brown centres in raw kernels

BACKGROUND Kernel brown centres in macadamia are a defect causing internal discolouration of kernels. This study investigates the effect on the incidence of brown centres in raw kernel after maintaining high moisture content in macadamia nuts-in-shell stored at temperatures of 30°C, 35°C, 40°C and 45°C. RESULTS Brown centres of raw kernel increased with nuts-in-shell storage time and temperature when high moisture content was maintained by sealing in polyethylene bags. Almost all kernels developed the defect when kept at high moisture content for 5 days at 45°C, and 44% developed brown centres after only 2 days of storage at high moisture content at 45°C. This contrasted with only 0.76% when stored for 2 days at 45°C but allowed to dry in open-mesh bags. At storage temperatures below 45°C, there were fewer brown centres, but there were still significant differences between those stored at high moisture content and those allowed to dry (P < 0.05). CONCLUSION Maintenance of high moisture content during macadamia nuts-in-shell storage increases the incidence of brown centres in raw kernels and the defect increases with time and temperature. On-farm nuts-in-shell drying and storage practices should rapidly remove moisture to reduce losses. Ideally, nuts-in-shell should not be stored at high moisture content on-farm at temperatures over 30°C. © 2013 Society of Chemical Industry

Relation between Chandrasekhar's X-function and the eigenvalues of integral operators with difference kernels

Abstract is not available.

Kernels for large margin time-series classification

In this paper we propose a novel family of kernels for multivariate time-series classification problems. Each time-series is approximated by a linear combination of piecewise polynomial functions in a Reproducing Kernel Hilbert Space by a novel kernel interpolation technique. Using the associated kernel function a large margin classification formulation is proposed which can discriminate between two classes. The formulation leads to kernels, between two multivariate time-series, which can be efficiently computed. The kernels have been successfully applied to writer independent handwritten character recognition.

Extended kac-akhiezer formulae and the fredholm determinant of finite section hilbert-schmidt kernels

This paper deals with some results (known as Kac-Akhiezer formulae) on generalized Fredholm determinants for Hilbert-Schmidt operators on L2-spaces, available in the literature for convolution kernels on intervals. The Kac-Akhiezer formulae have been obtained for kernels which are not necessarily of convolution nature and for domains in R(n).

Efficient algorithms for learning kernels from multiple similarity matrices with general convex loss functions

In this paper we consider the problem of learning an n × n kernel matrix from m(1) similarity matrices under general convex loss. Past research have extensively studied the m = 1 case and have derived several algorithms which require sophisticated techniques like ACCP, SOCP, etc. The existing algorithms do not apply if one uses arbitrary losses and often can not handle m > 1 case. We present several provably convergent iterative algorithms, where each iteration requires either an SVM or a Multiple Kernel Learning (MKL) solver for m > 1 case. One of the major contributions of the paper is to extend the well knownMirror Descent(MD) framework to handle Cartesian product of psd matrices. This novel extension leads to an algorithm, called EMKL, which solves the problem in O(m2 log n 2) iterations; in each iteration one solves an MKL involving m kernels and m eigen-decomposition of n × n matrices. By suitably defining a restriction on the objective function, a faster version of EMKL is proposed, called REKL,which avoids the eigen-decomposition. An alternative to both EMKL and REKL is also suggested which requires only an SVMsolver. Experimental results on real world protein data set involving several similarity matrices illustrate the efficacy of the proposed algorithms.

Structural Alignment based Kernels for Protein Structure Classification

Structural alignments are the most widely used tools for comparing proteins with low sequence similarity. The main contribution of this paper is to derive various kernels on proteins from structural alignments, which do not use sequence information. Central to the kernels is a novel alignment algorithm which matches substructures of fixed size using spectral graph matching techniques. We derive positive semi-definite kernels which capture the notion of similarity between substructures. Using these as base more sophisticated kernels on protein structures are proposed. To empirically evaluate the kernels we used a 40% sequence non-redundant structures from 15 different SCOP superfamilies. The kernels when used with SVMs show competitive performance with CE, a state of the art structure comparison program.

Accelerating Numerical Linear Algebra Kernels on a Scalable Run Time Reconfigurable Platform

Numerical Linear Algebra (NLA) kernels are at the heart of all computational problems. These kernels require hardware acceleration for increased throughput. NLA Solvers for dense and sparse matrices differ in the way the matrices are stored and operated upon although they exhibit similar computational properties. While ASIC solutions for NLA Solvers can deliver high performance, they are not scalable, and hence are not commercially viable. In this paper, we show how NLA kernels can be accelerated on REDEFINE, a scalable runtime reconfigurable hardware platform. Compared to a software implementation, Direct Solver (Modified Faddeev's algorithm) on REDEFINE shows a 29X improvement on an average and Iterative Solver (Conjugate Gradient algorithm) shows a 15-20% improvement. We further show that solution on REDEFINE is scalable over larger problem sizes without any notable degradation in performance.