Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

Partial Least Square – Path Modeling: metodologia, software e aplicação

Trabalho de Projeto apresentado como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Valuing American Derivatives by Least Squares Methods

Least Squares estimators are notoriously known to generate sub-optimal exercise decisions when determining the optimal stopping time. The consequence is that the price of the option is underestimated. We show how variance reduction methods can be implemented to obtain more accurate option prices. We also extend the Longsta¤ and Schwartz (2001) method to price American options under stochastic volatility. These are two important contributions that are particularly relevant for practitioners. Finally, we extend the Glasserman and Yu (2004b) methodology to price Asian options and basket options.

Dominant partial least square factors of consumer purchase behaviour of passenger cars

Globalization and liberalization, with the entry of many prominent foreign manufacturers, changed the automobile scenario in India, since early 1990’s. World Leaders in automobile manufacturing such as Ford, General Motors, Honda, Toyota, Suzuki, Hyundai, Renault, Mitsubishi, Benz, BMW, Volkswagen and Nissan set up their manufacturing units in India in joint venture with their Indian counterpart companies, by making use of the Foreign Direct Investment policy of the Government of India, These manufacturers started capturing the hearts of Indian car customers with their choice of technological and innovative product features, with quality and reliability. With the multiplicity of choices available to the Indian passenger car buyers, it drastically changed the way the car purchase scenario in India and particularly in the State of Kerala. This transformed the automobile scene from a sellers’ market to buyers’ market. Car customers started developing their own personal preferences and purchasing patterns, which were hitherto unknown in the Indian automobile segment. The main purpose of this paper is to develop a model with major variables, which influence the consumer purchase behaviour of passenger car owners in the State of Kerala. Though there are innumerable studies conducted in other countries, there are very few thesis and research work conducted to study the consumer behaviour of the passenger car industry in India and specifically in the State of Kerala. The results of the research contribute to the practical knowledge base of the automobile industry, specifically to the passenger car segment. It has also a great contributory value addition to the manufacturers and dealers for customizing their marketing plans in the State

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Sparse multioutput radial basis function network construction using combined locally regularised orthogonal least square and D-optimality experimental design

A construction algorithm for multioutput radial basis function (RBF) network modelling is introduced by combining a locally regularised orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximised model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious RBF network model with excellent generalisation performance. The D-optimality design criterion enhances the model efficiency and robustness. A further advantage of the combined approach is that the user only needs to specify a weighting for the D-optimality cost in the combined RBF model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

DETERMINATION of SILICON IN LUBRICANT OIL BY HIGH-RESOLUTION CONTINUUM SOURCE FLAME ATOMIC ABSORPTION SPECTROMETRY USING LEAST-SQUARE BACKGROUND CORRECTION and INTERNAL STANDARDIZATION

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

Constrained least square pre-distortion scheme for multiuser ultra-wideband

The study proposes a constrained least square (CLS) pre-distortion scheme for multiple-input single-output (MISO) multiple access ultra-wideband (UWB) systems. In such a scheme, a simple objective function is defined, which can be efficiently solved by a gradient-based algorithm. For the performance evaluation, scenarios CM1 and CM3 of the IEEE 802.15.3a channel model are considered. Results show that the CLS algorithm has a fast convergence and a good trade-off between intersymbol interference (ISI) and multiple access interference (MAI) reduction and signal-to-noise ratio (SNR) preservation, performing better than time-reversal (TR) pre-distortion.

Fourier Series by Least Square Minimization

An introduction to Fourier Series based on the minimization of the least square error between an approximate series representation and the exact function.

Comparison of aerodynamic stability derivatives obtained from analysis of F-100A dynamic lateral flight test data by two least squares methods.

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Estimação de fatores de correção do perímetro escrotal para idade e peso corporal em touros jovens da raça Nelore

Neste trabalho foram estudados os efeitos de idade e peso sobre o perímetro escrotal (PE) de touros jovens da raça Nelore e estimados os fatores de correção (FC) do PE para esses efeitos. As informações utilizadas pertencem aos Registros de Produção da Associação Paraguaia dos Criadores de Nelore, obtidos entre 1986 e 1997, de 110 criatórios, totalizando 7458 observações. Os coeficientes de regressão que permitiram o cálculo dos FCs para o PE foram estimados pelo método dos quadrados mínimos, empregando-se um modelo que considerou o grupo contemporâneo (animais nascidos no mesmo ano, estação, rebanho, avaliados na mesma data e do mesmo grupo de manejo alimentar na desmama e no sobreano), o efeito linear da idade em dias e os efeitos linear e quadrático do peso aos 570 dias de idade (P570). O efeito da idade sobre o PE foi igual a 0,0383(±0,0024) cm/dia e do P570 sobre o PE corrigido para essa idade, 0,0708(±0,0049) cm/kg, efeito linear, e -0,0000413(±0,0000074) cm/kg², efeito quadrático. A idade e o peso do animal foram importantes fontes de variação a serem removidas do PE, como indicativo da precocidade sexual de touros de sobreano.