Solving Least Squares Problems.
About: This article is published in Journal of the American Statistical Association.The article was published on 1977-12-01. It has received 1350 citations till now. The article focuses on the topics: Iteratively reweighted least squares & Least squares.
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TL;DR: In this paper, the authors investigate the accuracy of the parametric recovery of the line-of-sight velocity distribution (LOSVD) of the stars in a galaxy while working in pixel space.
Abstract: We investigate the accuracy of the parametric recovery of the line‐of‐sight velocity distribution (LOSVD) of the stars in a galaxy while working in pixel space. Problems appear when the data have a low signal‐to‐noise ratio or the observed LOSVD is not well sampled by the data. We propose a simple solution based on maximum penalized likelihood, and we apply it to the common situation in which the LOSVD is described by a Gauss‐Hermite series. We compare different techniques by extracting the stellar kinematics from observations of the barred lenticular galaxy NGC 3384 obtained with the SAURON integral‐field spectrograph.
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TL;DR: This letter proposes two projected gradient methods for nonnegative matrix factorization, both of which exhibit strong optimization properties and discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach.
Abstract: Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.
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Cites background from "Solving Least Squares Problems."
...The simplest possible weighting is based on the norm of the columns of the lead field matrix (Lawson and Hanson, 1974)....
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TL;DR: The design of a new methodology for representing the relationship between two sets of spectral envelopes and the proposed transform greatly improves the quality and naturalness of the converted speech signals compared with previous proposed conversion methods.
Abstract: Voice conversion, as considered in this paper, is defined as modifying the speech signal of one speaker (source speaker) so that it sounds as if it had been pronounced by a different speaker (target speaker). Our contribution includes the design of a new methodology for representing the relationship between two sets of spectral envelopes. The proposed method is based on the use of a Gaussian mixture model of the source speaker spectral envelopes. The conversion itself is represented by a continuous parametric function which takes into account the probabilistic classification provided by the mixture model. The parameters of the conversion function are estimated by least squares optimization on the training data. This conversion method is implemented in the context of the HNM (harmonic+noise model) system, which allows high-quality modifications of speech signals. Compared to earlier methods based on vector quantization, the proposed conversion scheme results in a much better match between the converted envelopes and the target envelopes. Evaluation by objective tests and formal listening tests shows that the proposed transform greatly improves the quality and naturalness of the converted speech signals compared with previous proposed conversion methods.
1,109 citations
Cites background from "Solving Least Squares Problems."
...The form of (11) is that of a standard least-squares problem whose solution is given by the normal equations [25], [22]...
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TL;DR: In this paper, a new procedure is discussed which fits either the weighted or simple Euclidian model to data that may (a) be defined at either the nominal, ordinal, interval or ratio levels of measurement; (b) have missing observations; (c) be symmetric or asymmetric; (d) be conditional or unconditional; (e) be replicated or unreplicated; (f) be continuous or discrete.
Abstract: A new procedure is discussed which fits either the weighted or simple Euclidian model to data that may (a) be defined at either the nominal, ordinal, interval or ratio levels of measurement; (b) have missing observations; (c) be symmetric or asymmetric; (d) be conditional or unconditional; (e) be replicated or unreplicated; and (f) be continuous or discrete. Various special cases of the procedure include the most commonly used individual differences multidimensional scaling models, the familiar nonmetric multidimensional scaling model, and several other previously undiscussed variants. The procedure optimizes the fit of the model directly to the data (not to scalar products determined from the data) by an alternating least squares procedure which is convergent, very quick, and relatively free from local minimum problems. The procedure is evaluated via both Monte Carlo and empirical data. It is found to be robust in the face of measurement error, capable of recovering the true underlying configuration in the Monte Carlo situation, and capable of obtaining structures equivalent to those obtained by other less general procedures in the empirical situation.
961 citations