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Dimensionality reduction for visualization of normal and pathological speech data
(Elsevier, 2009-07)
For an adequate analysis of pathological speech signals, a sizeable number of parameters is required, such as those related to jitter, shimmer and noise content. Often this kind of high-dimensional signal representation ...
Supersymmetric soliton solution in a dimensionally reduced schrödinger-chern-simons model
(American Physical Society, 2011-02)
We obtain, by dimensional reduction, a (1+1) supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally, novel solitonic ...
A dimension reduction scheme for the computation of optimal unions of subspaces
(Sampling Publishing, 2011-11)
Given a set of points F in a high dimensional space, the problem of finding a union of subspaces U_i V_i ⊆ R^N that best explains the data F increases dramatically with the dimension of R^N. In this article, we study a ...
Clustering biological data with SOMs: on topology preservation in non-linear dimensional reduction
(Pergamon-Elsevier Science Ltd, 2013-07)
Dimensional reduction is a widely used technique for exploratory analysis of large volume of data. In biological datasets, each object is described by a large number of variables (or dimensions) and it is crucial to perform ...
Unsupervised Feature Selection Methodology for Clustering in High Dimensionality Datasets
(Instituto de Informática - Universidade Federal do Rio Grande do Sul, 2020)
Gdpc: An R package for generalized dynamic principal components
(Journal Statistical Software, 2020-02-23)
Gdpc is an R package for the computation of the generalized dynamic principal components proposed in Peña and Yohai (2016). In this paper, we briefly introduce the problem of dynamical principal components, propose a ...
The index of symmetry of three-dimensional Lie groups with a left-invariant metric
(De Gruyter, 2018-10)
We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive ...
Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
(American Statistical Association, 2019-02)
We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal ...
Multipeak Solutions for the Yamabe Equation
(Springer, 2019-08)
Let (M, g) be a closed Riemannian manifold of dimension n≥ 3 and x∈ M be an isolated local minimum of the scalar curvature sg of g. For any positive integer k we prove that for ϵ> 0 small enough the subcritical Yamabe ...
Generalized Dynamic Principal Components
(American Statistical Association, 2016-07)
Brillinger defined dynamic principal components (DPC) for time series based on a reconstruction criterion. He gave a very elegant theoretical solution and proposed an estimator which is consistent under stationarity. Here, ...