Parametric subspace modeling of speech transitions

Reinhard, K.; Niranjan, Mahesan

doi:10.1016/s0167-6393(98)00067-3

Cited by 29 publications

(14 citation statements)

References 35 publications

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“…[85,53,54,26]. More recently, the principal curves algorithm by Hastie and Stuetzle [25] has also been applied to the modeling of freeway traffic streams [9] and the learning of high-precision GPS data from low-precision counterpart [84].…”

Section: Algorithmic Developmentsmentioning

confidence: 99%

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Developments and Applications of Nonlinear Principal Component Analysis – a Review

Krüger

Zhang

Xie

2008

Lecture Notes in Computational Science and Enginee

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Summary.Although linear principal component analysis (PCA) originates from the work of Sylvester [67] and Pearson [51], the development of nonlinear counterparts has only received attention from the 1980s. Work on nonlinear PCA, or NLPCA, can be divided into the utilization of autoassociative neural networks, principal curves and manifolds, kernel approaches or the combination of these approaches. This article reviews existing algorithmic work, shows how a given data set can be examined to determine whether a conceptually more demanding NLPCA model is required and lists developments of NLPCA algorithms. Finally, the paper outlines problem areas and challenges that require future work to mature the NLPCA research field. IntroductionPCA is a data analysis technique that relies on a simple transformation of recorded observation, stored in a vector z ∈ R N , to produce statistically independent score variables, stored in t ∈ R n , n ≤ N :(1.1)Here, P is a transformation matrix, constructed from orthonormal column vectors. Since the first applications of PCA [21], this technique has found its way into a wide range of different application areas, for example signal processing [75], factor analysis [29,44], system identification [77], chemometrics [20,66] and more recently, general data mining [11,70,58] including image processing [17,72] and pattern recognition [47,10], as well as process 2 U. Kruger, J. Zhang, and L. Xie monitoring and quality control [1,82] including multiway [48], multiblock [52] and multiscale [3] extensions. This success is mainly related to the ability of PCA to describe significant information/variation within the recorded data typically by the first few score variables, which simplifies data analysis tasks accordingly. Sylvester [67] formulated the idea behind PCA, in his work the removal of redundancy in bilinear quantics, that are polynomial expressions where the sum of the exponents are of an order greater than 2, and Pearson [51] laid the conceptual basis for PCA by defining lines and planes in a multivariable space that present the closest fit to a given set of points. Hotelling [28] then refined this formulation to that used today. Numerically, PCA is closely related to an eigenvector-eigenvalue decomposition of a data covariance, or correlation matrix and numerical algorithms to obtain this decomposition include the iterative NIPALS algorithm [78], which was defined similarly by Fisher and MacKenzie earlier on [80], and the singular value decomposition. Good overviews concerning PCA are given in Mardia et al. [45], Joliffe [32], Wold et al. [80] and Jackson [30].The aim of this article is to review and examine nonlinear extensions of PCA that have been proposed over the past two decades. This is an important research field, as the application of linear PCA to nonlinear data may be inadequate [49]. The first attempts to present nonlinear PCA extensions include a generalization, utilizing a nonmetric scaling, that produces a nonlinear optimization problem [42] and constructing a curves...

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Section: Algorithmic Developmentsmentioning

confidence: 99%

“…Following the above derivative, the steepest descent direction for the training network weights between the input and hidden layer can be obtained as follows: 54) which is given by…”

Section: Neural Network Approachesmentioning

confidence: 99%

Developments and Applications of Nonlinear Principal Component Analysis – a Review

Krüger

Zhang

Xie

2008

Lecture Notes in Computational Science and Enginee

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“…Roughly, the purpose is to search for a curve passing through the middle of the observations, as illustrated in Figure 1. Principal curves have a broad range of applications in many different areas, such as physics (Hastie and Stuetzle [26], Friedsam and Oren [23]), character and speech recognition (Kégl and Krzyżak [29], Reinhard and Niranjan [39]), mapping and geology (Brunsdon [10], Stanford and Raftery [43], Banfield and Raftery [4], Einbeck, Tutz and Evers [20,21]), natural sciences (De'ath [14], Corkeron, Anthony and Martin [13], Einbeck, Tutz and Evers [20]) and medicine (Wong and Chung [46], Caffo, Crainiceanu, Deng and Hendrix [11]). …”

Section: Principal Curvesmentioning

confidence: 99%

Parameter Selection for Principal Curves

Biau

Fischer

2012

IEEE Trans. Inform. Theory

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-Principal curves are nonlinear generalizations of the notion of first principal component. Roughly, a principal curve is a parameterized curve in R d which passes through the "middle" of a data cloud drawn from some unknown probability distribution. Depending on the definition, a principal curve relies on some unknown parameters (number of segments, length, turn. . . ) which have to be properly chosen to recover the shape of the data without interpolating. In the present paper, we consider the principal curve problem from an empirical risk minimization perspective and address the parameter selection issue using the point of view of model selection via penalization. We offer oracle inequalities and implement the proposed approaches to recover the hidden structures in both simulated and real-life data.

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“…Principal curves have been successfully applied to solve various practical problems, such as the alignment of magnets of the Stanford linear collier [22], ice floe identification in satellite images [23], handwriting classification [24], and speech recognition [25]. A detailed overview of PCs can be seen in [26].…”

Section: Theory Of Pcs and Its Algorithmmentioning

confidence: 99%

Freeway Traffic Stream Modeling Based on Principal Curves and Its Analysis

Chen

Zhang

Tang

et al. 2004

IEEE Trans. Intell. Transport. Syst.

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In this paper, we have proposed to use the method of principal curves to describe and analyze the interaction among freeway traffic-stream variables and their joint behaviors without utilizing conventional assumptions made on the functional forms of interactions, as in previous studies. As a nonparameter modeling approach, the performance of the proposed method depends only on the data used and involves no assumed knowledge regarding the relationship among the traffic-stream variables. First, we discuss the basic algorithm for data analysis using principal curves and the corresponding data filter algorithm for determining principal curves for application in traffic-steam analysis. Second, a case study is used to compare the performance of the proposed method to that of the classical model proposed by Greenshields; results indicate that the proposed model is better than the classical one in both data accuracy and curve shape. Finally, the traffic-stream models generated with principal curves at different locations and lanes are compared with each others and the three-dimensional traffic-stream models developed from principal curves are discussed. Clearly, our results have demonstrated the feasibility and advantages of applying principal curves in freeway traffic-stream modeling and analysis.

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Parametric subspace modeling of speech transitions

Cited by 29 publications

References 35 publications

Developments and Applications of Nonlinear Principal Component Analysis – a Review

Developments and Applications of Nonlinear Principal Component Analysis – a Review

Parameter Selection for Principal Curves

Freeway Traffic Stream Modeling Based on Principal Curves and Its Analysis

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