Representing Complex Data Using Localized Principal Components with Application to Astronomical Data

Einbeck, Jochen; Evers, Ludger; Bailer‐Jones, C. A. L.

doi:10.1007/978-3-540-73750-6_7

Cited by 17 publications

(13 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The preferential use of principal curves over alternative modeling methods in this context has been argued in [7], [29], and [30]. A more recent application by the authors [8] showed that the conceptual ACKPC algorithm does not suffer from the computational burden of the HSPC approach.…”

Section: Analysis Of Recorded Traffic Datamentioning

confidence: 97%

Adaptive Constraint K-Segment Principal Curves for Intelligent Transportation Systems

Zhang

Chen

Krüger

2008

IEEE Trans. Intell. Transport. Syst.

View full text Add to dashboard Cite

This paper revisits the construction of principal curves. Although they have a solid theoretical foundation as a nonlinear extension to principal components, this paper shows that they are difficult to implement in practice if the data distribution is sparse and uneven or if the data contain outliers. These issues may hamper the application of principal curves to an intelligent transportation system. To address these problems, this paper introduces an adaptive constraint K-segment principal curve (ACKPC) algorithm that can be applied in the presence of uneven and sparse distributions, as well as outliers. The benefits of the ACKPC algorithm are as follows: 1) It utilizes predefined endpoints of the curve to reduce the computational effort, and 2) it shows to be less sensitive to parameter settings and outliers. These benefits are demonstrated using two benchmark studies and experimental data from a freeway traffic stream system as well as recorded data from a Global Positioning System (GPS) data from a low-precision GPS receiver.Index Terms-Adaptive constraint K-segment principal curves (ACKPCs), freeway traffic stream modeling, Global Positioning System (GPS).

show abstract

Section: Analysis Of Recorded Traffic Datamentioning

confidence: 97%

Adaptive Constraint K-Segment Principal Curves for Intelligent Transportation Systems

Zhang

Chen

Krüger

2008

IEEE Trans. Intell. Transport. Syst.

View full text Add to dashboard Cite

show abstract

“…Since the input space is threedimensional, and since the remaining 16 variables are generated from this input space, there is a strong argument for an intrinsic dimension of 3. On the other hand, the 16dimensional data cloud of photon counts, which has been simulated in some complex manner from the APs, will arguably increase the ID of the whole data set at least to some extent, where it is known that this increase should be less than three since the first three principal component scores of the 16-dimensional photon counts are strongly correlated [7]. This is reflected in the ID of 5 obtained through the correlation dimension technique.…”

Section: Gaia Datamentioning

confidence: 99%

Intrinsic Dimensionality Estimation for High-dimensional Data Sets: New Approaches for the Computation of Correlation Dimension

Einbeck

Kalantan

2013

JETWI

Self Cite

View full text Add to dashboard Cite

The analysis of high–dimensional data is usually challenging since many standard modelling approaches tend to break down due to the so–called “curse of dimensionality”. Dimension reduction techniques, which reduce the data set (explicitly or implicitly) to a smaller number of variables, make the data analysis more efficient and are furthermore useful for visualization purposes. However, most dimension reduction techniques require fixing the intrinsic dimension of the low-dimensional subspace in advance. The intrinsic dimension can be estimated by fractal dimension estimation methods, which exploit the intrinsic geometry of a data set. The most popular concept from this family of methods is the correlation dimension, which requires estimation of the correlation integral for a ball of radius tending to 0. In this paper we propose approaches to approximate the correlation integral in this limit. Experimental results on real world and simulated data are used to demonstrate the algorithms and compare to other methodology. A simulation study which verifies the effectiveness of the proposed methods is also provided

show abstract

“…There exist more sophisticated methods of dimensionality reduction which could be used in the future, such as local and nonlinear variations on PCA (see Einbeck et al (2007) for a review and astronomical application).…”

Section: Principal Component Analysis (Pca)mentioning

confidence: 99%

Estimation of stellar atmospheric parameters from SDSS/SEGUE spectra

Fiorentin

Bailer‐Jones

Lee

et al. 2007

A&A

View full text Add to dashboard Cite

We present techniques for the estimation of stellar atmospheric parameters (T eff , log g, [Fe/H]) for stars from the SDSS/SEGUE survey. The atmospheric parameters are derived from the observed medium-resolution (R = 2000) stellar spectra using non-linear regression models trained either on (1) pre-classified observed data or (2) synthetic stellar spectra. In the first case we use our models to automate and generalize parametrization produced by a preliminary version of the SDSS/SEGUE Spectroscopic Parameter Pipeline (SSPP). In the second case we directly model the mapping between synthetic spectra (derived from Kurucz model atmospheres) and the atmospheric parameters, independently of any intermediate estimates. After training, we apply our models to various samples of SDSS spectra to derive atmospheric parameters, and compare our results with those obtained previously by the SSPP for the same samples. We obtain consistency between the two approaches, with RMS deviations on the order of 150 K in T eff , 0.35 dex in log g, and 0.22 dex in [Fe/H]. The models are applied to pre-processed spectra, either via Principal Component Analysis (PCA) or a Wavelength Range Selection (WRS) method, which employs a subset of the full 3850-9000 Å spectral range. This is both for computational reasons (robustness and speed), and because it delivers higher accuracy (better generalization of what the models have learned). Broadly speaking, the PCA is demonstrated to deliver more accurate atmospheric parameters when the training data are the actual SDSS spectra with previously estimated parameters, whereas WRS appears superior for the estimation of log g via synthetic templates, especially for lower signal-to-noise spectra. From a subsample of some 19 000 stars with previous determinations of the atmospheric parameters, the accuracies of our predictions (mean absolute errors) for each parameter are T eff to 170/170 K, log g to 0.36/0.45 dex, and [Fe/H] to 0.19/0.26 dex, for methods (1) and (2), respectively. We measure the intrinsic errors of our models by training on synthetic spectra and evaluating their performance on an independent set of synthetic spectra. This yields RMS accuracies of 50 K, 0.02 dex, and 0.03 dex on T eff , log g, and [Fe/H], respectively. Our approach can be readily deployed in an automated analysis pipeline, and can easily be retrained as improved stellar models and synthetic spectra become available. We nonetheless emphasise that this approach relies on an accurate calibration and pre-processing of the data (to minimize mismatch between the real and synthetic data), as well as sensible choices concerning feature selection. From an analysis of cluster candidates with available SDSS spectroscopy (M 15, M 13, M 2, and NGC 2420), and assuming the age, metallicity, and distances given in the literature are correct, we find evidence for small systematic offsets in T eff and/or log g for the parameter estimates from the model trained on real data with the SSPP. Thus, this model turns out to derive more pr...

show abstract

Representing Complex Data Using Localized Principal Components with Application to Astronomical Data

Cited by 17 publications

References 41 publications

Adaptive Constraint K-Segment Principal Curves for Intelligent Transportation Systems

Adaptive Constraint K-Segment Principal Curves for Intelligent Transportation Systems

Intrinsic Dimensionality Estimation for High-dimensional Data Sets: New Approaches for the Computation of Correlation Dimension

Estimation of stellar atmospheric parameters from SDSS/SEGUE spectra

Contact Info

Product

Resources

About