Invariant Co-Ordinate Selection

Tyler, David E.; Critchley, Frank; Dümbgen, Lutz; Oja, Hannu

doi:10.1111/j.1467-9868.2009.00706.x

Cited by 112 publications

(137 citation statements)

References 53 publications

(65 reference statements)

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“…Thus, for a particular data combination there is only one possible solution which eliminates the ambiguity between different test results. The size of the LUT is a limiting factor; therefore to reduce its dimensionality the ICS transformation is applied (Nordhausen et al, 2008;Tyler et al, 2009). It utilises the principal component analyses (PCA) (Mardia et al, 1979) and two scatter matrices in order to construct independent components which do not rely on a distribution mean.…”

Section: Spectral Features Employed In the Pcm Methodsmentioning

confidence: 99%

Probabilistic approach to cloud and snow detection on Advanced Very High Resolution Radiometer (AVHRR) imagery

et al. 2014

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Abstract. Derivation of probability estimates complementary to geophysical data sets has gained special attention over the last years. Information about a confidence level of provided physical quantities is required to construct an error budget of higher-level products and to correctly interpret final results of a particular analysis. Regarding the generation of products based on satellite data a common input consists of a cloud mask which allows discrimination between surface and cloud signals. Further the surface information is divided between snow and snow-free components. At any step of this discrimination process a misclassification in a cloud/snow mask propagates to higher-level products and may alter their usability. Within this scope a novel probabilistic cloud mask (PCM) algorithm suited for the 1 km × 1 km Advanced Very High Resolution Radiometer (AVHRR) data is proposed which provides three types of probability estimates between: cloudy/clear-sky, cloudy/snow and clearsky/snow conditions. As opposed to the majority of available techniques which are usually based on the decision-tree approach in the PCM algorithm all spectral, angular and ancillary information is used in a single step to retrieve probability estimates from the precomputed look-up tables (LUTs). Moreover, the issue of derivation of a single threshold value for a spectral test was overcome by the concept of multidimensional information space which is divided into small bins by an extensive set of intervals. The discrimination between snow and ice clouds and detection of broken, thin clouds was enhanced by means of the invariant coordinate system (ICS) transformation. The study area covers a wide range of environmental conditions spanning from Iceland through central Europe to northern parts of Africa which exhibit diverse difficulties for cloud/snow masking algorithms. The retrieved PCM cloud classification was compared to the Polar Platform System (PPS) version 2012 and Moderate Resolution Imaging Spectroradiometer (MODIS) collection 6 cloud masks, SYNOP (surface synoptic observations) weather reports, Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) vertical feature mask version 3 and to MODIS collection 5 snow mask. The outcomes of conducted analyses proved fine detection skills of the PCM method with results comparable to or better than the reference PPS algorithm.

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Section: Spectral Features Employed In the Pcm Methodsmentioning

confidence: 99%

Probabilistic approach to cloud and snow detection on Advanced Very High Resolution Radiometer (AVHRR) imagery

et al. 2014

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“…Theorem 5.5 of [22] and our assumption that Z has independent and symmetric marginals imply that S (F Z ), = 1, 2 are diagonal matrices, so that this submodel actually only imposes that the quantities Ω rr , r = 1, . .…”

Section: Estimation Of λmentioning

confidence: 99%

Signed-rank tests for location in the symmetric independent component model

Nordhausen

Oja

Paindaveine

2009

Journal of Multivariate Analysis

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a b s t r a c tThe so-called independent component (IC) model states that the observed p-vector X is generated via X = ΛZ + µ, where µ is a p-vector, Λ is a full-rank matrix, and the centered random vector Z has independent marginals. We consider the problem of testing the null hypothesis H 0 : µ = 0 on the basis of i.i.d. observations X 1 , . . . , X n generated by the symmetric version of the IC model above (for which all ICs have a symmetric distribution about the origin). In the spirit of [M. Hallin, D. Paindaveine, Optimal tests for multivariate location based on interdirections and pseudo-Mahalanobis ranks, Annals of Statistics, 30 (2002), 1103-1133], we develop nonparametric (signed-rank) tests, which are valid without any moment assumption and are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at given densities. Our tests are measurable with respect to the marginal signed ranks computed in the collection of null residualŝ Λ −1 X i , whereΛ is a suitable estimate of Λ. Provided thatΛ is affine-equivariant, the proposed tests, unlike the standard marginal signed-rank tests developed in [M.L. Puri, P.K. Sen, Nonparametric Methods in Multivariate Analysis, Wiley & Sons, New York, 1971] or any of their obvious generalizations, are affine-invariant. Local powers and asymptotic relative efficiencies (AREs) with respect to Hotelling's T 2 test are derived. Quite remarkably, when Gaussian scores are used, these AREs are always greater than or equal to one, with equality in the multinormal model only. Finite-sample efficiencies and robustness properties are investigated through a Monte Carlo study.

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“…MatrixẐ gives the observations in an invariant coordinate system (Tyler et al (2009)). Still another invariant coordinate system (maximal invariant statistic) based on p + 1 observations was proposed by Chakraborty and Chaudhuri (1999).…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

“…In the case of mixtures of elliptical distributions, a subset of invariant coordinates corresponds to Fisher's linear discriminant subspace (Tyler et al (2009)). Invariant coordinate selection may thus be seen as a tool for dimension reduction as well.…”

Section: Invariant Coordinate Selectionmentioning

confidence: 99%

Characteristics of multivariate distributions and the invariant coordinate system

Ilmonen

Nevalainen

Oja

2010

Statistics & Probability Letters

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We consider a semiparametric multivariate location-scatter model where the standardized random vector of the model is fixed using simultaneously two location vectors and two scatter matrices. The approach using location and scatter functionals based on the first four moments serves as our main example. The four functionals yield in a natural way the corresponding skewness, kurtosis and unmixing matrix functionals. Affine transformation based on the unmixing matrix transforms the variable to an invariant coordinate system. The limiting properties of the skewness, kurtosis, and unmixing matrix estimates are derived under general conditions. We discuss related statistical inference problems, the role of the sample statistics in testing for normality and ellipticity, and connections to invariant coordinate selection and independent component analysis.

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Invariant Co-Ordinate Selection

Cited by 112 publications

References 53 publications

Probabilistic approach to cloud and snow detection on Advanced Very High Resolution Radiometer (AVHRR) imagery

Probabilistic approach to cloud and snow detection on Advanced Very High Resolution Radiometer (AVHRR) imagery

Signed-rank tests for location in the symmetric independent component model

Characteristics of multivariate distributions and the invariant coordinate system

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