Geometric representation of high dimension, low sample size data

By Hall Peter Gavin, James Stephen Marron, A. Neeman. 2005

567 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/89227d150b531658bbcd23a5b02c8d147b96ed10

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Citations in the corpus

Analytic estimation of statistical significance maps for support vector machine based multi-variate image analysis and classification (2013, unknown): “This equivalence between the SVM and LS-SVM for high dimensional low sample size data was also previously noted in Ye and Xiong (2007) where it was based on observations about the distribution of such data as elucidated in Hall et al. (2005).”
PCA CONSISTENCY IN HIGH DIMENSION, LOW SAMPLE SIZE CONTEXT (2009, methodology): “Section 2 develops conditions that guarantee the nonzero eigenvalues of the sample covariance matrix tend to an increasing constant, which are much more general than those of Hall, Marron and Neeman [8] and Ahn et al.”
Least squares linear discriminant analysis (2007, unknown): “Following some recent results from [ 15 ], we plan to carry out theoretical analysis on this property in the future.”
Variable selection for support vector machines via smoothing spline anova (2006, background): “This fact is related to the asymptotic results in Hall and Marron (2004): when d → ∞ with n fixed, the pairwise distances between any two points are asymptotically identical to each other, so the points form an n-simplex.”
Deriving statistical significance maps for SVM based image classification and group comparisons (2012, methodology): “This equivalence between the SVM and LS-SVM for high dimensional low sample size data was also previously noted in [11] where it was based on observations about the distribution of such data as elucidated in [12].”
PCA Consistency for Non-Gaussian Data in High Dimension, Low Sample Size Context (2009, background): “The HDLSS asymptotics, where only d → while n is fixed, were studied by Hall et al. (2005) and Ahn et al. (2007).”
Model-based clustering of high-dimensional data: A review (2014, background): “Indeed, model-based clustering methods require the estimation of a number of parameters which directly depends on the dimension of the observed space.”
On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators (2018, background): “As pointed out by various authors (see, in the context of statistics and random matrix theory [8,13,20]), the Gaussian distribution has a very peculiar geometry in high-dimension.”
Outlier identification in high dimensions (2008, background): “Also, if robust estimators T and C are applied to a large data set in which the non-outliers are normally distributed, Hardin and Rocke (2005) found that the squared distances could be described by a scaled F -distribution. However, for non-normal data, it is not clear how the outlier boundary shoul”
Sure independence screening for ultrahigh dimensional feature space (2006, background): “This is exemplified by the data piling problems in high dimensional space that were observed in Hall et al. (2005). A challenge with high dimensionality is that important predictors can be highly correlated with some unimportant ones, which usually increases with dimensionality.”