16,495 research outputs found

    Validation of archetypal analysis

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    We use an information-theoretic criterion to assess the goodness-of-fit of the output of archetypal analysis (AA), also intended as a fuzzy clustering tool. It is an adaptation of an existing AIC-like measure to the specifics of AA. We test its effectiveness using artificial data and some data sets arising from real life problems. In most cases, the results achieved are similar to those provided by an external similarity index. The average reconstruction accuracy is about 93%.info:eu-repo/semantics/acceptedVersio

    Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data

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    We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do not coincide with common ridge penalties. Subsequently, starting from a common ridge penalty, analytic expressions are derived for two alternative ridge estimators of the precision matrix. The alternative estimators are compared to the archetypes with regard to eigenvalue shrinkage and risk. The alternatives are also compared to the graphical lasso within the context of graphical modeling. The comparisons may give reason to prefer the proposed alternative estimators

    An Artificial Intelligence Approach to Detect Visual Field Progression in Glaucoma Based on Spatial Pattern Analysis.

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    Purpose: To detect visual field (VF) progression by analyzing spatial pattern changes. Methods: We selected 12,217 eyes from 7360 patients with at least five reliable 24-2 VFs and 5 years of follow-up with an interval of at least 6 months. VFs were decomposed into 16 archetype patterns previously derived by artificial intelligence techniques. Linear regressions were applied to the 16 archetype weights of VF series over time. We defined progression as the decrease rate of the normal archetype or any increase rate of the 15 VF defect archetypes to be outside normal limits. The archetype method was compared with mean deviation (MD) slope, Advanced Glaucoma Intervention Study (AGIS) scoring, Collaborative Initial Glaucoma Treatment Study (CIGTS) scoring, and the permutation of pointwise linear regression (PoPLR), and was validated by a subset of VFs assessed by three glaucoma specialists. Results: In the method development cohort of 11,817 eyes, the archetype method agreed more with MD slope (kappa: 0.37) and PoPLR (0.33) than AGIS (0.12) and CIGTS (0.22). The most frequently progressed patterns included decreased normal pattern (63.7%), and increased nasal steps (16.4%), altitudinal loss (15.9%), superior-peripheral defect (12.1%), paracentral/central defects (10.5%), and near total loss (10.4%). In the clinical validation cohort of 397 eyes with 27.5% of confirmed progression, the agreement (kappa) and accuracy (mean of hit rate and correct rejection rate) of the archetype method (0.51 and 0.77) significantly (P \u3c 0.001 for all) outperformed AGIS (0.06 and 0.52), CIGTS (0.24 and 0.59), MD slope (0.21 and 0.59), and PoPLR (0.26 and 0.60). Conclusions: The archetype method can inform clinicians of VF progression patterns

    Probabilistic Archetypal Analysis

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    Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be real valued. This, unfortunately, is not compatible with many practical situations. In this paper we revisit archetypal analysis from the basic principles, and propose a probabilistic framework that accommodates other observation types such as integers, binary, and probability vectors. We corroborate the proposed methodology with convincing real-world applications on finding archetypal winter tourists based on binary survey data, archetypal disaster-affected countries based on disaster count data, and document archetypes based on term-frequency data. We also present an appropriate visualization tool to summarize archetypal analysis solution better.Comment: 24 pages; added literature review and visualizatio
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