Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

Ma, Zhiliang; Cardinal-Stakenas, Adam James; Park, Youngser; Trosset, Michael W.; Priebe, Carey E.

doi:10.1007/s00357-010-9059-3

Cited by 6 publications

(7 citation statements)

References 25 publications

(19 reference statements)

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“…PCA rotates the data into orthogonal principal components while maintaining the information content. Because principal components are independent of each other, some prefer to use them instead of the raw data in multivariate statistical analyses [21]. The first PCA axis (PC1) represents size, unless size has been removed from the data before analysis.…”

Section: (B) Sex Identificationmentioning

confidence: 99%

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

et al. 2015

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The evolutionary history of sexual selection in the geologic past is poorly documented based on quantification, largely because of difficulty in sexing fossil specimens. Even such essential ecological parameters as adult sex ratio (ASR) and sexual size dimorphism (SSD) are rarely quantified, despite their implications for sexual selection. To enable their estimation, we propose a method for unbiased sex identification based on sexual shape dimorphism, using size-independent principal components of phenotypic data. We applied the method to test sexual selection in Keichousaurus hui, a Middle Triassic (about 237 Ma) sauropterygian with an unusually large sample size for a fossil reptile. Keichousaurus hui exhibited SSD biased towards males, as in the majority of extant reptiles, to a minor degree (sexual dimorphism index 20.087). The ASR is about 60% females, suggesting higher mortality of males over females. Both values support sexual selection of males in this species. The method may be applied to other fossil species. We also used the Gompertz allometric equation to study the sexual shape dimorphism of K. hui and found that two sexes had largely homogeneous phenotypes at birth except in the humeral width, contrary to previous suggestions derived from the standard allometric equation.

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Section: (B) Sex Identificationmentioning

confidence: 99%

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

et al. 2015

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“…Ideally both sources of data contain complementary information so that their fusion leads to larger power in testing and higher accuracy in classification than using either textual content data or graph structure data alone. We achieve the fusion by combining the embeddings obtained in the P-or W-approach via the Cartesian product [6].…”

Section: Fusionmentioning

confidence: 99%

“…In feature level fusion, feature vectors extracted from different data sources are combined into the Cartesian product space, directly [6] or via some data transformation procedures [3]. Decision level fusion involves combining results obtained separately from all data sources.…”

Section: Introductionmentioning

confidence: 99%

Fusion and inference from multiple data sources in a commensurate space

Marchette

Priebe

2012

Statistical Analysis

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Given objects measured under multiple conditions-for example, indoor lighting versus outdoor lighting for face recognition, multiple language translation for document matching, etc.-the challenging task is to perform data fusion and utilize all the available information for inferential purposes. We consider two exploitation tasks: (i) how to determine whether a set of feature vectors represent a single object measured under different conditions; and (ii) how to create a classifier based on training data from one condition in order to classify objects measured under other conditions. The key to both problems is to transform data from multiple conditions into one commensurate space, where the (transformed) feature vectors are comparable and would be treated as if they were collected under the same condition. Toward this end, we studied Procrustes analysis and developed a new approach, which uses the interpoint dissimilarities for each condition. We impute the dissimilarities between measurements of different conditions to create one omnibus dissimilarity matrix, which is then embedded into Euclidean space. We illustrate our methodology on English and French documents collected from Wikipedia, demonstrating superior performance compared to that obtained via standard Procrustes transformation. 

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“…Combining information from disparate data sources when the information in the various spaces is fundamentally incommensurate -that is, a separate collection of useful features can be extracted from each space but their interpoint geometry precludes profitable alignment in a common space -is considered via Cartesian product space embedding in [12].…”

Section: Related Workmentioning

confidence: 99%

Manifold Matching: Joint Optimization of Fidelity and Commensurability

Priebe

Marchette²,

Ma³

et al. 2011

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Fusion and inference from multiple and massive disparate data sources -the requirement for our most challenging data analysis problems and the goal of our most ambitious statistical pattern recognition methodologies -has many and varied aspects which are currently the target of intense research and development. One aspect of the overall challenge is manifold matching -identifying embeddings of multiple disparate data spaces into the same low-dimensional space where joint inference can be pursued. We investigate this manifold matching task from the perspective of jointly optimizing the fidelity of the embeddings and their commensurability with one another, with a specific statistical inference exploitation task in mind. Our results demonstrate when and why our joint optimization methodology is superior to either version of separate optimization. The methodology is illustrated with simulations and an application in document matching.

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Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

Cited by 6 publications

References 25 publications

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

Fusion and inference from multiple data sources in a commensurate space

Manifold Matching: Joint Optimization of Fidelity and Commensurability

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