Quality assessment of dimensionality reduction: Rank-based criteria

Lee, John A.; Verleysen, Michel

doi:10.1016/j.neucom.2008.12.017

Cited by 245 publications

(230 citation statements)

References 22 publications

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“…Interestingly, even slight changes of the dissimilarity such as a shift can severely influence the result of an unsupervised algorithm, as shown in [8]. Apart from generic mathematical considerations, indications for the answer to this question may be taken from attempts to formalize axioms for unsupervised learning [1,17,33,14]. Here, guidelines such as scale-invariance, rank-invariance, or information retrieval perspectives are formalized.…”

Section: How To Compare Dissimilarity Measures?mentioning

confidence: 99%

“…In the last years, a few formal mathematical evaluation measures of dimensionality reduction have been proposed in the literature. We argue that one of these measures, the co-ranking framework proposed in [14,16], is directly suitable as a highly flexible and generic tool to evaluate the preservation of pairwise relationships in different dissimilarity measures.…”

Section: The Co-ranking Frameworkmentioning

confidence: 99%

“…Analogously, the rank of r ij for the projections can be defined based on d ij . The co-ranking matrix Q [14] is defined by Q kl = |{(i, j) | ρ ij = k and r ij = l}|. Errors of a dimensionality reduction correspond to rank errors, i.e.…”

Section: The Co-ranking Frameworkmentioning

confidence: 99%

“…Usually, the focus of dimensionality reduction is on the preservation of local relationships. In [14], an intuitive measure of rank-preservation has been proposed, the Quality…”

Section: The Co-ranking Frameworkmentioning

confidence: 99%

“…all K-neighborhoods corresponds to the value Q NX (K) approaching 1. Interestingly, this framework can be linked to an information theoretic point of view as specified in [33] and it subsumes several previous evaluation criteria, see [14,20]. It is possible to extend this framework to a point-wise evaluation as introduced in [20].…”

Section: The Co-ranking Frameworkmentioning

confidence: 99%

See 4 more Smart Citations

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

Mokbel

Groß

Lux

et al. 2012

Artificial Neural Networks in Pattern Recognition

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For complex data sets, the pairwise similarity or dissimilarity of data often serves as the interface of the application scenario to the machine learning tool. Hence, the final result of training is severely influenced by the choice of the dissimilarity measure. While dissimilarity measures for supervised settings can eventually be compared by the classification error, the situation is less clear in unsupervised domains where a clear objective is lacking. The question occurs, how to compare dissimilarity measures and their influence on the final result in such cases. In this contribution, we propose to use a recent quantitative measure introduced in the context of unsupervised dimensionality reduction, to compare whether and on which scale dissimilarities coincide for an unsupervised learning task. Essentially, the measure evaluates in how far neighborhood relations are preserved if evaluated based on rankings, this way achieving a robustness of the measure against scaling of data. Apart from a global comparison, local versions allow to highlight regions of the data where two dissimilarity measures induce the same results.

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Section: How To Compare Dissimilarity Measures?mentioning

confidence: 99%

Section: The Co-ranking Frameworkmentioning

confidence: 99%

Section: The Co-ranking Frameworkmentioning

confidence: 99%

“…Usually, the focus of dimensionality reduction is on the preservation of local relationships. In [14], an intuitive measure of rank-preservation has been proposed, the Quality…”

Section: The Co-ranking Frameworkmentioning

confidence: 99%

Section: The Co-ranking Frameworkmentioning

confidence: 99%

See 3 more Smart Citations

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

Mokbel

Groß

Lux

et al. 2012

Artificial Neural Networks in Pattern Recognition

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A survey on unsupervised outlier detection in high‐dimensional numerical data

Zimek

Schubert

Kriegel

2012

Statistical Analysis

705

413

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High‐dimensional data in Euclidean space pose special challenges to data mining algorithms. These challenges are often indiscriminately subsumed under the term ‘curse of dimensionality’, more concrete aspects being the so‐called ‘distance concentration effect’, the presence of irrelevant attributes concealing relevant information, or simply efficiency issues. In about just the last few years, the task of unsupervised outlier detection has found new specialized solutions for tackling high‐dimensional data in Euclidean space. These approaches fall under mainly two categories, namely considering or not considering subspaces (subsets of attributes) for the definition of outliers. The former are specifically addressing the presence of irrelevant attributes, the latter do consider the presence of irrelevant attributes implicitly at best but are more concerned with general issues of efficiency and effectiveness. Nevertheless, both types of specialized outlier detection algorithms tackle challenges specific to high‐dimensional data. In this survey article, we discuss some important aspects of the ‘curse of dimensionality’ in detail and survey specialized algorithms for outlier detection from both categories. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012

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Data visualization by nonlinear dimensionality reduction

Gisbrecht

Hammer

2015

WIREs Data Min & Knowl

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In this overview, commonly used dimensionality reduction techniques for data visualization and their properties are reviewed. Thereby, the focus lies on an intuitive understanding of the underlying mathematical principles rather than detailed algorithmic pipelines. Important mathematical properties of the technologies are summarized in the tabular form. The behavior of representative techniques is demonstrated for three benchmarks, followed by a short discussion on how to quantitatively evaluate these mappings. In addition, three currently active research topics are addressed: how to devise dimensionality reduction techniques for complex non-vectorial data sets, how to easily shape dimensionality reduction techniques according to the users preferences, and how to device models that are suited for big data sets.Dimensionality reduction in its original form addresses the projection of high-dimensional vectors to a low-dimensional space. Often, however, data are not given in the form of vectors, but as pairwise relations between data points. Alternatively, data can possess additional structural elements such as a time dynamics, or as an underlying graph structure that can be captured by natural dissimilarity measures such as alignment.There has been quite some effort to develop dimensionality reduction techniques for structures such as graph structures or time series, see, e.g., Ref 69 for a very promising graph drawing approach developed in the context of machine learning, or the

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Quality assessment of dimensionality reduction: Rank-based criteria

Cited by 245 publications

References 22 publications

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

How to Quantitatively Compare Data Dissimilarities for Unsupervised Machine Learning?

A survey on unsupervised outlier detection in high‐dimensional numerical data

Data visualization by nonlinear dimensionality reduction

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