Pooled variable scaling for cluster analysis

Raymaekers, Jakob; Zamar, Ruben H.

doi:10.1093/bioinformatics/btaa243

Cited by 11 publications

(20 citation statements)

References 25 publications

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“…Table 2 also confirms what has been known since the recent introduction of scaling by 1/σ pool k , which is that proceeding in this way, once again in the case of Iris, leads to superior performance. The table goes farther than this, however, since it also makes clear that the fallback role of σ k as a surrogate for σ pool k in the approach of [5] may be taken more frequently than initially realized. This is shown in the table for all but the Iris data set.…”

Section: Discussionmentioning

confidence: 97%

Shape complexity in cluster analysis

Aguilar¹,

Barbosa²

2022

Preprint

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In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the workhorse in this preprocessing phase has been to divide the data by the standard deviation along each dimension. Like division by the standard deviation, the great majority of scaling techniques can be said to have roots in some sort of statistical take on the data. Here we explore the use of multidimensional shapes of data, aiming to obtain scaling factors for use prior to clustering by some method, like k-means, that makes explicit use of distances between samples. We borrow from the field of cosmology and related areas the recently introduced notion of shape complexity, which in the variant we use is a relatively simple, data-dependent nonlinear function that we show can be used to help with the determination of appropriate scaling factors. Focusing on what might be called "midrange" distances, we formulate a constrained nonlinear programming problem and use it to produce candidate scalingfactor sets that can be sifted on the basis of further considerations of the data, say via expert knowledge. We give results on some iconic data sets, highlighting the strengths and potential weaknesses of the new approach. These results are generally positive across all the data sets used.

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Section: Discussionmentioning

confidence: 97%

Shape complexity in cluster analysis

Aguilar¹,

Barbosa²

2022

Preprint

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“…Partitioning based clustering was mainly implemented as k-means clustering [ 14 ]; however, partitioning around medoids (PAM) was used for comparison [ 18 ]. Hierarchical clustering with Ward's linkage [ 19 ] was used; however, average and complete linkage were used for comparison in analogy to the choice made in [ 6 ]. The Euclidean distance was used as the target of the transformation method presented here.…”

Section: Methodsmentioning

confidence: 99%

“…A particular problem with Euclidean distance is that it is not scale invariant, i.e., multiplying the data by a common factor changes the distance. Recognizing this potential pitfall in clustering approaches, adapted scaling methods have been proposed that take into account the scale dependence of the Euclidean distance, such as pooled variable scaling (PVS) [ 6 ]. In this report, an alternative to the standard z-transform of biomedical data is proposed as a more appropriate approach for clustering biomedical data.…”

Section: Introductionmentioning

confidence: 99%

“…In this report, an alternative to the standard z-transform of biomedical data is proposed as a more appropriate approach for clustering biomedical data. The "Euclidean Distance Optimized" (EDO) data transformation addresses the scale dependence of Euclidean distance, but treats each variable separately and therefore does not introduce clustering at the transformation level as alternative approaches do [ 6 ]. It specifically takes into account that the squaring function in the definition of Euclidean distance results a breakpoint for distances within (inner)clusters versus distances between (inter)clusters at a value of 1.…”

Section: Introductionmentioning

confidence: 99%

“…It specifically takes into account that the squaring function in the definition of Euclidean distance results a breakpoint for distances within (inner)clusters versus distances between (inter)clusters at a value of 1. Thus, while in [ 6 ] the goal is to make the scales of different variables comparable, the present approach aims at minimizing differences within classes and maximizing differences between classes. It is therefore more focused on finding clusters in the data.…”

Section: Introductionmentioning

confidence: 99%

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Euclidean distance-optimized data transformation for cluster analysis in biomedical data (EDOtrans)

Ultsch

Lötsch

2022

BMC Bioinformatics

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Background Data transformations are commonly used in bioinformatics data processing in the context of data projection and clustering. The most used Euclidean metric is not scale invariant and therefore occasionally inappropriate for complex, e.g., multimodal distributed variables and may negatively affect the results of cluster analysis. Specifically, the squaring function in the definition of the Euclidean distance as the square root of the sum of squared differences between data points has the consequence that the value 1 implicitly defines a limit for distances within clusters versus distances between (inter-) clusters. Methods The Euclidean distances within a standard normal distribution (N(0,1)) follow a N(0,$$\sqrt{2}$$ 2 ) distribution. The EDO-transformation of a variable X is proposed as $$EDO= X/(\sqrt{2}\cdot s)$$ E D O = X / ( 2 · s ) following modeling of the standard deviation s by a mixture of Gaussians and selecting the dominant modes via item categorization. The method was compared in artificial and biomedical datasets with clustering of untransformed data, z-transformed data, and the recently proposed pooled variable scaling. Results A simulation study and applications to known real data examples showed that the proposed EDO scaling method is generally useful. The clustering results in terms of cluster accuracy, adjusted Rand index and Dunn’s index outperformed the classical alternatives. Finally, the EDO transformation was applied to cluster a high-dimensional genomic dataset consisting of gene expression data for multiple samples of breast cancer tissues, and the proposed approach gave better results than classical methods and was compared with pooled variable scaling. Conclusions For multivariate procedures of data analysis, it is proposed to use the EDO transformation as a better alternative to the established z-standardization, especially for nontrivially distributed data. The “EDOtrans” R package is available at https://cran.r-project.org/package=EDOtrans.

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Comparative assessment of projection and clustering method combinations in the analysis of biomedical data

Lötsch,

Ultsch

2024

Informatics in Medicine Unlocked

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Pooled variable scaling for cluster analysis

Cited by 11 publications

References 25 publications

Shape complexity in cluster analysis

Shape complexity in cluster analysis

Euclidean distance-optimized data transformation for cluster analysis in biomedical data (EDOtrans)

Comparative assessment of projection and clustering method combinations in the analysis of biomedical data

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