Scale Invariant Correspondence Analysis
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909850921861120 |
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| author | Choulakian, Vartan |
| author_facet | Choulakian, Vartan |
| contents | Correspondence analysis is a dimension reduction method for visualization of nonnegative data sets, in particular contingency tables ; but it depends on the marginals of the data set. Two transformations of the data have been proposed to render correspondence analysis row and column scales invariant : These two kinds of transformations change the initial form of the data set into a bistochastic form. The power transorfmation applied by Greenacre (2010) has one positive parameter. While the transormation applied by Mosteller (1968) and Goodman (1996) has (I+J) positive parameters, where the raw data is row and column scaled by the Sinkhorn (RAS or ipf) algorithm to render it bistochastic. Goodman (1996) named correspondence analsis of a bistochastic matrix marginal-free correspondence analysis. We discuss these two transformations, and further generalize Mosteller-Goodman approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17594 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scale Invariant Correspondence Analysis Choulakian, Vartan Methodology 62H25, 62H30 Correspondence analysis is a dimension reduction method for visualization of nonnegative data sets, in particular contingency tables ; but it depends on the marginals of the data set. Two transformations of the data have been proposed to render correspondence analysis row and column scales invariant : These two kinds of transformations change the initial form of the data set into a bistochastic form. The power transorfmation applied by Greenacre (2010) has one positive parameter. While the transormation applied by Mosteller (1968) and Goodman (1996) has (I+J) positive parameters, where the raw data is row and column scaled by the Sinkhorn (RAS or ipf) algorithm to render it bistochastic. Goodman (1996) named correspondence analsis of a bistochastic matrix marginal-free correspondence analysis. We discuss these two transformations, and further generalize Mosteller-Goodman approach. |
| title | Scale Invariant Correspondence Analysis |
| topic | Methodology 62H25, 62H30 |
| url | https://arxiv.org/abs/2311.17594 |