Statistical Depth for Text Data: An Application to the Classification of Healthcare Data
This manuscript introduces a new concept of statistical depth function: the compositional <i>D</i>-depth. It is the first data depth developed exclusively for text data, in particular, for those data vectorized according to a frequency-based criterion, such as the <i>tf-idf</i&g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/228 |
| _version_ | 1797440434324111360 |
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| author | Sergio Bolívar Alicia Nieto-Reyes Heather L. Rogers |
| author_facet | Sergio Bolívar Alicia Nieto-Reyes Heather L. Rogers |
| author_sort | Sergio Bolívar |
| collection | DOAJ |
| description | This manuscript introduces a new concept of statistical depth function: the compositional <i>D</i>-depth. It is the first data depth developed exclusively for text data, in particular, for those data vectorized according to a frequency-based criterion, such as the <i>tf-idf</i> (term frequency–inverse document frequency) statistic, which results in most vector entries taking a value of zero. The proposed data depth consists of considering the inverse discrete Fourier transform of the vectorized text fragments and then applying a statistical depth for functional data, <i>D</i>. This depth is intended to address the problem of sparsity of numerical features resulting from the transformation of qualitative text data into quantitative data, which is a common procedure in most natural language processing frameworks. Indeed, this sparsity hinders the use of traditional statistical depths and machine learning techniques for classification purposes. In order to demonstrate the potential value of this new proposal, it is applied to a real-world case study which involves mapping Consolidated Framework for Implementation and Research (CFIR) constructs to qualitative healthcare data. It is shown that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><msup><mi>D</mi><mi>G</mi></msup></mrow></semantics></math></inline-formula>-classifier yields competitive results and outperforms all studied traditional machine learning techniques (logistic regression with LASSO regularization, artificial neural networks, decision trees, and support vector machines) when used in combination with the newly defined compositional <i>D</i>-depth. |
| first_indexed | 2024-03-09T12:08:06Z |
| format | Article |
| id | doaj.art-db5370ce129c4662bf50941419a5a280 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T12:08:06Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-db5370ce129c4662bf50941419a5a2802023-11-30T22:55:45ZengMDPI AGMathematics2227-73902023-01-0111122810.3390/math11010228Statistical Depth for Text Data: An Application to the Classification of Healthcare DataSergio Bolívar0Alicia Nieto-Reyes1Heather L. Rogers2Department of Mathematics, Statistics and Computer Science, Universidad de Cantabria, 39005 Santander, SpainDepartment of Mathematics, Statistics and Computer Science, Universidad de Cantabria, 39005 Santander, SpainBiocruces Bizkaia Health Research Institute, 48903 Barakaldo, SpainThis manuscript introduces a new concept of statistical depth function: the compositional <i>D</i>-depth. It is the first data depth developed exclusively for text data, in particular, for those data vectorized according to a frequency-based criterion, such as the <i>tf-idf</i> (term frequency–inverse document frequency) statistic, which results in most vector entries taking a value of zero. The proposed data depth consists of considering the inverse discrete Fourier transform of the vectorized text fragments and then applying a statistical depth for functional data, <i>D</i>. This depth is intended to address the problem of sparsity of numerical features resulting from the transformation of qualitative text data into quantitative data, which is a common procedure in most natural language processing frameworks. Indeed, this sparsity hinders the use of traditional statistical depths and machine learning techniques for classification purposes. In order to demonstrate the potential value of this new proposal, it is applied to a real-world case study which involves mapping Consolidated Framework for Implementation and Research (CFIR) constructs to qualitative healthcare data. It is shown that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><msup><mi>D</mi><mi>G</mi></msup></mrow></semantics></math></inline-formula>-classifier yields competitive results and outperforms all studied traditional machine learning techniques (logistic regression with LASSO regularization, artificial neural networks, decision trees, and support vector machines) when used in combination with the newly defined compositional <i>D</i>-depth.https://www.mdpi.com/2227-7390/11/1/228compositional depthmultivariate datanatural language processingqualitative datastatistical depthsupervised classification |
| spellingShingle | Sergio Bolívar Alicia Nieto-Reyes Heather L. Rogers Statistical Depth for Text Data: An Application to the Classification of Healthcare Data Mathematics compositional depth multivariate data natural language processing qualitative data statistical depth supervised classification |
| title | Statistical Depth for Text Data: An Application to the Classification of Healthcare Data |
| title_full | Statistical Depth for Text Data: An Application to the Classification of Healthcare Data |
| title_fullStr | Statistical Depth for Text Data: An Application to the Classification of Healthcare Data |
| title_full_unstemmed | Statistical Depth for Text Data: An Application to the Classification of Healthcare Data |
| title_short | Statistical Depth for Text Data: An Application to the Classification of Healthcare Data |
| title_sort | statistical depth for text data an application to the classification of healthcare data |
| topic | compositional depth multivariate data natural language processing qualitative data statistical depth supervised classification |
| url | https://www.mdpi.com/2227-7390/11/1/228 |
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