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Variable-Weighted Ultrametric Optimization for Mixed-Type Data (VWUO-MD)
Data mining software for hypothesis generation
Scientific research begins with hypothesis generation, for which cluster analysis (CA) can be used. Traditionally, CA involves continuous variables weighted equally, and the subjective choice of linkage and stopping rules. Variable weighting for cluster analysis (VWCA), beginning with De Soete (1985/6), produces weights that may be useful for hypothesis generation. De Soete’s VWCA optimized ultrametricity, a property of better separated clusters, without requiring CA.
We developed variable-weighted ultrametric optimization for mixed-type data (VWUO-MD), starting with a variable-weighted, multivariate distance for data with any number of continuous, ordinal, nominal, binary symmetric and binary asymmetric (e.g., rare disease) variables. In Monte Carlo simulations we found that weights are consistent with a priori relationships between variables, under several distributions. On some relationships (e.g., single group linear), the method performs poorly. Compared to De Soete, VWUO-MD better penalizes for 0-weights, and better ensures a unique solution with a strategic random restart procedure. The bootstrap covariance matrix is slightly conservative. For mixtures of at least four continuous/nominal variables, a U-statistic-based covariance matrix performs well. Point estimates and covariances are invariant to column/category/record order and affine transformations.
We analyzed a subset of the Joint Canada/United States Survey of Health: working, mature students 50+ years old who received health services in the past year (n=167), split into training and testing segments. Prescreening within types and backwards elimination with VWUO-MD reduced the space. The final 14 variable weights were plotted as a scree plot. On the testing segment, a model was fit from the upper scree plot variables. Similar models were fit from the lower scree plot, prescreening and backwards elimination reject variables. Models were ordered on overall statistical significance and the upper model had the best fit, indicating that VWUO-MD had successfully mined these data for hypotheses. We learned that reduction in activities due to a long term health condition was associated with consultations with a mental health professional in the past year (odds ratio=12.25, 95% CI=1.67, 90.02). While needing additional research, in its present form VWUO-MD produces variable weights that may be informative for hypothesis generation on data with varied mixtures of data types.
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data mining software, hypothesis generation, hypothesis generator, expert systems knowledge acquisition, ultrametric optimization, cluster analysis
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The VWUO.exe software was developed for Windows in C++. The program comes with a VWUO.ini file containing all the default options described in the user's guide with one exception: I provide the non-default normalizing multipliers obtained in the thesis (which you are free to change). The software also includes a short list of keys and command line parameters not all listed in the user's guide.
The PhD thesis provides relevant background and mathematical formulas. The self-contained, illustrated user's guide (approximately 40 pages) is Chapter 3. It contains screenshots, example data sets, commands, as well as walking you through sample analyses. Chapter 6 shows an application of successfully mining a real dataset for hypotheses using VWUO-MD. The thesis can be downloaded free of charge (with a limited license as explained in the PDF) from Simon Fraser University Library's Institutional Repository. (Full text and abstract: https://summit.sfu.ca/item/9744)
The following License Agreements apply to the VWUO-MD software:
Software Performance Limitations
Before purchasing this software, it is STRONGLY RECOMMENDED that you download and try the free trial version of VWUO-MD (VWUO.exe) software. The ultrametric optimization algorithm used is approximately order n-cubed, and is also dependent on the number of input variables. As such, adding a small number of variables and/or data records may dramatically increase the run time of this software. For example, 5 times the data records might translate into 125 times the run time. If the data get too large, the software may not run at all due in part to memory limitations. These numbers are ballpark figures only; no guarantees of any kind about run time should be construed by this paragraph. You may review the analyses I performed in my PhD thesis to get an approximate idea of realistic input sizes on a high performance machine, before purchasing the full, unlocked version. I also discuss the issue in Chapter 7 of the thesis, suggesting some approaches that may allow for analysis of bigger data sets (e.g., "bagging"). Refer to the thesis for more details.
End User Software License Agreement ("Agreement")
This license agreement governs VWUO-MD (VWUO.exe) (tm) ("Software"). By downloading and/or running this software, you enter into the terms of this binding contract between you ("you" or "User") and Eric C. Sayre, PhD. If you do not agree with the terms of this license, do not download or run VWUO-MD (VWUO.exe). Installation of the Software constitutes acceptance of the terms of this License Agreement.
Grant of License: Subject to the terms and conditions of this Agreement, Eric C. Sayre hereby grants you a limited, nonexclusive license to install and use the object code version of the Software, a copy of which is provided herewith, on a single personal computer.
Limitations: The Software is licensed, not sold, to you. You must retain all copyright and related notices of Eric C. Sayre's ownership and other rights in the Software in the product, labeling and documentation provided. Furthermore, you may not: (a) modify, translate, de-compile, reverse engineer, disassemble or otherwise decode the Software; (b) copy any of the Software other than as reasonably required for your own personal use of the Software in accordance with this Agreement; or (c) sublicense, sell, rent, lend, transfer, post, transmit, distribute or otherwise make the Software available to anyone else, except that you may permanently transfer the Software and accompanying materials provided you retain no copies and the recipient agrees to the terms of this Agreement.
Trademarks: You acknowledge that Eric C. Sayre, VWUO-MD (VWUO.exe) (tm) and related logos and designs are trademarks of Eric C. Sayre, PhD and that no rights in such trademarks are granted to you by this Agreement.
Support: Eric C. Sayre reserves the right to modify the Software from time to time without obligation to notify you, or any other person or organization of such revision or change. Eric C. Sayre explicitly states that no technical support for this Software should be expected from him in any form. Eric C. Sayre's PhD thesis contains a user's guide for this Software. However, Eric C. Sayre does not guarantee that Simon Fraser University will continue to supply the PDF of the thesis free of charge or at all, nor does he attest to the completeness, accuracy or relevance of the user's guide for your particular purposes.
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