Sparse STATIS-Dual via Elastic Net
Abstract
:1. Introduction
2. Materials and Methods
2.1. STATIS-Dual Method
2.2. STATIS-Dual Steps
3. Sparse STATIS-Dual
Algorithm 1. Sparse STATIS-Dual. |
Step 1. Consider an array of data nxp. Step 2. A tolerance value is set (1 × 10−5). Step 3. The data are transformed (center or standardize). Step 4. Matrices of cross products are obtained.Step 5. The cosine matrix between studies is obtained. Step 6. A PCA is performed on . Step 7. The compromise matrix is obtained. Step 8. The decomposition in SVD of the compromise matrix is carried out. Step 9. We take as the charges of the first m components . Step 10. is calculated by: Step 14. The columns , are normalized. Step 15. The restricted loads are obtained to project the variables in the compromise. Step 16. The STATIS-dual Sparse obtained through the previous steps is plotted. |
4. Illustrative Example
5. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Indicator Code | Description |
---|---|
INSTITUTIONS (IN) | |
IN1 | Political and operational stability |
IN2 | Government effectiveness |
IN3 | Regulatory quality |
IN4 | Rule of law |
IN5 | Cost of redundancy dismissal, salary weeks |
IN6 | Ease of starting a business |
IN7 | Ease of resolving insolvency |
HUMAN CAPITAL & RESEARCH (HC) | |
HC1 | Expenditure on education, % GDP |
HC2 | Government funding/pupil, secondary, % GDP/cap |
HC3 | School life expectancy, years |
HC4 | PISA scales in reading, maths, & science |
HC5 | Pupil-teacher ratio, secondary |
HC6 | Tertiary enrolment, % gross |
HC7 | Graduates in science & engineering, % |
HC8 | Tertiary inbound mobility, % |
HC9 | Researchers, FTE/mn pop |
HC10 | Gross expenditure on R&D, % GDP |
HC11 | Global R&D companies, avg. exp. top 3, mn $US |
HC12 | QS university ranking, average score top 3 |
INFRASTRUCTURE (IF) | |
IF1 | ICT access |
IF2 | ICT use |
IF3 | Government’s online service |
IF4 | E-participation |
IF5 | Electricity output, kWh/mn pop |
IF6 | Logistics performance |
IF7 | Gross capital formation, % GDP |
IF8 | GDP/unit of energy use |
IF9 | Environmental performance |
IF10 | ISO 14001 environmental certificates/bn PPP$ GDP |
MARKET SOPHISTICATION (MS) | |
MS1 | Ease of getting credit |
MS2 | Domestic credit to private sector, % GDP |
MS3 | Microfinance gross loans, % GDP |
MS4 | Ease of protecting minority investors |
MS5 | Market capitalization, % GDP |
MS6 | Venture capital deals/bn PPP$ GDP |
MS7 | Applied tariff rate, weighted avg., % |
MS8 | Intensity of local competition† |
MS9 | Domestic market scale, bn PPP$ |
BUSINESS SOPHISTICATION (BS) | |
BS1 | Knowledge-intensive employment, % |
BS2 | Firms offering formal training, % |
BS3 | GERD performed by business, % GDP |
BS4 | GERD financed by business, % |
BS5 | Females employed w/advanced degrees, % |
BS6 | University/industry research collaboration |
BS7 | State of cluster development |
BS8 | GERD financed by abroad, % GDP |
BS9 | JV-strategic alliance deals/bn PPP$ GDP |
BS10 | Patent families 2+ offices/bn PPP$ GDP |
BS11 | Intellectual property payments, % total trade |
BS12 | High-tech imports, % total trade |
BS13 | ICT services imports, % total trade |
BS14 | FDI net inflows, % GDP |
BS15 | Research talent, % in business enterprise |
KNOWLEDGE & TECHNOLOGY OUTPUTS (KT) | |
KT1 | Patents by origin/bn PPP$ GDP |
KT2 | PCT patents by origin/bn PPP$ GDP |
KT3 | Utility models by origin/bn PPP$ GDP |
KT4 | Scientific & technical articles/bn PPP$ GDP |
KT5 | Citable documents H-index |
KT6 | Growth rate of PPP$ GDP/worker, % |
KT7 | New businesses/th pop. 15−64 |
KT8 | Computer software spending, % GDP |
KT9 | ISO 9001 quality certificates/bn PPP$ GDP |
KT10 | High- and medium-high-tech manufacturing |
KT11 | Intellectual property receipts, % total trade |
KT12 | High-tech net exports, % total trade |
KT13 | ICT services exports, % total trade |
KT14 | FDI net outflows, % GDP |
CREATIVE OUTPUTS (CP) | |
CP1 | Trademarks by origin/bn PPP$ GDP |
CP2 | Generic top-level domains (TLDs)/th pop. 15−69 |
CP3 | Country-code TLDs/th pop. 15−69 |
CP4 | Wikipedia edits/mn pop. 15−69 |
CP5 | Mobile app creation/bn PPP$ GDP |
CP6 | Cultural & creative services exports, % total trade |
CP7 | National feature films/mn pop. 15−69 |
CP8 | Entertainment & Media market/th pop. 15−69 |
CP9 | Printing and other media, % manufacturing |
CP10 | Creative goods exports, % total trade |
CP11 | Global brand value, top 5000, % GDP |
CP12 | Industrial designs by origin/bn PPP$ GDP |
CP13 | ICTs & organizational model creation |
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Axis | Weights |
---|---|
2016 | 0.3956 |
2017 | 0.3994 |
2018 | 0.3941 |
2019 | 0.1672 |
2020 | 0.1881 |
Indicators | STATIS-Dual | Sparse STATIS-Dual | ||||
---|---|---|---|---|---|---|
Axis 1 | Axis 2 | Axis 3 | Axis 1 | Axis 2 | Axis 3 | |
IN1 | −9.407 | −4.458 | 0.171 | −11.496 | 0.958 | 0 |
IN2 | −12.876 | −1.326 | −0.389 | −22.754 | 0 | 0 |
IN3 | −12.318 | −2.665 | −0.639 | −20.605 | 0 | 0 |
IN4 | −12.484 | −2.132 | −1.767 | −20.992 | 0 | 0 |
IN5 | −4.026 | −4.586 | −1.891 | 0 | 0 | 0 |
IN6 | −6.850 | −3.741 | 0.712 | −0.969 | 0 | 0 |
IN7 | −10.728 | −0.710 | 1.185 | −12.158 | 0 | 0 |
HC1 | −3.481 | −3.195 | −0.607 | 0 | 0 | 0 |
HC2 | −2.865 | −2.996 | −1.373 | 0 | 0 | 0 |
HC3 | −8.772 | −2.766 | 4.567 | 0 | 0 | 9.612 |
HC4 | −9.469 | 1.214 | −1.286 | −0.266 | 0 | 0 |
HC5 | −4.693 | −3.414 | 4.649 | 0 | 0 | 3.718 |
HC6 | −9.290 | −2.582 | 6.100 | −3.022 | 0 | 14.754 |
HC7 | −2.803 | 0.316 | 3.349 | 0 | 0 | 5.670 |
HC8 | −6.828 | −2.935 | −4.465 | −3.267 | 0 | −0.486 |
HC9 | −11.442 | −0.319 | −2.178 | −17.242 | 0 | 0 |
HC10 | −11.081 | 2.269 | −1.695 | −5.776 | 0 | 0 |
HC11 | −11.225 | 4.429 | −1.061 | −13.263 | −3.114 | 0 |
HC12 | −11.041 | 5.776 | 0.397 | −14.666 | −9.619 | 0 |
IF1 | −11.859 | −2.339 | 2.262 | −18.329 | 0 | 0.239 |
IF2 | −12.420 | −1.966 | 1.659 | −20.854 | 0 | 0 |
IF3 | −10.434 | 1.375 | 3.590 | −3.783 | 0 | 1.138 |
IF4 | −9.901 | 1.247 | 4.421 | 0 | 0 | 3.205 |
IF5 | −8.606 | −0.725 | −1.401 | −1.525 | 0 | 0 |
IF6 | −11.629 | 2.461 | −0.939 | −12.690 | 0 | 0 |
IF7 | 0.191 | 1.429 | 1.250 | 0 | 0 | 0 |
IF8 | −4.145 | 0.592 | −0.230 | 0 | 0 | 0 |
IF9 | −9.568 | −3.322 | 3.980 | −3.609 | 0.462 | 4.520 |
IF10 | −7.677 | −3.558 | 6.018 | 0 | 1.566 | 8.599 |
MS1 | −4.201 | −0.216 | 3.565 | 0 | 0 | 0 |
MS2 | −9.960 | 1.334 | −0.915 | −8.587 | 0 | 0 |
MS3 | 3.327 | −2.018 | 1.068 | 0 | 0 | 0 |
MS4 | −7.436 | −0.783 | 2.959 | 0 | 0 | 0.237 |
MS5 | −5.774 | 4.606 | −4.881 | 0 | −3.755 | −5.575 |
MS6 | −7.587 | −0.569 | −6.428 | −1.185 | 0 | −6.019 |
MS7 | −8.395 | −2.652 | 2.479 | −0.832 | 0 | 0 |
MS8 | −7.511 | 3.223 | 0.710 | 0 | 0 | 0 |
MS9 | −6.558 | 9.565 | 3.786 | 0 | −20.989 | 0 |
BS1 | −11.226 | −3.558 | 0.899 | −21.651 | 3.505 | 0 |
BS2 | 3.009 | −0.892 | 6.874 | 0 | 0 | 1.667 |
BS3 | −9.907 | 2.885 | −2.446 | −1.032 | 0 | −2.004 |
BS4 | −10.032 | 3.291 | 0.352 | 0 | 0 | 0 |
BS5 | −9.483 | −4.497 | 3.686 | −10.185 | 3.437 | 2.683 |
BS6 | −10.513 | 3.552 | −2.799 | −1.244 | 0 | 0 |
BS7 | −9.400 | 5.219 | −2.592 | 0 | −0.551 | 0 |
BS8 | −1.327 | −3.702 | −1.609 | 0 | 2.673 | 0 |
BS9 | −7.488 | −1.205 | −5.744 | −3.558 | 0 | −4.372 |
BS10 | −11.026 | −0.062 | −3.100 | −16.404 | 0 | −0.797 |
BS11 | −8.365 | 1.145 | −0.748 | −6.938 | 0 | 0 |
BS12 | −4.837 | 6.407 | 3.225 | 0 | −12.855 | 0 |
BS13 | −4.864 | −4.774 | −4.248 | 0 | 0 | 0 |
BS14 | −0.612 | −2.777 | −3.615 | 0 | 0 | −5.485 |
BS15 | −9.403 | 3.468 | −2.028 | 0 | 0 | −0.856 |
KT1 | −9.955 | 1.870 | 0.468 | −7.369 | 0 | 0 |
KT2 | −10.164 | 0.004 | −2.983 | −12.489 | 0 | −1.787 |
KT3 | −2.164 | 0.883 | 5.046 | 0 | 0 | 0 |
KT4 | −10.422 | −3.882 | 0.282 | −10.594 | 1.2813 | 0 |
KT5 | −11.100 | 4.453 | 0.386 | −10.928 | −4.2657 | 0 |
KT6 | −1.226 | 3.740 | −0.109 | 0 | 0 | 0 |
KT7 | −6.606 | −6.269 | −0.608 | −0.164 | 2.363 | 0 |
KT8 | −9.858 | 3.351 | −0.238 | −3.083 | −1.333 | 0 |
KT9 | −7.257 | −3.439 | 6.139 | 0 | 1.189 | 9.004 |
KT10 | −8.638 | 5.197 | 1.039 | 0 | −0.883 | 0 |
KT11 | −9.057 | 0.498 | −3.782 | −7.295 | 0 | −3.882 |
KT12 | −8.141 | 5.118 | 3.562 | 0 | −4.118 | −0.215 |
KT13 | −3.332 | −3.059 | −2.231 | 0 | 0 | 0 |
KT14 | −5.959 | −0.173 | −2.480 | −11.464 | 0 | −0.857 |
CP1 | −5.059 | −2.849 | 4.737 | 0 | 0 | 0 |
CP2 | −5.852 | 0.891 | 3.246 | 0 | 0 | 0 |
CP3 | −9.621 | 2.315 | −0.623 | 0 | 0 | 0 |
CP4 | −10.598 | 2.492 | −0.640 | 0 | 0 | 0 |
CP5 | −6.902 | −3.051 | −0.116 | 0 | 2.161 | 0 |
CP6 | −6.999 | −6.115 | −1.789 | −0.657 | 7.923 | 0 |
CP7 | −9.002 | 1.380 | −5.604 | −10.456 | 0 | −1.136 |
CP8 | −2.694 | −4.406 | −1.410 | 0 | 2.859 | 0 |
CP9 | −7.449 | 5.332 | 5.023 | 0 | −5.683 | 0 |
CP10 | −10.576 | −2.898 | −3.105 | −20.054 | 0 | 0 |
CP11 | −10.249 | −3.175 | −0.456 | −19.742 | 0 | 0 |
CP12 | −10.576 | −4.470 | 0.979 | −13.762 | 6.030 | 0 |
CP13 | −9.352 | −0.128 | −1.566 | −1.162 | 0 | 0 |
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Rodríguez-Martínez, C.C.; Cubilla-Montilla, M.; Vicente-Galindo, P.; Galindo-Villardón, P. Sparse STATIS-Dual via Elastic Net. Mathematics 2021, 9, 2094. https://doi.org/10.3390/math9172094
Rodríguez-Martínez CC, Cubilla-Montilla M, Vicente-Galindo P, Galindo-Villardón P. Sparse STATIS-Dual via Elastic Net. Mathematics. 2021; 9(17):2094. https://doi.org/10.3390/math9172094
Chicago/Turabian StyleRodríguez-Martínez, Carmen C., Mitzi Cubilla-Montilla, Purificación Vicente-Galindo, and Purificación Galindo-Villardón. 2021. "Sparse STATIS-Dual via Elastic Net" Mathematics 9, no. 17: 2094. https://doi.org/10.3390/math9172094
APA StyleRodríguez-Martínez, C. C., Cubilla-Montilla, M., Vicente-Galindo, P., & Galindo-Villardón, P. (2021). Sparse STATIS-Dual via Elastic Net. Mathematics, 9(17), 2094. https://doi.org/10.3390/math9172094