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Estimation of Body Fat Percentage Using Support Vector Machine and Random Forest Methods

Year 2021, Volume: 9 Issue: 3 - Additional Issue, 430 - 445, 29.05.2021
https://doi.org/10.29130/dubited.815454

Abstract

Obesity is a significant health problem, and its prevalence is increasing. It is known that this disease is the trigger and precursor of many other diseases. Before the treatment of obesity disease, it is important to determine the body fat percentage correctly. Body fat percentage can be measured precisely with high-cost methods. However, these methods are not common to use. In this study, support vector regression and random forest tree regression methods were applied to accurately and cost-effectively estimate body fat percentage with anthropometric data set taken from individuals. In regression methods, model parameter values, number of data, number of features and feature selection are important in prediction performance. In the study based on a 13-featured body fat percentage data set, a new data set was created with 25 statistical methods (skewness, central moment, kurtosis, etc.) frequently used in the literature, and it was observed that the performance of the new data set was higher than other studies in the literature. Estimation accuracy has been increased by determining the regression parameters with grid scanning methods. In addition, features that are highly correlated with body fat percentage were determined with feature reduction methods. It was observed that the prediction success performance of the regression methods performed with the selected features was higher than other similar studies. As the best mean square error values, the value of 2.2519 was obtained in the experiment performed with the Random Forest Trees Method and the new data set created by the statistical method, while the value of 3.174 was reached in the regression experiment with Decision Support Machines and the properties with the best 6 f-score values.

References

  • [1] F. McLellan, "Obesity rising to alarming levels around the world," The Lancet, c. 359, s. 9315, ss. 1412, 2002.
  • [2] C. L. Edelman, C. L. Mandle ve E. C. Kudzma, Health Promotion Throughout the Life Span-E-Book, 9. baskı, Missouri, United States of America: Elsevier Health Sciences, 2017, böl. 2, ss. 23-24.
  • [3] I. G. Polat, "Effect of Er stress and Sik2 Reciprocal relationship on human precursor fat cell (LiSa-2) differentiation," Doktora Tezi, Gebze Teknik Üniversitesi, Kocaeli, Türkiye, 2017.
  • [4] F. Ortega, C. Lavie ve S. Blair, "Obesity and cardiovascular disease," Circulation Research, c. 118, s. 11, ss. 1752-1770, 2016.
  • [5] C. Lavie, A. Schutter, P. Parto, E. Jahangir, P. Kokkinos, F. Ortega, R. Arena ve R. Milani, "Obesity and prevalence of cardiovascular diseases and prognosis—the obesity paradox updated," Progress in Cardiovascular Diseases, c. 58, s. 5, ss. 537-547, 2016.
  • [6] A. Keys, F. Fidanza, M. Karvonen, N. Kimura ve H. Taylor, "Indices of relative weight and obesity," Journal of Chronic Diseases, c. 25, s. 6-7, ss. 329-343, 1972.
  • [7] R. Huxley, S. Mendis, E. Zheleznyakov, S. Reddy ve J. Chan, "Body mass index, waist circumference and waist:hip ratio as predictors of cardiovascular risk," Obesity and Metabolism, c. 8, s. 1, ss. 69-69, 2011.
  • [8] C. Lee, R. Huxley, R. Wildman ve M. Woodward, "Indices of abdominal obesity are better discriminators of cardiovascular risk factors than BMI: A meta-analysis," Journal of Clinical Epidemiology, c. 61, s. 7, ss. 646-653, 2008.
  • [9] B. Srdić, B. Obradović, G. Dimitrić, E. Stokić ve S. Babović, "Relationship between body mass index and body fat in children—age and gender differences," Obesity Research & Clinical Practice, c. 6, s. 2, ss. 167-173, 2012.
  • [10] A. Kupusinac, E. Stokić ve R. Doroslovački, "Predicting body fat percentage based on gender, age and BMI by using artificial neural networks," Computer Methods and Programs in Biomedicine, c. 113, s. 2, ss. 610-619, 2014.
  • [11] P. Deurenberg ve M. Yap, "The Assessment of Obesity: Methods for measuring body fat and global prevalence of obesity," Best Practice & Research Clinical Endocrinology & Metabolism, c. 13, s. 1, ss. 1-11, 1999.
  • [12] N. Jensky-Squires, C. Dieli-Conwright, A. Rossuello, D. Erceg, S. McCauley ve E. Schroeder, "Validity and reliability of body composition analysers in children and adults," British Journal of Nutrition, c. 100, s. 4, ss. 859-865, 2008.
  • [13] W. Beeson, M. Batech, E. Schultz, L. Salto, A. Firek, M. Deleon, H. Balcazar ve Z. Cordero-Macintyre, "Comparison of body composition by bioelectrical ımpedance analysis and dual-energy X-ray absorptiometry in hispanic diabetics," International Journal of Body Composition Research, c. 8, s. 2, ss. 45-50, 2010.
  • [14] A. M. Bongiolo, K. Castro ve M. A. da Silva. "Bioelectrical ımpedance analysis: body composition in children and adolescents with Down Syndrome," Minerva Pediatrica, c. 69, s. 6, ss. 560-563, 2017.
  • [15] D. Anblagan, R. Deshpande, N. Jones, C. Costigan, G. Bugg, N. Raine-Fenning, P. Gowland ve P. Mansell, "Measurement of fetal fatin uteroin normal and diabetic pregnancies using magnetic resonance ımaging," Ultrasound in Obstetrics & Gynecology, c. 42, s. 3, ss. 335-340, 2013.
  • [16] J. Josefson, M. Nodzenski, O. Talbot, D. Scholtens ve P. Catalano, "Fat mass estimation in neonates: anthropometric models compared with air displacement plethysmography," British Journal of Nutrition, c. 121, s. 3, ss. 285-290, 2019.
  • [17] D. Fukuda, M. Wray, K. Kendall, A. Smith-Ryan ve J. Stout, "Validity of near-ınfrared ınteractance (FUTREX 6100/XL) for estimating body fat percentage in elite rowers," Clinical Physiology and Functional Imaging, c. 37, s. 4, ss. 456-458, 2017.
  • [18] A. Fernández-Sánchez, E. Madrigal-Santillán, M. Bautista, J. Esquivel-Soto, Á. Morales-González, C. Esquivel-Chirino, I. Durante-Montiel, G. Sánchez-Rivera, C. Valadez-Vega ve J. A. Morales-González, "Inflammation, oxidative stress, and obesity," International Journal of Molecular Sciences, c. 12, s. 5, ss. 3117-3132, 2011.
  • [19] T. Ferenci, "Two Applications Of Biostatistics in The Analysis of Pathophysiological Processes," Doktora Tezi, Óbuda Univeristy, Budapest, Hungary, 2013.
  • [20] T. Ferenci ve L. Kovács, "Predicting body fat percentage from anthropometric and laboratory measurements using artificial neural networks," Applied Soft Computing, c. 67, ss. 834-839, 2018.
  • [21] S. Balasundaram, "On lagrangian support vector regression," Expert Systems with Applications, c. 37, s. 12, ss. 8784-8792, 2010.
  • [22] Y. Xu ve L. Wang, "A weighted twin support vector regression," Knowledge-Based Systems, c. 33, ss. 92-101, 2012.
  • [23] R. Chiong, Z. Fan, Z. Hu ve F. Chiong, "Using an improved relative error support vector machine for body fat prediction," Computer Methods and Programs in Biomedicine, c. 198, ss. 105749, 2020.
  • [24] P. Deurenberg, M. Yap ve W. van Staveren, "Body mass index and percent body fat: a meta analysis among different ethnic groups," International Journal of Obesity, c. 22, s. 12, ss. 1164-1171, 1998.
  • [25] A. Jackson P. Stanforth, J. Gagnon, T. Rankinen, A. Leon, D. Rao, J. Skinner, C. Bouchard ve J. Wilmore, "The Effect of sex, age and race on estimating percentage body fat from body mass index: the heritage family study," International Journal of Obesity, c. 26, s. 6, ss. 789-796, 2002.
  • [26] Y. Shao, "Body fat percentage prediction using ıntelligent hybrid approaches," The Scientific World Journal, c. 2014, ss. 1-8, 2014.
  • [27] M. Uçar, Z. Uçar, F. Köksal ve N. Daldal, "Estimation of body fat percentage using hybrid machine learning algorithms," Measurement, c. 167, ss. 108173, 2020.
  • [28] K. DeGregory, P. Kuiper, T. DeSilvio, J. D. Pleuss, R. Miller, J. W. Roginski, C. B. Fisher, D. Harness, S. Viswanath, S. B. Heymsfield, I. Dungan ve D. M. Thomas, "A review of machine learning in obesity," Obesity Reviews, c. 19, s. 5, ss. 668-685, 2018.
  • [29] M. Akman, M. K. Uçar, Z. Uçar, K. Uçar, B. Baraklı ve M. R. Bozkurt, “Determination of body fat percentage by gender based with photoplethysmography signal using machine learning algorithm,” Innovation and Research in BioMedical Engineering, Basımda.
  • [30] C. Cortes ve V. Vapnik, "Support-vector networks," Machine learning, c. 20, s. 3, ss. 273-297. 1995.
  • [31] T. K. Ho, "Random decision forests", In: Proceedings of 3rd İnternational Conference on Document Analysis and Recognition. IEEE, Montreal, QC, Canada, 1995, ss. 278-282.
  • [32] R. Johnson, "Fitting percentage of body fat to simple body measurements," Journal of Statistics Education, c. 4, s. 1, 1996.
  • [33] W. E. Siri, "body composition from fluid spaces and density: analysis of methods," University of Michigan Library, ss. 1-33, 1956.
  • [34] X. Yan ve S. Xiaogang, "Linear regression analysis: theory and computing," World Scientific, ss. 1-2, 2009.
  • [35] H. B. Curry, “The method of steepest descent for non-linear minimization problems,” Quart. Appl. Math., s. 2, ss. 258–261, 1944.
  • [36] S. Boyd ve L. Vandenberghe, “Convex Optimization”, 7. baskı, Newyork, United States of America: Cambridge University Press, 2004, böl. 5, ss. 215-216.
  • [37] L. Breiman, J. Friedman, C. J., Stone ve R. A. Olshen, "Classification and Regression Trees," 1. baskı, London, England: CRC Press, 1984, böl. 11, ss. 246-259
  • [38] L. Breiman, "Random forests," Machine Learning, c. 45, s. 1, ss. 5-32, 2001.
  • [39] B. Schölkopf, “Statistical Learning and Kernel Methods”, In: Data Fusion and Perception, G. Della Riccia, HJ. Lenz, R. Kruse, International Centre for Mechanical Sciences Book Series, 1. baskı, Vienna, Austria :Springer, 2001, böl. 431, ss. 3-24.

Karar Destek Makineleri ve Rastgele Orman Ağaçları Yöntemleri ile Vücut Yağ Yüzdesinin Tahmini

Year 2021, Volume: 9 Issue: 3 - Additional Issue, 430 - 445, 29.05.2021
https://doi.org/10.29130/dubited.815454

Abstract

Obezite, önemli bir sağlık problemidir ve yaygınlığı giderek artmaktadır. Bu hastalığın, diğer birçok hastalığın tetikleyicisi ve habercisi olduğu bilinmektedir. Obezite hastalığının tedavi sürecinden önce, vücut yağ yüzdesinin doğru bir şekilde tespit edilmesi önemlidir. Yüksek maliyetli yöntemler ile vücut yağ yüzdesi kesin olarak ölçülmektedir. Bu çalışmada, kişilerden alınan antropometrik veri seti ile vücut yağı yüzdesi tespitinin doğru ve maliyetsiz bir şekilde tahmin edilebilmesi için destek vektör regresyonu ile rastgele orman ağaçları regresyon yöntemleri uygulanmıştır. Regresyon yöntemlerinde, model parametre değerleri, veri sayısı, özellik sayısı ve özellik seçimi tahmin başarımında önemlidir. 13 özellikli vücut yağ yüzdesi veri seti baz olarak alınan çalışmada, literatürde sıklıkla kullanılan 25 istatiski yöntem (çarpıklık, merkezi moment, basıklık vb.) ile yeni bir veri seti oluşturulmuş ve elde edilen yeni veri setinin başarım performansının literatürde yer alan diğer çalışmalardan yüksek olduğu görülmüştür. Regresyon parametrelerinin ızgara tarama yöntemleriyle belirlenmesi sayesinde tahmin doğrulukları arttırılmıştır. Ayrıca özellik azaltma yöntemleri ile vücut yağ yüzdesi ile yüksek ilintili özellikler belirlenmiştir. Seçilen özellikler ile gerçekleştirilen regresyon yöntemlerinin tahmin başarı performansının da benzer diğer çalışmalardan yüksek olduğu gözlenmiştir. En iyi ortalama karesel hata değerleri olarak, Rasgele Orman Ağaçları Yöntemi ve istatistiki yöntemle oluşturulan yeni veri seti ile gerçekleştirilen deneyde 2,2519 değeri elde edilirken, Karar Destek Makinaları ve en iyi 6 F-skor değerine sahip özellikler ile yapılan regresyon deneyinde 3,174 değerine ulaşılmıştır.

References

  • [1] F. McLellan, "Obesity rising to alarming levels around the world," The Lancet, c. 359, s. 9315, ss. 1412, 2002.
  • [2] C. L. Edelman, C. L. Mandle ve E. C. Kudzma, Health Promotion Throughout the Life Span-E-Book, 9. baskı, Missouri, United States of America: Elsevier Health Sciences, 2017, böl. 2, ss. 23-24.
  • [3] I. G. Polat, "Effect of Er stress and Sik2 Reciprocal relationship on human precursor fat cell (LiSa-2) differentiation," Doktora Tezi, Gebze Teknik Üniversitesi, Kocaeli, Türkiye, 2017.
  • [4] F. Ortega, C. Lavie ve S. Blair, "Obesity and cardiovascular disease," Circulation Research, c. 118, s. 11, ss. 1752-1770, 2016.
  • [5] C. Lavie, A. Schutter, P. Parto, E. Jahangir, P. Kokkinos, F. Ortega, R. Arena ve R. Milani, "Obesity and prevalence of cardiovascular diseases and prognosis—the obesity paradox updated," Progress in Cardiovascular Diseases, c. 58, s. 5, ss. 537-547, 2016.
  • [6] A. Keys, F. Fidanza, M. Karvonen, N. Kimura ve H. Taylor, "Indices of relative weight and obesity," Journal of Chronic Diseases, c. 25, s. 6-7, ss. 329-343, 1972.
  • [7] R. Huxley, S. Mendis, E. Zheleznyakov, S. Reddy ve J. Chan, "Body mass index, waist circumference and waist:hip ratio as predictors of cardiovascular risk," Obesity and Metabolism, c. 8, s. 1, ss. 69-69, 2011.
  • [8] C. Lee, R. Huxley, R. Wildman ve M. Woodward, "Indices of abdominal obesity are better discriminators of cardiovascular risk factors than BMI: A meta-analysis," Journal of Clinical Epidemiology, c. 61, s. 7, ss. 646-653, 2008.
  • [9] B. Srdić, B. Obradović, G. Dimitrić, E. Stokić ve S. Babović, "Relationship between body mass index and body fat in children—age and gender differences," Obesity Research & Clinical Practice, c. 6, s. 2, ss. 167-173, 2012.
  • [10] A. Kupusinac, E. Stokić ve R. Doroslovački, "Predicting body fat percentage based on gender, age and BMI by using artificial neural networks," Computer Methods and Programs in Biomedicine, c. 113, s. 2, ss. 610-619, 2014.
  • [11] P. Deurenberg ve M. Yap, "The Assessment of Obesity: Methods for measuring body fat and global prevalence of obesity," Best Practice & Research Clinical Endocrinology & Metabolism, c. 13, s. 1, ss. 1-11, 1999.
  • [12] N. Jensky-Squires, C. Dieli-Conwright, A. Rossuello, D. Erceg, S. McCauley ve E. Schroeder, "Validity and reliability of body composition analysers in children and adults," British Journal of Nutrition, c. 100, s. 4, ss. 859-865, 2008.
  • [13] W. Beeson, M. Batech, E. Schultz, L. Salto, A. Firek, M. Deleon, H. Balcazar ve Z. Cordero-Macintyre, "Comparison of body composition by bioelectrical ımpedance analysis and dual-energy X-ray absorptiometry in hispanic diabetics," International Journal of Body Composition Research, c. 8, s. 2, ss. 45-50, 2010.
  • [14] A. M. Bongiolo, K. Castro ve M. A. da Silva. "Bioelectrical ımpedance analysis: body composition in children and adolescents with Down Syndrome," Minerva Pediatrica, c. 69, s. 6, ss. 560-563, 2017.
  • [15] D. Anblagan, R. Deshpande, N. Jones, C. Costigan, G. Bugg, N. Raine-Fenning, P. Gowland ve P. Mansell, "Measurement of fetal fatin uteroin normal and diabetic pregnancies using magnetic resonance ımaging," Ultrasound in Obstetrics & Gynecology, c. 42, s. 3, ss. 335-340, 2013.
  • [16] J. Josefson, M. Nodzenski, O. Talbot, D. Scholtens ve P. Catalano, "Fat mass estimation in neonates: anthropometric models compared with air displacement plethysmography," British Journal of Nutrition, c. 121, s. 3, ss. 285-290, 2019.
  • [17] D. Fukuda, M. Wray, K. Kendall, A. Smith-Ryan ve J. Stout, "Validity of near-ınfrared ınteractance (FUTREX 6100/XL) for estimating body fat percentage in elite rowers," Clinical Physiology and Functional Imaging, c. 37, s. 4, ss. 456-458, 2017.
  • [18] A. Fernández-Sánchez, E. Madrigal-Santillán, M. Bautista, J. Esquivel-Soto, Á. Morales-González, C. Esquivel-Chirino, I. Durante-Montiel, G. Sánchez-Rivera, C. Valadez-Vega ve J. A. Morales-González, "Inflammation, oxidative stress, and obesity," International Journal of Molecular Sciences, c. 12, s. 5, ss. 3117-3132, 2011.
  • [19] T. Ferenci, "Two Applications Of Biostatistics in The Analysis of Pathophysiological Processes," Doktora Tezi, Óbuda Univeristy, Budapest, Hungary, 2013.
  • [20] T. Ferenci ve L. Kovács, "Predicting body fat percentage from anthropometric and laboratory measurements using artificial neural networks," Applied Soft Computing, c. 67, ss. 834-839, 2018.
  • [21] S. Balasundaram, "On lagrangian support vector regression," Expert Systems with Applications, c. 37, s. 12, ss. 8784-8792, 2010.
  • [22] Y. Xu ve L. Wang, "A weighted twin support vector regression," Knowledge-Based Systems, c. 33, ss. 92-101, 2012.
  • [23] R. Chiong, Z. Fan, Z. Hu ve F. Chiong, "Using an improved relative error support vector machine for body fat prediction," Computer Methods and Programs in Biomedicine, c. 198, ss. 105749, 2020.
  • [24] P. Deurenberg, M. Yap ve W. van Staveren, "Body mass index and percent body fat: a meta analysis among different ethnic groups," International Journal of Obesity, c. 22, s. 12, ss. 1164-1171, 1998.
  • [25] A. Jackson P. Stanforth, J. Gagnon, T. Rankinen, A. Leon, D. Rao, J. Skinner, C. Bouchard ve J. Wilmore, "The Effect of sex, age and race on estimating percentage body fat from body mass index: the heritage family study," International Journal of Obesity, c. 26, s. 6, ss. 789-796, 2002.
  • [26] Y. Shao, "Body fat percentage prediction using ıntelligent hybrid approaches," The Scientific World Journal, c. 2014, ss. 1-8, 2014.
  • [27] M. Uçar, Z. Uçar, F. Köksal ve N. Daldal, "Estimation of body fat percentage using hybrid machine learning algorithms," Measurement, c. 167, ss. 108173, 2020.
  • [28] K. DeGregory, P. Kuiper, T. DeSilvio, J. D. Pleuss, R. Miller, J. W. Roginski, C. B. Fisher, D. Harness, S. Viswanath, S. B. Heymsfield, I. Dungan ve D. M. Thomas, "A review of machine learning in obesity," Obesity Reviews, c. 19, s. 5, ss. 668-685, 2018.
  • [29] M. Akman, M. K. Uçar, Z. Uçar, K. Uçar, B. Baraklı ve M. R. Bozkurt, “Determination of body fat percentage by gender based with photoplethysmography signal using machine learning algorithm,” Innovation and Research in BioMedical Engineering, Basımda.
  • [30] C. Cortes ve V. Vapnik, "Support-vector networks," Machine learning, c. 20, s. 3, ss. 273-297. 1995.
  • [31] T. K. Ho, "Random decision forests", In: Proceedings of 3rd İnternational Conference on Document Analysis and Recognition. IEEE, Montreal, QC, Canada, 1995, ss. 278-282.
  • [32] R. Johnson, "Fitting percentage of body fat to simple body measurements," Journal of Statistics Education, c. 4, s. 1, 1996.
  • [33] W. E. Siri, "body composition from fluid spaces and density: analysis of methods," University of Michigan Library, ss. 1-33, 1956.
  • [34] X. Yan ve S. Xiaogang, "Linear regression analysis: theory and computing," World Scientific, ss. 1-2, 2009.
  • [35] H. B. Curry, “The method of steepest descent for non-linear minimization problems,” Quart. Appl. Math., s. 2, ss. 258–261, 1944.
  • [36] S. Boyd ve L. Vandenberghe, “Convex Optimization”, 7. baskı, Newyork, United States of America: Cambridge University Press, 2004, böl. 5, ss. 215-216.
  • [37] L. Breiman, J. Friedman, C. J., Stone ve R. A. Olshen, "Classification and Regression Trees," 1. baskı, London, England: CRC Press, 1984, böl. 11, ss. 246-259
  • [38] L. Breiman, "Random forests," Machine Learning, c. 45, s. 1, ss. 5-32, 2001.
  • [39] B. Schölkopf, “Statistical Learning and Kernel Methods”, In: Data Fusion and Perception, G. Della Riccia, HJ. Lenz, R. Kruse, International Centre for Mechanical Sciences Book Series, 1. baskı, Vienna, Austria :Springer, 2001, böl. 431, ss. 3-24.
There are 39 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Burhan Baraklı 0000-0002-7947-2312

Ahmet Küçüker 0000-0001-9412-5223

Publication Date May 29, 2021
Published in Issue Year 2021 Volume: 9 Issue: 3 - Additional Issue

Cite

APA Baraklı, B., & Küçüker, A. (2021). Karar Destek Makineleri ve Rastgele Orman Ağaçları Yöntemleri ile Vücut Yağ Yüzdesinin Tahmini. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 9(3), 430-445. https://doi.org/10.29130/dubited.815454
AMA Baraklı B, Küçüker A. Karar Destek Makineleri ve Rastgele Orman Ağaçları Yöntemleri ile Vücut Yağ Yüzdesinin Tahmini. DUBİTED. May 2021;9(3):430-445. doi:10.29130/dubited.815454
Chicago Baraklı, Burhan, and Ahmet Küçüker. “Karar Destek Makineleri Ve Rastgele Orman Ağaçları Yöntemleri Ile Vücut Yağ Yüzdesinin Tahmini”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi 9, no. 3 (May 2021): 430-45. https://doi.org/10.29130/dubited.815454.
EndNote Baraklı B, Küçüker A (May 1, 2021) Karar Destek Makineleri ve Rastgele Orman Ağaçları Yöntemleri ile Vücut Yağ Yüzdesinin Tahmini. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 9 3 430–445.
IEEE B. Baraklı and A. Küçüker, “Karar Destek Makineleri ve Rastgele Orman Ağaçları Yöntemleri ile Vücut Yağ Yüzdesinin Tahmini”, DUBİTED, vol. 9, no. 3, pp. 430–445, 2021, doi: 10.29130/dubited.815454.
ISNAD Baraklı, Burhan - Küçüker, Ahmet. “Karar Destek Makineleri Ve Rastgele Orman Ağaçları Yöntemleri Ile Vücut Yağ Yüzdesinin Tahmini”. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 9/3 (May 2021), 430-445. https://doi.org/10.29130/dubited.815454.
JAMA Baraklı B, Küçüker A. Karar Destek Makineleri ve Rastgele Orman Ağaçları Yöntemleri ile Vücut Yağ Yüzdesinin Tahmini. DUBİTED. 2021;9:430–445.
MLA Baraklı, Burhan and Ahmet Küçüker. “Karar Destek Makineleri Ve Rastgele Orman Ağaçları Yöntemleri Ile Vücut Yağ Yüzdesinin Tahmini”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, vol. 9, no. 3, 2021, pp. 430-45, doi:10.29130/dubited.815454.
Vancouver Baraklı B, Küçüker A. Karar Destek Makineleri ve Rastgele Orman Ağaçları Yöntemleri ile Vücut Yağ Yüzdesinin Tahmini. DUBİTED. 2021;9(3):430-45.