Bağımsız Bileşenler Analizinin İstatistiksel Bakış Açısıyla Değerlendirilmesi ve Temel Bileşenler Analizi ile Karşılaştırılması

Abstract

İstatistik ve ilgili alanlardaki en önemli problemlerden biri, çok değişkenli verinin uygun bir temsilinin bulunmasıdır. Burada temsilden kasıt; veriyi, esas yapısı daha görünür (ulaşılır) bir şekle dönüştürmektir. Bağımsız Bileşenler Analizi (BBA); çok değişkenli verinin altında yatan bileşenleri bularak esas yapısını daha görünür hale getiren istatistiksel bir yöntemdir. Bu açıdan BBA, Temel Bileşenler Analizi’nin (TBA) bir uzantısı olarak da görülebilir. Ancak BBA, TBA’nın aksine ilişkisizlik yerine istatistiksel bağımsızlığı temel alır ve istatistiksel bağımsızlık, ilişkisizliğe göre çok daha güçlü bir özelliktir. Ayrıca TBA’da elde edilen bileşenlerin normal dağılması istenirken, BBA’da tam tersi bağımsız bileşenlerin normal dağılmaması istenmektedir. Çalışmada, çok değişkenli istatistiksel bir yöntem olmasına rağmen istatistik alanında pek fazla bilinmeyen ve daha çok mühendislik alanında kullanılan BBA konusu ayrıntılı bir şekilde ele alınmış ve konuyla ilgili kısıtlı istatistik literatürüne katkıda bulunulmuştur. Uygulama bölümünde BBA, benzer bir yöntem olan TBA ile karşılaştırılmıştır. Her iki analiz yapay bir veri kümesine uygulanmış ve BBA’nın normal olmayan bileşenleri ortaya çıkarmada TBA’dan çok daha başarılı olduğu sonucuna ulaşılmıştır.

Keywords

• Bağımsız bileşenler analizi
• Çok değişkenli istatistiksel yöntemler
• Kör kaynak ayrıştırma problemi
• Temel bileşenler analizi

Evaluation of Independent Components Analysis from Statistical Perspective and Its Comparison with Principal Components Analysis

Abstract

One of the most important problems in statistics and related fields is that finding an appropriate representation of multivariate data. Here is meant by representation; to transform the data into a more visible (accessible) form. Independent Components Analysis (ICA) is a statistical method used to find the underlying components of multivariate data and makes its main structure more visible. In this respect, ICA can also be seen as an extension of the Principal Components Analysis (PCA). However, ICA, contrary to PCA, is based on statistical independence rather than unrelatedness and statistical independence is a much stronger feature than unrelatedness. In addition, while the normal distribution of the components obtained in PCA is desired, the independent components of ICA are requested not to distribute normally. In the study, although it is a multivariate statistical method, the subject of ICA, which is not well known in the field of statistics and which is mostly used in engineering, was discussed in detail and contributed to the limited statistical literature on the subject. In the application part, ICA was compared with a similar method, PCA. Both analyzes were applied to an artificial dataset and it was concluded that ICA was much more successful than PCA in detecting non-normal components.

Keywords

• Independent components analysis
• Multivariate statistical methods
• Blind source separation problem
• Principal components analysis

References

1. [1] Hyvärinen, A., Karhunen, J., Oja, E. 2001. Independent Component Analysis. John Wiley&Sons, New York, 504p.
2. [2] Shlens, J. 2014. A Tutorial on Independent Component Analysis. https://arxiv.org/pdf/1404.2986.pdf (Accessed Date: 01.21.2019).
3. [3] Ozdamar, E.O. 2009. EEG Analizinde Bağımsız Bileşenler. Mimar Sinan University, Graduate School of Science and Engineering, Doctoral Thesis, 125p, Istanbul.
4. [4] Bursa, N. 2019. Bağımsız Bileşenler Analizi ile Çoklu Bağlantı Sorununa Bir Yaklaşım. Hacettepe University, Graduate School of Science and Engineering, Doctoral Thesis, 151p, Ankara.
5. [5] Hérault, J., Jutten, C., Ans, C. 1998. Détection de Grandeurs Primitives dans un Message Composite par une Architecture de Calcul Neuromimétique en Apprentissage non Suprévise.http://documents.irevues.inist.fr/bitstream/handle/2042/10937/AR12_9.pdf?sequence=1 (Accessed Date: 05.23.2019).
6. [6] Jutten C., Hérault, J. 1991. Blind Separation of Sources, Part I: An Adaptive Algorithm Based on Neuromimetric Architecture. Signal Processing, 24(1), 1-10.
7. [7] Jutten, C., Hérault, J. 1991. Blind Separation of Sources, Part II: Problems Statement. Signal Processing, 24(1), 11-20.
8. [8] Jutten, C., Hérault, J. 1991. Blind Separatrion of Sources, Part III: Stability Analysis. Signal Processing, 24(1), 21-29.

9. [9] Comon, P. 1994. Independent Component Analysis, a New Concept?, Signal Processing, 36(3), 287-314.
10. [10] Artoni, F., Delorme, A., Makeig, S. 2019. A Visual Working Memory Dataset Collection with Bootstrap Independent Component Analysis for Comparison of Electroencephalographic Preprocessing Pipelines. Data in Brief, 22, 787-793.
11. [11] Tierney, J.E., Wilkes, D.M., Byram, B.C. 2019. Independent Component Analysis-Based Tissue Clutter Filtering for Plane Wave Perfusion Ultrasound Imaging. Medical Imaging: Ultrasonic Imaging and Tomography, 17-18 February, San Diego, 2.
12. [12] Baker, B.T., Abrol, A., Silva, R.F., Damaraju, E., Sarwate, A.D., Calhoun, V.D., Plis, S.M. 2019. Decentralized Temporal Independent Component Analysis: Leveraging Fmrı Data in Collaborative Settings. Neurolmage, 186, 557-569.
13. [13] Albert, S.A., Bowman, D.C. 2018. Tracking Scattered Signals in the Acoustic Coda Using Independent Component Analysis in a Topographically Complex Setting. Geophysical Journal International, 216(2), 767-776.
14. [14] de Lauro, E., Petrosino, S., Falanga, M. 2018. Independent Component Analysis as a Monitoring Tool in Geophysical Environment: The Case of Campi Flegrei (Italy). IEEE Workshop on Environmental, Energy, and Structural Monitoring Systems, 21-22 June, Salerno, 1-6.
15. [15] Cohen-Waeber, J., Bürgmann, R., Chaussard, E., Giannico, C., Ferretti, A. 2018. Spatiotemporal Patterns of Precipitation‐Modulated Landslide Deformation from Independent Component Analysis of InSAR Time Series. Geophysical Research Letters, 45(4), 1878-1887.
16. [16] Garcia-Bracamonte, J.E., Rangel-Magdaleno, J., Ramirez-Cortes, J.M., Gomez-Gill, P., Paregrina-Barreto, H. 2018. Induction Motors Fault Detection Using Independent Component Analysis on Phase Current Signals, IEEE International Instrumentation and Measurement Technology Conference, 14-17 May, Houstan, 1-6.
17. [17] Yu, J., Yoo, J. , Jang, J., Park, J.H., Kim, S. 2018. A Novel Hybrid of Auto-Associative Kernel Regression and Dynamic Independent Component Analysis for Fault Detection in Nonlinear Multimode Processes. Journal of Process Control, 68, 129-144.
18. [18] Li, Z., Yan, X. 2018. Adaptive Selective Ensemble-Independent Component Analysis Models for Process Monitoring. Industrial & Engineering Chemistry Research, 57(24), 8240-8252.
19. [19] Lahaw, Z.B., Essaidani, D., Seddik, H. 2018. Robust Face Recognition Approaches Using PCA, ICA, LDA Based on DWT and SVM Algorithms. 41st International Conference on Telecommunications and Signal Processing, 4-6 July, Atheans, 1-5.
20. [20] Wang, Y., Guo, Y. 2019. A Hierarchical Independent Component Analysis Model for Longitudinal Neuroimaging Studies. Neurolmage, 189, 380-400.
21. [21] Koush, Y., Masala, N., Scharnowski, F., De Ville, D.V. 2019. Data-Driven Tensor Independent Component Analysis for Model-Based Connectivity Neurofeedback. Neurolmage, 184, 214-226.
22. [22] Jiang, C., Zhang, H., Ren, Y., Han, Z., Chen, K., Hanzo, L. 2017. Machine Learning Paradigms for Next-Generation Wireless Networks. IEEE Wireless Communications, 24(2), 98-105.
23. [23] Wang, C., Xu, Y., Tang, M., Wang, L. 2018. Blind Source Separation Based on Variational Bayesian Independent Component Analysis. IEEE 3rd Advanced Information Technology. Electronic and Automation Control Conference, 12-14 October, Chongqing, 1614-1618.
24. [24] Aveta, F., Refai, H., Lo Presti, P., Tedder, A.S., Schoenholz, B.L. 2018. Independent Component Analysis for Processing Optical Signals in Support of Multi-User Communication. Free-Space Laser Communication and Atmospheric Propagation XXX, 29-30 January, San Francisco, 1-9.
25. [25] Gouriéroux, C., Monfort, A., Renne, J.P. 2017. Statistical Inference for Independent Component Analysis: Application to Structural VAR Models. Journal of Econometrics, 196(1), 111-126.
26. [26] Chowdhury, U.N., Chakravarty, S.K., Hossain, M.T. 2018. Short-Term Financial Time Series Forecasting Integrating Principal Component Analysis and Independent Component Analysis with Support Vector Regression. Journal of Computer and Communications, 6(3), 51-67.
27. [27] Chen, Y., Niu, L., Chen, R.B., He. Q. 2019. Sparse-Group Independent Component Analysis with Application to Yield Curves Prediction. Computational Statistics & Data Analysis, 133, 76-89, 2019.
28. [28] Witten, I.H., Frank, E., Hall, M.A., Pal, C.J. 2016. Data Mining: Practical Machine Learning Tools and Techniques, Elsevier, San Francisco, 525p.
29. [29] Thomas, M.C., Zhu, W., Romagnoli, J.A. 2018. Data Mining and Clustering in Chemical Process Databases for Monitoring and Knowledge Discovery. Journal of Process Control, 67, 160-175.
30. [30] Gultepe, E., Makrehchi, M. 2018. Improving Clustering Performance Using Independent Component Analysis and Unsupervised Feature Learning. Human-centric Computing and Information Sciences, 8(25), 1-19.
31. [31] Zhou W., Altman, R.B. 2018. Data-Driven Human Transcriptomic Modules. BMC Bioinformatics, 19(327), 1-25.
32. [32] Kamal, M.S., Trivdedi, M.C., Alam, J.B., Dey, N., Ashour, A.S., Shi, F., Tavares, J.M.R. 2018. Big DNA Datasets Analysis Under Push Down Automata. Journal of Intelligent & Fuzzy Systems, 35(2), 1555-1565.
33. [33] Ghosh, M., Adhikary, S., Kanti Ghosh, K., Sardar, A., Begum, S., Sarkar, R. 2019. Genetic Algorithm Based Cancerous Gene Identification from Microarray Data Using Ensemble of Filter Methods. Medical & Biological Engineering & Computing, 57(1), 159-176.
34. [34] Liu, Y., Xu, H., Xia, Z., Gong, Z. 2018. Multi-Spectrometer Calibration Transfer Based On Independent Component Analysis. Analyst, 143(5), 1274-1280.
35. [35] Alves, F.C.G.B.S., Coqueiro, A., Março, P.H., Valderrama, P. 2019. Evaluation of Olive Oils from the Mediterranean Region by UV–Vis Spectroscopy and Independent Component Analysis. Food Chemistry, 273, 124-129.
36. [36] Delaporte, G., Cladiére, M., Bouveresse, D.J.R., Camel, V. 2019. Untargeted Food Contaminant Detection Using UHPLC-HRMS Combined with Multivariate Analysis: Feasibility Study on Tea. Food Chemistry, 277, 54-62.
37. [37] Stone, J.V. 2004. Independent Component Analysis: A Tutorial Introduction. MIT Press, London, 191p.
38. [38] Nordhausen K., Oja, H. 2018. Independent Component Analysis: A Statistical Perspective. Wiley Interdisciplinary Reviews: Computational Statistics, 10(5), 1-23.
39. [39] Hyvärinen, A. 2013. Independent Component Analysis: Recent Advances. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371, 1-19.
40. [40] Hyvärinen, A., Oja, E. 2000. Independent Component Analysis: Algorithms and Applications. Neural Networks, 13(4-5), 411-430.
41. [41] Tharwat, A. 2018. Independent Component Analysis: An Introduction, Applied Computing and Informatics. https://doi.org/10.1016/j.aci.2018.08.006 (Accessed Date: 01.28.2018).
42. [42] Hyvärinen, A. 1999. Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks, 10(3), 626-634.
43. [43] Matthias, K., Haueisen, J., Ivanova, G. 2009. Independent Component Analysis: Comparison of Algorithms for the Investigation of Surface Electrical Brain Activity. Medical & Biological Engineering & Computing, 47(4), 413-423.
44. [44] Naik, G.R. 2011. A Comparison of ICA Algorithms in Surface EMG Signal Processing. International Journal of Biomedical Engineering and Technology, 6(4), 363-374.
45. [45] Dharmaprani, D., Nguyen, H.K., Lewis, T.W., DeLosAngeles, D., Willoughby, J.O., Pope, K.J. 2016. A Comparison of Independent Component Analysis Algorithms and Measures to Discriminate Between EEG and Artifact Components. 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 16-20 August, Orlando, 825-828.
46. [46] Sahonero-Alvarez, G., Calderon, H. 2017. A Comparison of SOBI, FastICA, JADE and Infomax Algorithms. 8th International Multi-Conference on Complexity, Informatics and Cybernetics, 21-24 March, Orlando, 17-22. [47] R Core Team. 2019. R: A Language and Environment for Statistical Computing. https://www.r-project.org/ (Accessed Date: 03.01.2020).
47. [48] Miettinen, J., Nordhausen, K., Taskinen, S. 2017. Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp, Journal of Statistical Software, 76(2), 1-31.
48. [49] Miettinen, J., Nordhausen, K., Oja, H., Taskinen, S. 2017. fICA: Classical, Reloaded and Adaptive Fastıca Algorithms. https://cran.r-project.org/web/packages/fICA/index.html (Accessed Date: 08.11.2019).
49. [50] Helwig. N.E. 2015. Ica: Independent Component Analysis. https://cran.r-project.org/web/packages/ica/index.html (Accessed Date: 08.11.2019).
50. [51] Marchini, J.L., Heaton, C., Ripley. B.D. 2017. fastICA: FastICA Algorithms to Perform ICA and Projection Pursuit. https://cran.r-project.org/web/packages/fastICA/index.html (Accessed Date: 09.11.2019).
51. [52] Naik, G.R., Kumar, D.K. 2011. An Overview of Independent Component Analysis and Its Applications. Informatica, 35(2011), 63-81.
52. [53] Mutihac, R., Van Hulle, M.M. 2004. Comparison of Principal Component Analysis and Independent Component Analysis for Blind Source Separation. Romanion Reports in Physics, 56(1), 20-32.