Abstract

The surface morphology of electrospun fibers largely determines their application scenarios. Conventional scanning electron microscopy is usually used to observe the microstructure of polymer electrospun fibers, which is time consuming and will cause damage to the samples. In this paper, we use backscattering Mueller polarimetry to classify the microstructural features of materials by statistical learning methods. Before feeding the Mueller matrix (MM) data into the classifier, we use a two-stage feature extraction method to find out representative polarization parameters. First, we filter out the irrelevant MM elements according to their characteristic powers measured by mutual information. Then we use Correlation Explanation (CorEx) method to group interdependent elements and extract parameters that represent their relationships in each group. The extracted parameters are evaluated by the random forest classifier in a wrapper forward feature selection way and the results show the effectiveness in classification performance, which also shows the possibility to detect nonporous electrospun fibers automatically in real time.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2018 (4)

A. Haider, S. Haider, and I. K. Kang, “A comprehensive review summarizing the effect of electrospinning parameters and potential applications of nanofibers in biomedical and biotechnology,” Arab. J. Chem. 11(8), 1165–1188 (2018).
[Crossref]

X. Li, Y. Zhu, H. Ma, and Y. Sheng, “A polarization method for quickly distinguishing the morphology of electro-spun ultrafine fibers,” Chin. Chem. Lett. 29(8), 1317–1320 (2018).
[Crossref]

C. Heinrich, J. Rehbinder, A. Nazac, B. Teig, A. Pierangelo, and J. Zallat, “Mueller polarimetric imaging of biological tissues: classification in a decision-theoretic framework,” J. Opt. Soc. Am. A 35(12), 2046–2057 (2018).
[Crossref]

P. Li, D. Lv, H. He, and H. Ma, “Separating azimuthal orientation dependence in polarization measurements of anisotropic media,” Opt. Express 26(4), 3791–3800 (2018).
[Crossref]

2017 (1)

2016 (4)

V. V. Tuchin, “Polarized light interaction with tissues,” J. Biomed. Opt. 21(7), 071114 (2016).
[Crossref]

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21(7), 071113 (2016).
[Crossref]

X. Chen, W. Du, K. Yuan, J. Chen, H. Jiang, C. Zhang, and S. Liu, “Development of a spectroscopic mueller matrix imaging ellipsometer for nanostructure metrology,” Rev. Sci. Instrum. 87(5), 053707 (2016).
[Crossref]

Q. Zou, J. Zeng, L. Cao, and R. Ji, “A novel features ranking metric with application to scalable visual and bioinformatics data classification,” Neurocomputing 173, 346–354 (2016).
[Crossref]

2015 (4)

M. Bennasar, Y. Hicks, and R. Setchi, “Feature selection using joint mutual information maximisation,” Expert. Syst. with Appl. 42(22), 8520–8532 (2015).
[Crossref]

C. He, H. He, J. Chang, Y. Dong, S. Liu, N. Zeng, Y. He, and H. Ma, “Characterizing microstructures of cancerous tissues using multispectral transformed Mueller matrix polarization parameters,” Biomed. Opt. Express 6(8), 2934–2945 (2015).
[Crossref]

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20(10), 105009 (2015).
[Crossref]

S. Liu, W. Du, X. Chen, H. Jiang, and C. Zhang, “Mueller matrix imaging ellipsometry for nanostructure metrology,” Opt. Express 23(13), 17316–17329 (2015).
[Crossref]

2014 (2)

2013 (2)

A. Jukić and M. Filipović, “Supervised feature extraction for tensor objects based on maximization of mutual information,” Pattern Recognit. Lett. 34(13), 1476–1484 (2013).
[Crossref]

H. He, N. Zeng, E. Du, Y. Guo, D. Li, R. Liao, and H. Ma, “A possible quantitative Mueller matrix transformation technique for anisotropic scattering media,” Photonics Lasers Med. 2(2), 129–137 (2013).
[Crossref]

2012 (1)

G. Brown, A. Pocock, M.-J. Zhao, and M. Luján, “Conditional likelihood maximisation: a unifying framework for information theoretic feature selection,” J. Mach. Learn. Res. 13, 27–66 (2012).

2008 (3)

P. E. Meyer, C. Schretter, and G. Bontempi, “Information-theoretic feature selection in microarray data using variable complementarity,” IEEE J. Sel. Top. Signal Process. 2(3), 261–274 (2008).
[Crossref]

D. H. Reneker and A. L. Yarin, “Electrospinning jets and polymer nanofibers,” Polymer 49(10), 2387–2425 (2008).
[Crossref]

C. Kriegel, A. Arrechi, K. Kit, D. McClements, and J. Weiss, “Fabrication, functionalization, and application of electrospun biopolymer nanofibers,” Crit. Rev. Food Sci. Nutr. 48(8), 775–797 (2008).
[Crossref]

2007 (2)

B. G. Hoover and J. S. Tyo, “Polarization components analysis for invariant discrimination,” Appl. Opt. 46(34), 8364–8373 (2007).
[Crossref]

J. M. Leiva-Murillo and A. Artes-Rodriguez, “Maximization of mutual information for supervised linear feature extraction,” IEEE Trans. Neural Netw. 18(5), 1433–1441 (2007).
[Crossref]

2006 (2)

B. D. Cameron, Y. Li, and A. A. Nezhuvingal, “Determination of optical scattering properties in turbid media using Mueller matrix imaging,” J. Biomed. Opt. 11(5), 054031 (2006).
[Crossref]

M. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. Gupta, “Polar decomposition of 3× 3 Mueller matrix: a tool for quantitative tissue polarimetry,” Opt. Express 14(20), 9324–9337 (2006).
[Crossref]

2005 (2)

H. Peng, F. Long, and C. Ding, “Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy,” IEEE Trans. Pattern Anal. Machine Intell. 27(8), 1226–1238 (2005).
[Crossref]

C. Ding and H. Peng, “Minimum redundancy feature selection from microarray gene expression data,” J. Bioinf. Comput. Biol. 03(02), 185–205 (2005).
[Crossref]

2004 (2)

C. L. Casper, J. S. Stephens, N. G. Tassi, D. B. Chase, and J. F. Rabolt, “Controlling surface morphology of electrospun polystyrene fibers: effect of humidity and molecular weight in the electrospinning process,” Macromolecules 37(2), 573–578 (2004).
[Crossref]

F. Fleuret, “Fast binary feature selection with conditional mutual information,” J. Mach. learning research 5, 1531–1555 (2004).

2003 (1)

E. Schneidman, S. Still, M. J. Berry, and W. Bialek, “Network information and connected correlations,” Phys. Rev. Lett. 91(23), 238701 (2003).
[Crossref]

1994 (1)

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The polder mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32(3), 598–615 (1994).
[Crossref]

1992 (1)

1978 (1)

1960 (1)

S. Watanabe, “Information theoretical analysis of multivariate correlation,” IBM J. Res. Dev. 4(1), 66–82 (1960).
[Crossref]

1954 (1)

W. McGill, “Multivariate information transmission,” Trans. IRE Prof. Group Inf. Theory 4(4), 93–111 (1954).
[Crossref]

Al-Bashabsheh, A.

C. Chung, A. Al-Bashabsheh, H. P. Huang, M. Lim, D. S. H. Tam, and C. Zhao, “Neural entropic estimation: A faster path to mutual information estimation,” arXiv preprint arXiv:1905.12957 (2019).

Antó, J.

Arrechi, A.

C. Kriegel, A. Arrechi, K. Kit, D. McClements, and J. Weiss, “Fabrication, functionalization, and application of electrospun biopolymer nanofibers,” Crit. Rev. Food Sci. Nutr. 48(8), 775–797 (2008).
[Crossref]

Arteaga, O.

Artes-Rodriguez, A.

J. M. Leiva-Murillo and A. Artes-Rodriguez, “Maximization of mutual information for supervised linear feature extraction,” IEEE Trans. Neural Netw. 18(5), 1433–1441 (2007).
[Crossref]

Azzam, R.

Baldrís, M.

Bennasar, M.

M. Bennasar, Y. Hicks, and R. Setchi, “Feature selection using joint mutual information maximisation,” Expert. Syst. with Appl. 42(22), 8520–8532 (2015).
[Crossref]

Berry, M. J.

E. Schneidman, S. Still, M. J. Berry, and W. Bialek, “Network information and connected correlations,” Phys. Rev. Lett. 91(23), 238701 (2003).
[Crossref]

Bertran, E.

Bialek, W.

E. Schneidman, S. Still, M. J. Berry, and W. Bialek, “Network information and connected correlations,” Phys. Rev. Lett. 91(23), 238701 (2003).
[Crossref]

Bontempi, G.

P. E. Meyer, C. Schretter, and G. Bontempi, “Information-theoretic feature selection in microarray data using variable complementarity,” IEEE J. Sel. Top. Signal Process. 2(3), 261–274 (2008).
[Crossref]

Bréon, F. M.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The polder mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32(3), 598–615 (1994).
[Crossref]

Bricaud, A.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The polder mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32(3), 598–615 (1994).
[Crossref]

Brown, G.

G. Brown, A. Pocock, M.-J. Zhao, and M. Luján, “Conditional likelihood maximisation: a unifying framework for information theoretic feature selection,” J. Mach. Learn. Res. 13, 27–66 (2012).

Buddhiwant, P.

Buriez, J. C.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The polder mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32(3), 598–615 (1994).
[Crossref]

Cameron, B. D.

B. D. Cameron, Y. Li, and A. A. Nezhuvingal, “Determination of optical scattering properties in turbid media using Mueller matrix imaging,” J. Biomed. Opt. 11(5), 054031 (2006).
[Crossref]

Canillas, A.

Cao, L.

Q. Zou, J. Zeng, L. Cao, and R. Ji, “A novel features ranking metric with application to scalable visual and bioinformatics data classification,” Neurocomputing 173, 346–354 (2016).
[Crossref]

Casper, C. L.

C. L. Casper, J. S. Stephens, N. G. Tassi, D. B. Chase, and J. F. Rabolt, “Controlling surface morphology of electrospun polystyrene fibers: effect of humidity and molecular weight in the electrospinning process,” Macromolecules 37(2), 573–578 (2004).
[Crossref]

Chang, J.

C. He, H. He, J. Chang, Y. Dong, S. Liu, N. Zeng, Y. He, and H. Ma, “Characterizing microstructures of cancerous tissues using multispectral transformed Mueller matrix polarization parameters,” Biomed. Opt. Express 6(8), 2934–2945 (2015).
[Crossref]

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20(10), 105009 (2015).
[Crossref]

Chase, D. B.

C. L. Casper, J. S. Stephens, N. G. Tassi, D. B. Chase, and J. F. Rabolt, “Controlling surface morphology of electrospun polystyrene fibers: effect of humidity and molecular weight in the electrospinning process,” Macromolecules 37(2), 573–578 (2004).
[Crossref]

Chen, J.

X. Chen, W. Du, K. Yuan, J. Chen, H. Jiang, C. Zhang, and S. Liu, “Development of a spectroscopic mueller matrix imaging ellipsometer for nanostructure metrology,” Rev. Sci. Instrum. 87(5), 053707 (2016).
[Crossref]

Chen, X.

X. Chen, W. Du, K. Yuan, J. Chen, H. Jiang, C. Zhang, and S. Liu, “Development of a spectroscopic mueller matrix imaging ellipsometer for nanostructure metrology,” Rev. Sci. Instrum. 87(5), 053707 (2016).
[Crossref]

S. Liu, W. Du, X. Chen, H. Jiang, and C. Zhang, “Mueller matrix imaging ellipsometry for nanostructure metrology,” Opt. Express 23(13), 17316–17329 (2015).
[Crossref]

Chung, C.

C. Chung, A. Al-Bashabsheh, H. P. Huang, M. Lim, D. S. H. Tam, and C. Zhao, “Neural entropic estimation: A faster path to mutual information estimation,” arXiv preprint arXiv:1905.12957 (2019).

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of information theory (John Wiley & Sons, 2012), pp. 13–16.

Craven-Jones, J.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” in Polarization: Measurement, Analysis, and Remote Sensing XI, vol. 9099 (International Society for Optics and Photonics, 2014), p. 90990B.

De Martino, A.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” in Polarization: Measurement, Analysis, and Remote Sensing XI, vol. 9099 (International Society for Optics and Photonics, 2014), p. 90990B.

Deby, S.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21(7), 071113 (2016).
[Crossref]

Deschamps, P. Y.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The polder mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32(3), 598–615 (1994).
[Crossref]

Ding, C.

C. Ding and H. Peng, “Minimum redundancy feature selection from microarray gene expression data,” J. Bioinf. Comput. Biol. 03(02), 185–205 (2005).
[Crossref]

H. Peng, F. Long, and C. Ding, “Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy,” IEEE Trans. Pattern Anal. Machine Intell. 27(8), 1226–1238 (2005).
[Crossref]

Dong, Y.

Du, E.

H. He, N. Zeng, E. Du, Y. Guo, D. Li, R. Liao, and H. Ma, “A possible quantitative Mueller matrix transformation technique for anisotropic scattering media,” Photonics Lasers Med. 2(2), 129–137 (2013).
[Crossref]

Du, W.

X. Chen, W. Du, K. Yuan, J. Chen, H. Jiang, C. Zhang, and S. Liu, “Development of a spectroscopic mueller matrix imaging ellipsometer for nanostructure metrology,” Rev. Sci. Instrum. 87(5), 053707 (2016).
[Crossref]

S. Liu, W. Du, X. Chen, H. Jiang, and C. Zhang, “Mueller matrix imaging ellipsometry for nanostructure metrology,” Opt. Express 23(13), 17316–17329 (2015).
[Crossref]

Elson, D. S.

Escuti, M.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” in Polarization: Measurement, Analysis, and Remote Sensing XI, vol. 9099 (International Society for Optics and Photonics, 2014), p. 90990B.

Estévez, P. A.

J. R. Vergara and P. A. Estévez, “A review of feature selection methods based on mutual information,” Neural Comput. Appl. 24(1), 175–186 (2014).
[Crossref]

Filipovic, M.

A. Jukić and M. Filipović, “Supervised feature extraction for tensor objects based on maximization of mutual information,” Pattern Recognit. Lett. 34(13), 1476–1484 (2013).
[Crossref]

Fineschi, S.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” in Polarization: Measurement, Analysis, and Remote Sensing XI, vol. 9099 (International Society for Optics and Photonics, 2014), p. 90990B.

Fleuret, F.

F. Fleuret, “Fast binary feature selection with conditional mutual information,” J. Mach. learning research 5, 1531–1555 (2004).

Galstyan, A.

G. V. Steeg and A. Galstyan, “Discovering structure in high-dimensional data through correlation explanation,” in Advances in Neural Information Processing Systems, (2014), pp. 577–585.

G. V. Steeg and A. Galstyan, “Maximally informative hierarchical representations of high-dimensional data,” in Artificial Intelligence and Statistics, (2015), pp. 1004–1012.

Ghosh, N.

Goldstein, D. H.

Guo, Y.

H. He, N. Zeng, E. Du, Y. Guo, D. Li, R. Liao, and H. Ma, “A possible quantitative Mueller matrix transformation technique for anisotropic scattering media,” Photonics Lasers Med. 2(2), 129–137 (2013).
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F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” in Polarization: Measurement, Analysis, and Remote Sensing XI, vol. 9099 (International Society for Optics and Photonics, 2014), p. 90990B.

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He, H.

He, Y.

C. He, H. He, J. Chang, Y. Dong, S. Liu, N. Zeng, Y. He, and H. Ma, “Characterizing microstructures of cancerous tissues using multispectral transformed Mueller matrix polarization parameters,” Biomed. Opt. Express 6(8), 2934–2945 (2015).
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C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20(10), 105009 (2015).
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M. Bennasar, Y. Hicks, and R. Setchi, “Feature selection using joint mutual information maximisation,” Expert. Syst. with Appl. 42(22), 8520–8532 (2015).
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B. G. Hoover and J. S. Tyo, “Polarization components analysis for invariant discrimination,” Appl. Opt. 46(34), 8364–8373 (2007).
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C. Chung, A. Al-Bashabsheh, H. P. Huang, M. Lim, D. S. H. Tam, and C. Zhao, “Neural entropic estimation: A faster path to mutual information estimation,” arXiv preprint arXiv:1905.12957 (2019).

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X. Chen, W. Du, K. Yuan, J. Chen, H. Jiang, C. Zhang, and S. Liu, “Development of a spectroscopic mueller matrix imaging ellipsometer for nanostructure metrology,” Rev. Sci. Instrum. 87(5), 053707 (2016).
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C. L. Casper, J. S. Stephens, N. G. Tassi, D. B. Chase, and J. F. Rabolt, “Controlling surface morphology of electrospun polystyrene fibers: effect of humidity and molecular weight in the electrospinning process,” Macromolecules 37(2), 573–578 (2004).
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Appl. Opt. (3)

Arab. J. Chem. (1)

A. Haider, S. Haider, and I. K. Kang, “A comprehensive review summarizing the effect of electrospinning parameters and potential applications of nanofibers in biomedical and biotechnology,” Arab. J. Chem. 11(8), 1165–1188 (2018).
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Biomed. Opt. Express (2)

Chin. Chem. Lett. (1)

X. Li, Y. Zhu, H. Ma, and Y. Sheng, “A polarization method for quickly distinguishing the morphology of electro-spun ultrafine fibers,” Chin. Chem. Lett. 29(8), 1317–1320 (2018).
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Crit. Rev. Food Sci. Nutr. (1)

C. Kriegel, A. Arrechi, K. Kit, D. McClements, and J. Weiss, “Fabrication, functionalization, and application of electrospun biopolymer nanofibers,” Crit. Rev. Food Sci. Nutr. 48(8), 775–797 (2008).
[Crossref]

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M. Bennasar, Y. Hicks, and R. Setchi, “Feature selection using joint mutual information maximisation,” Expert. Syst. with Appl. 42(22), 8520–8532 (2015).
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IBM J. Res. Dev. (1)

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[Crossref]

IEEE Trans. Geosci. Remote Sensing (1)

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IEEE Trans. Neural Netw. (1)

J. M. Leiva-Murillo and A. Artes-Rodriguez, “Maximization of mutual information for supervised linear feature extraction,” IEEE Trans. Neural Netw. 18(5), 1433–1441 (2007).
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IEEE Trans. Pattern Anal. Machine Intell. (1)

H. Peng, F. Long, and C. Ding, “Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy,” IEEE Trans. Pattern Anal. Machine Intell. 27(8), 1226–1238 (2005).
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C. Ding and H. Peng, “Minimum redundancy feature selection from microarray gene expression data,” J. Bioinf. Comput. Biol. 03(02), 185–205 (2005).
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J. Biomed. Opt. (4)

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20(10), 105009 (2015).
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[Crossref]

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J. Mach. Learn. Res. (1)

G. Brown, A. Pocock, M.-J. Zhao, and M. Luján, “Conditional likelihood maximisation: a unifying framework for information theoretic feature selection,” J. Mach. Learn. Res. 13, 27–66 (2012).

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Figures (8)

Fig. 1.
Fig. 1. SEM photographs of electrospun fibers with different surface morphologies. (a) Nonporous surface, PLLA/PCL (25:75), Spinning solution (8wt%), N,N-Dimethylformamide (DMF, 6g); (b) Nonporous surface, PLLA/PCL (100:0), Spinning solution (8wt%), DMF (6g); (c) Meshed surface PLLA/PCL (100:0), Spinning solution (8wt%), DMF (4.6g); (d) Porous microspheres (25:75), Spinning solution (4wt%), DMF (4.8g).
Fig. 2.
Fig. 2. Experimental setup. (a) Intensity distribution from the CCD where the center region (red box) is cropped and analyzed. (b)Mueller matrix backscattering imaging system with two active polarimetric elements: a Polarization State Generator (PSG) and a Polarization State Analyzer (PSA). (c) Photograph of an electrospun fiber sample.
Fig. 3.
Fig. 3. 2D images of MMs of electrospun fibers. (a) Nonporous surface; (b) Meshed surface; (c) Porous microspheres. The color bar is from −0.5 to 0.5 for diagonal elements and from −0.1 to 0.1 for other elements.
Fig. 4.
Fig. 4. Mutual information (MI) scores of individual elements. (a) MI between each element and the class variable $C$, i.e. $I(M_{ij},C)$. The curve represents the cumulative percentage of MI. (b) An example of multi-information between $M_{44}$ and other elements, i.e. $I(M_{44},M_{ij}|C)-I(M_{44},M_{ij})$. Here we set the interaction values with $M_{44}$ itself as zero since the value is the opposite of $I(M_{44},C)$ (non-positive).
Fig. 5.
Fig. 5. Grouping results from CorEx given the group number $l=2$. (a) The MI between extracted parameters from each group and class variable. The horizontal axis is the number of possible values $r$ in Eq. (6). (b) The schematic diagram of grouping results generating by CorEx. Elements in the bottom row represents the input. $Y_{1}$ and $Y_{2}$ in the higher layers are learned parameters which explain the relationships in each group.
Fig. 6.
Fig. 6. The RF classification accuracy with the wrapper forward selection. Three lines denote the results on: (1) All 15 MM elements and two extracted parameters; (2) All 15 MM elements and two extracted parameters with setting the first picked feature as $Y_{2}$; (3) All 15 MM elements.
Fig. 7.
Fig. 7. ROC curves for classification results with RF. (a) Parameter sets before wrapper selection. The AUCs on original and enhanced sets are 0.894 and 0.865 respectively. (b) Parameter sets after wrapper selection. The AUCs on original and enhanced sets are 0.940 and 0.908 respectively.
Fig. 8.
Fig. 8. Feature importance of $Y_{1}$, $Y_{2}$ and MM elements.

Tables (1)

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Table 1. Performance comparison with and without { Y 1 , Y 2 }

Equations (6)

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I = a 0 + n = 1 12 ( a n cos 2 n θ 1 + b n sin 2 n θ 1 )
I ( M i j , C ) = H ( C ) H ( C | M i j ) ]
J ( M i j ) = I ( M i j , C ) β M i j S I ( M i j , M i j ) + γ M i j S I ( M i j , M i j | C )
T C ( S ) = M i j S H ( M i j ) H ( S )
T C ( S ; G ) = T C ( S ) T C ( S | G ) = M i j S I ( M i j , G ) I ( S , G )
max S j , p ( y j | S j ) j = 1 l T C ( S j ; Y j ) s . t . | Y j | = r , S j S j j =