Two-Dimensional Principal Component Analysis and Its Extensions

Sanguansat, Parinya

doi:10.5772/36892

Cited by 32 publications

(33 citation statements)

References 35 publications

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“…The Principal Components Analysis is a powerful statistical technique capable of identifying and quantifying orthogonal contributions to the total variance of a collection of data [18]. It has already been applied in the analysis of data of goniochormatic materials [14,15,[19][20][21][22].…”

Section: Appendix: Principal Components Analysis On Spectral Brdfmentioning

confidence: 99%

Color characterization of coatings with diffraction pigments

et al. 2016

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Coatings with diffraction pigments present high iridescence, which needs to be characterized to describe their appearance. The spectral Bidirectional Reflectance Distribution Function (BRDF) of six coatings with SpectraFlair diffraction pigments were measured using the robot-arm-based goniospectrophotometerer GEFE, designed and developed at CSIC. Principal Components Analysis (PCA) has been applied to study the coatings' BRDF data. From data evaluation and based in theoretical considerations, we propose a relevant geometric factor to study the spectral reflectance and color gamut variation of coatings with diffraction pigments. At fixed values of this geometrical variable, the spectral BRDF component due to diffraction is almost constant. Commercially-available portable goniospectrophotometers, extensively used in several industries (automotive and others), have to be provided with more aspecular measurement angles to characterize goniochromatic coatings based on diffraction pigments.

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Section: Appendix: Principal Components Analysis On Spectral Brdfmentioning

confidence: 99%

Color characterization of coatings with diffraction pigments

et al. 2016

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“…For 2DPCA, let data be represented by a matrix B with the dimension of m × n . Linear projection of the matrix B is considered as follows [3–5]:

\begin{matrix} y = B x . \end{matrix}

Here x is an n dimensional project axis, and y is the projected feature of this data on x called principal component vector. E is mean:

\begin{matrix} W_{x} = E (y - E y) {(y - E y)}^{T} . \end{matrix}

Here W x is the covariance matrix of the project feature vector.…”

Section: Methodsmentioning

confidence: 99%

“…The SSS problem will be removed when performing 2DPCA due to a different algorithm from the PCA. More detailed contents about the algorithm of 2DPCA can be read from the studies of Fukunnaga [3], Kong et al [4], and Sanguansat [5]. …”

Section: Methodsmentioning

confidence: 99%

Ionospheric Anomalies Related to the (M = 7.3), August 27, 2012, Puerto Earthquake, (M = 6.8), August 30, 2012 Jan Mayen Island Earthquake, and (M = 7.6), August 31, 2012, Philippines Earthquake: Two‐Dimensional Principal Component Analysis

Lin

2013

The Scientific World Journal

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Two-dimensional principal component analysis (2DPCA) and principal component analysis (PCA) are used to examine the ionospheric total electron content (TEC) data during the time period from 00:00 on August 21 to 12: 45 on August 31 (UT), which are 10 days before the M = 7.6 Philippines earthquake at 12:47:34 on August 31, 2012 (UT) with the depth at 34.9 km. From the results by using 2DPCA, a TEC precursor of Philippines earthquake is found during the time period from 4:25 to 4:40 on August 28, 2012 (UT) with the duration time of at least 15 minutes. Another earthquake-related TEC anomaly is detectable for the time period from 04:35 to 04:40 on August 27, 2012 (UT) with the duration time of at least 5 minutes during the Puerto earthquake at 04: 37:20 on August 27, 2012 (UT) (M w = 7.3) with the depth at 20.3 km. The precursor of the Puerto earthquake is not detectable. TEC anomaly is not to be found related to the Jan Mayen Island earthquake (M w = 6.8) at 13:43:24 on August 30, 2012 (UT). These earthquake-related TEC anomalies are detectable by using 2DPCA rather than PCA. They are localized nearby the epicenters of the Philippines and Puerto earthquakes.

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“…This contribution represents, the relative importance of the indicators (weights) shown in Table 4 (Alleva and Falorsi, 2009;Sanguansat, 2012). The aggregation method chosen in this paper is the "Weighted Linear Combination" (WLC) that was already applied in other works on environmental analysis (Comber et al, 2010;Carver et al, 2012Carver et al, , 2013Orsi et al, 2013).…”

Section: Biodiversity In Tuscany Regionmentioning

confidence: 99%