Three-Mode Abstracts, Part Y

INDEX

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• Yakovleva, E., Hopke, P.K., & Wallace, L. (1999).
  Receptor modeling assessment of particle total exposure assessment methodology data. Environmental Science & Technology, 33, 3645-3652.
  Data from the 1991 Particle Total Exposure Assessment Methodology (PTEAM) study in Riverside, CA, were analyzed using a new receptor modeling method. Positive matrix factorization analysis (Paatero, 1997) was performed on the three-way array that was constructed with the following modes: (1) elemental concentrations (18 variables), (2) samples (303 measurements), (3) sampling type (personal PM₁₀, indoor PM₁₀, outdoor PM₁₀, indoor PM_2.5, outdoor PM_2.5) in order to describe the sources of personal exposure. The three-way PMF solution for these data yielded both factor profiles and their contributions and in addition provided the distribution of each source between personal/indoor/outdoor fine/coarse PM, allowing the analysis of the influence of outdoor sources on personal particulate exposure. To identify relative contribution of different sources, regression of the particulate matter mass against the factor contributions was performed.

• Yanai, H. (1994).
  Tahenryo data kaiseki-ho: Riron to ohyo [Methods of multivariate data analysis: Theory and applications]. Chapter 8 (pp. 151-159). Tokyo: Asakura-shoten.
  Overview of three-way methods and their estimation, e.g. Tucker3, INDSCAL and PARAFAC.

                             

• Yoshino, Y. (1986).
  Dimensional subtypes of depression derived by three-mode factor analysis. Kyushu Neuro psychiatry, 32, 245-257.
  Studied the dimensional subtypes of depression reflecting the therapeutic response to 4 wks of antidepressant therapy. Human subjects: 55 male and female Japanese adults (aged 20-79 yrs) (depression). Psychic and somatic changes were assessed before drug administration and weekly thereafter for 4 wks using the Clinical Psychopharmacology Research Group Depression Rating Scale for Doctor's Use. Longitudinal data were subjected to three-mode factor analysis (55 Ss * 20 scales * 5 occasions).

• Yoshizawa, T. (1975).
  Models for quantification techniques in multiple contingency tables: The theoretical approach. Kodokeiryogaku (Japanese Journal of Behaviormetrics), 3, 1-11.; English abstract, p. 82.
  Models which may decompose the three variable interaction in rxsxt contingency tables are proposed, the models for the additive and multiplicative definition of no interaction being extended. One of those models makes possible an interferential approach to Iwatsubo's (1974) quantification technique, which is regarded as a statistically description-oriented method. The equivalence of our chi- square criterion to the maximization of the third order correlation coefficient p (rho) is shown. Several properties of the new models are derived, including the n.s. conditions that the p vanishes and the exact upper bound of p squared. Many versions of the models and testing procedures for them are suggested.

  

• Yoshizawa, T. (1976).
  A generalized definition of interactions and singular value decomposition of multiway arrays. Kodokeiryogaku (Japanese Journal of Behaviormetrics), 4, 32-42.; English abstract, p. 87.
  A generalized definition of the sth order interactions is given for multiway arrays, from which the similar properties with ANOVA model are derived. The problem of maximization of the highest order correlation function is solved. Moreover, an expression decomposing multiway arrays is shown as a recurrent algorithm that is an extension of the singular value decomposition of matrices. Applications of the decomposition to multiway contingency tables and to the multiway classified data are outlined. This research develops Iwatsubo (1974) and Yoshizawa (1975), and relates with Bahadur's expression and Lancaster's definition of no interaction for contingency tables. The definition and expression given here are more general and constructive than theirs.

• Yoshizawa, T. (1988).
  Singular value decomposition of multiarray data and its applications. In E. Diday, C. Hayashi, M. Jambu, & N. Ohsumi (Eds.), Recent Developments in Clustering and Data Analysis: Proceedings of the Japanese-French Scientific Seminar, March 24-26, 1987 (pp. 241-257). Boston: Academic Press, Inc.
  In this paper, the theory of singular value decomposition of multiarray data is roughly sketched. The configuration of the extended singular value decomposition is demonstrated, in comparison with the Tucker-3 model for three way data. Next, the criteria and algorithms needed to derive the decomposition, the nested configuration and its interpretation are described. Finally, some applications are given.

• Young, F.W. (1981).
  Quantitative analysis of qualitative data.Psychometrika,46, 357-388
  Presents an overview of an approach to the quantitative analysis of qualitative data with theoretical and methodological explanations of its basis in alternating least squares and optimal scaling. Using these 2 principles, analysis procedures originally proposed for quantitative (interval or ratio) data are extended to qualitative (nominal or ordinal) data, including common factor and three-mode factor analysis and multidimensional scaling. If a least squares procedure is known for analyzing quantitative data, it can be extended to qualitative data and the resulting algorithm will be convergent.

  
             

• Yue, H. H., Qin, S. J., Markle, R. J., Nauert, C., & Gatto, M. (2000).
  Fault detection of plasma etchers using optical emission spectra. IEEE Transactions on Semiconductor Manufacturing, 13, 374-385.
  The objective of this paper is to investigate the suitability of using optical emission spectroscopy (OES) for the fault detection and classification of plasma etchers. The OES sensor system used in this study can collect spectra at up to 512 different wavelengths, Multiple scans of the spectra are taken from a wafer, and the spectra data are available for multiple wafers, As a result, the amount of the OES data is typically large, This poses a difficulty in extracting relevant information for fault detection and classification, In this paper, we propose the use of multiway principal component analysis (PCA) to analyze the sensitivity of the multiple scans within a wafer with respect to typical faults such as etch stop, which is a fault that occurs when the polymer deposition rate is larger than the etch rate, Several PCA-based schemes are tested for the purpose of fault detection and wavelength selection, A sphere criterion is proposed for wavelength selection and compared with an existing method in the literature. To construct the final monitoring model, the OES data of selected wavelengths are properly scaled to calculate fault detection indices, Reduction in the number of wavelengths implies reduced cost for implementing the fault detection system. All experiments are conducted on an Applied Materials 5300 oxide etcher at Advanced Micro Devices (AMD) in Austin, TX.

           

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