Multivariate Statistics Between Two-Observation Spaces

As mentioned in the previous chapter, industrial data are usually divided into two categories, process data and quality data, belonging to different measurement spaces. The vast majority of smart manufacturing problems, such as soft measurement, control, monitoring, optimization, etc., inevitably require modeling the data relationships between the two kinds of measurement variables. This chapter’s subject is to discover the correlation between the sets in different observation spaces.

Temporal and Spatial Water Quality Assessment for Rivers in Metropolitan Areas Using Multivariate Statistics and Water Quality Indices: A Case Study of the Geumho River, Korea

The Geumho River in South Korea passes through a metropolitan area with a high population density and multiple industrial complexes and, therefore, the water quality of this river is of significance for human health and economic activities. This study aims to assess the water quality of the Geumho River to inform river water quality management and improve pollution control using multivariate statistics and the Korean Water Quality Index (KWQI). Principal component and factor analysis identified those factors related to organic pollutants and metabolism (principal factor 1), and phosphorus and fecal coliform content (principal factor 2). In a cluster analysis, time was considered by distinguishing between seasons (spring, summer, autumn, and winter) and space was considered based on upstream (US), midstream (MS), and downstream (DS) river sections. Seven temporal variables and six spatial variables were extracted from the discriminant analysis (DA) results; the most important water quality variables were high during the spring and summer seasons and in the MS and DS regions. Temporally, the KWQI was highest in winter (70.9) and lowest in spring (59.2), whereas spatially, KWQI values were highest in the US (67.5) and lowest in the MS (56.4) sections. These results indicate that to be most effective, water management interventions in the Geumho River should focus on the urban midstream section and spring seasons.

Raman Spectroscopy and Oncology: Multivariate Statistics Methods for Cancer Grading

Over the last decade, Raman spectroscopy was demonstrated as a label-free and destructive optical spectroscopy that was able to improve diagnostic accuracy in cancer diagnosis. This ability is principally based on the great amount of biochemical information produced by the Raman scattering while investigating biological tissues. However, to achieve the relevant clinical requirements, the spectroscopic analysis and its ability to grade cancer tissues require sophisticated multivariate statistics. In this paper, we critically review multivariate statistics methods analyzed in light of their ability to process datasets generated by Raman spectroscopy in chondrogenic tumors, where distinguishing between enchondroma and the first grade of malignancy is a critical problem for pathologists.