Compositional analysis of archaeological glasses

At CoDaWork'03 we presented work on the analysis of archaeological glass composi- tional data. Such data typically consist of geochemical compositions involving 10-12 variables and approximates completely compositional data if the main component, sil- ica, is included. We suggested that what has been termed `crude' principal component analysis (PCA) of standardized data often identi ed interpretable pattern in the data more readily than analyses based on log-ratio transformed data (LRA). The funda- mental problem is that, in LRA, minor oxides with high relative variation, that may not be structure carrying, can dominate an analysis and obscure pattern associated with variables present at higher absolute levels. We investigate this further using sub- compositional data relating to archaeological glasses found on Israeli sites. A simple model for glass-making is that it is based on a `recipe' consisting of two `ingredients', sand and a source of soda. Our analysis focuses on the sub-composition of components associated with the sand source. A `crude' PCA of standardized data shows two clear compositional groups that can be interpreted in terms of di erent recipes being used at di erent periods, re ected in absolute di erences in the composition. LRA analysis can be undertaken either by normalizing the data or de ning a `residual'. In either case, after some `tuning', these groups are recovered. The results from the normalized LRA are di erently interpreted as showing that the source of sand used to make the glass di ered. These results are complementary. One relates to the recipe used. The other relates to the composition (and presumed sources) of one of the ingredients. It seems to be axiomatic in some expositions of LRA that statistical analysis of compositional data should focus on relative variation via the use of ratios. Our analysis suggests that absolute di erences can also be informativeGeologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Consell Social de la Universitat de Girona; Ministerio de Ciencia i Tecnología

Big Data Analysis for PV Applications

With increasing photovoltaic (PV) installations, large amounts of time series data from utility-scale PV systems such as meteorological data and string level measurements are collected [1, 2]. Due to fluctuations in irradiance and temperature, PV data is highly stochastic. Spatio-temporal differences with potential time-lagged correlation are also exhibited, due to the wind directions affecting cloud movements [3]. Coupling these variations with different types of PV systems in terms of power output and wiring configuration, as well as localised PV effects like partial shading and module mismatches, lengthy time series data from solar systems are highly multi-dimensional and challenging to process. In addition, these raw datasets can rarely be used directly due to the possibly high noise and irrelevant information embedded in them. Moreover, it is challenging to operate directly on the raw datasets, especially when it comes to visualizing and analyzing these data. On this point, the Pareto principle, or better-known as the 80/20 rule, commonly applies: researchers and solar engineers often spend most of their time collecting, cleaning, filtering, reducing and formatting the data. In this work, a data analytics algorithm is applied to mitigate some of the complexities and make sense of the large time series data in PV systems. Each time series is treated as an individual entity which can be characterized by a set of generic or application-specific features. This reduces the dimension of the data, i.e., from hundreds of samples in a time series to a few descriptive features. It is is also easier to visualize big time series data in the feature space, as compared to the traditional time series visualization methods, such as the spaghetti plot and horizon plot, which are informative but not very scalable. The time series data is processed to extract features through clustering and identify correspondence between specific measurements and geographical location of the PV systems. This characterisation of the time series data can be used for several PV applications, namely, (1) PV fault identification, (2) PV network design and (3) PV type pre-design for PV installation in locations with different geographical attributes

BiplotGUI: Interactive Biplots in R

Biplots simultaneously provide information on both the samples and the variables of a data matrix in two- or three-dimensional representations. The BiplotGUI package provides a graphical user interface for the construction of, interaction with, and manipulation of biplots in R. The samples are represented as points, with coordinates determined either by the choice of biplot, principal coordinate analysis or multidimensional scaling. Various transformations and dissimilarity metrics are available. Information on the original variables is incorporated by linear or non-linear calibrated axes. Goodness-of-fit measures are provided. Additional descriptors can be superimposed, including convex hulls, alpha-bags, point densities and classification regions. Amongst the interactive features are dynamic variable value prediction, zooming and point and axis drag-and-drop. Output can easily be exported to the R workspace for further manipulation. Three-dimensional biplots are incorporated via the rgl package. The user requires almost no knowledge of R syntax.

Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.defuzzification, fuzzy coding, indicator matrix, measure of fit, multivariate data, multiple correspondence analysis, principal component analysis.

The coupling of action and perception in musical meaning formation

The embodied perspective on music cognition has stressed the central role of the body and body move- ments in musical meaning formation processes. In the present study, we investigate by means of a behavioral experiment how free body movements in response to music (i.e., action) can be linked to specific linguistic, metaphorical descriptions people use to describe the expressive qualities they perceive in the music (i.e., per- ception). We introduce a dimensional model based on the Effort/Shape theory of Laban in order to target musical expressivity from an embodied perspective. Also, we investigate whether a coupling between action and perception is dependent on the musical background of the participants (i.e., trained versus untrained). The results show that the physical appearance of the free body movements that participants perform in response to music are reliably linked to the linguistic descriptions of musical expressiveness in terms of the underlying quality. Moreover, this result is found to be independent of the participants’ musical background