Welcome to the AMADA - Analysis of Muldimensional Astronomical DAtasets
AMADA allows an iterative exploration and information retrieval of high-dimensional data sets. This is done by performing a hierarchical clustering analysis for different choices of correlation matrices and by doing a principal components analysis in the original data. Additionally, AMADA provides a set of modern visualization data-mining diagnostics. The user can switch between them using the different tabs.
AMADA allows the users to either use available datasets or upload their own. Check the bottom of the 'Import Dataset' panel to see if the data have been properly imported. The data can be seen on the screen by clicking in the tab "Dataset" on the main page.
The enclosed datasets are examples following the same nomenclature of their respective source articles. I suggest the user to check the original articles or catalogs for a better understanding of their meaning.
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Supernova host properties (Table 1, Sako, M. et al. 2014): Type Ia and II Supernova host-galaxy properties from Sloan Digital Sky Survey multi-band photometry.
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Mock galaxy catalog (Guo et al. 2011): Galaxy semi-analytic formation models build on top of the Millennium (Springel et al. 2005) and Millenium II simulations (Boylan-Kolchin et al. 2009).
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ZENS catalog (Carollo et al. 2012, Cibinel et al. 2012, Cibinel et al. 2013): The Zurich ENvironmental Study (ZENS) is a survey of galaxy groups in the local universe. The sample consists of 141 groups in the redshift range 0.05 < z < 0.0585.
Data must be imported as a CSV/TXT format, columns are named and separated by spaces. It may contain an arbitrary number of columns and rows. If missing data is present, it should be marked as NA.
On the left panel, the user can choose among different methods of analysis and visualization. Once the combination is chosen, click on the button "make it so" to update the plots.
Fraction of data to display choose the percentage of data displayed on the screen.
Correlation method: pearson, spearman or maximum information coefficient.
Display numbers choose if correlation coefficients should be displayed in the heatmap.
Dendrogram type: phylogram, cladrogram or fan.
Graph layout: spring or circular.
Number of PCs choose the number or principal components to display as Nightingale charts.
PCA method: standard PCA or robust PCA.
The current version of AMADA allows the user to choose among different types of correlation methods and PCA analysis.
PCA A orthogonal transformation that linearly convert a dataset into a set of uncorrelated variables called principal components (PCs). The PCs are computed by diagonalization of the data correlation matrix, with the resulting eigenvectors corresponding to PCs and the resulting eigenvalues to the variance explained by the PCs. The eigenvector corresponding to the largest eigenvalue gives the direction of greatest variance (PC1), the second largest eigenvalue gives the direction of the next highest variance (PC2), and so on (e.g., Jolliffe 2002).
Robust PCA Robust principal component analysis using the Projection–Pursuit principle. The data is projected on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized (Croux, Filzmoser and Oliveira, 2007).
One of the advantages of hierarchical clustering is the needless of a prior specification of the number of clusters to be searched. Instead, the method requires a measurement of dissimilarity between groups of observations, which is based on the pairwise dissimilarities among the observations within each of two groups. The outcome is a hierarchical representations in which the clusters at each level of the hierarchy are created by merging clusters at the next lower level. We employ an agglomerative approach. Initially each variable is assigned to its own cluster, then the method recursively merges a selected pair of clusters into a single cluster, where each new pair composed by merging the two groups with the smallest dissimilarity in the immediately lower level.
Number of Clusters To guide the user, we display an optimal number of clusters via Calinski and Harabasz, 1972 index. The groups are color-coded in the dendrogram and graph visualizations.
Pearson a measure of the linear correlation between two variables X and Y (Pearson 1895).
Spearman a measure of the monotonic correlation between two variables X and Y (Spearman 1904).
Maximum Information Coefficient a measure of linear or non-linear correlation between two variables X and Y (Reshef et al. 2011). The current version of MIC does not support NA.
AMADA offers many different plots to analyze your data set using correlation analysis and unsupervised learning.
These are the standard types of plots:
Heatmap Plots a correlation matrix color-coded by the correlation level between each pair of variables (e.g., Raivo Kolde, 2013).
Distogram Plots a distance matrix containing the distances, taken pairwise, of a all sets of variables (e.g., Aron Eklund, 2012). The distance being used is the correlation distance, given by d(x,y)= 1-|corr(x,y)|.
Dendrogram Plots the dendrogram of the hierarchical clustering applied to the catalog variables. Options are: Phylogram, Cladrogram or Fan. This type visualization is adapted from tools for Phylogenetic studies (e.g., Paradis et al. 2003).
Graph Plots a clustered graph is built in which vertices represent features and edge widths are weighted by the degree of correlation between each pair or variables (Epskamp et al. 2012).
Nightingale chart Plots a polar barplot whose lenght of the strips displays the relative contribution of each variable to the i-th Principal Component. This plot is inspired by the original chart from Nightingale 1858.
Probably one of the most influential visualizations of all time used by Florence Nightingale to convince Queen Victoria about improving hygiene at military hospitals, therefore saving lives of thousands of soldiers.
R Core Team (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL [http://www.R-project.org/](http://www. -project.org/).
ape, phytools, squash, fpc, minerva, MASS, corrplot, qgraph, ggplot2, ggthemes, reshape, pcaPP, mvtnorm