PCA Tomography: how to extract information from data cubes

Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies, it is possible to obtain data cubes in which one combines both techniques simultaneously, producing images with spectral resolution. To extract information from them can be quite complex, and hence the development of new methods of data analysis is desirable. We present a method of analysis of data cube (data from single field observations, containing two spatial and one spectral dimension) that uses Principal Component Analysis (PCA) to express the data in the form of reduced dimensionality, facilitating efficient information extraction from very large data sets. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates ordered by principal components of decreasing variance. The new coordinates are referred to as eigenvectors, and the projections of the data on to these coordinates produce images we will call tomograms. The association of the tomograms (images) to eigenvectors (spectra) is important for the interpretation of both. The eigenvectors are mutually orthogonal, and this information is fundamental for their handling and interpretation. When the data cube shows objects that present uncorrelated physical phenomena, the eigenvector`s orthogonality may be instrumental in separating and identifying them. By handling eigenvectors and tomograms, one can enhance features, extract noise, compress data, extract spectra, etc. We applied the method, for illustration purpose only, to the central region of the low ionization nuclear emission region (LINER) galaxy NGC 4736, and demonstrate that it has a type 1 active nucleus, not known before. Furthermore, we show that it is displaced from the centre of its stellar bulge.

Use of Information Visualization Methods Eliminating Cross Talk in Multiple Sensing Units Investigated for a Light-Addressable Potentiometric Sensor

The integration of nanostructured films containing biomolecules and silicon-based technologies is a promising direction for reaching miniaturized biosensors that exhibit high sensitivity and selectivity. A challenge, however, is to avoid cross talk among sensing units in an array with multiple sensors located on a small area. In this letter, we describe an array of 16 sensing units, of a light-addressable potentiometric sensor (LAPS), which was made with layer-by-Layer (LbL) films of a poly(amidomine) dendrimer (PAMAM) and single-walled carbon nanotubes (SWNTs), coated with a layer of the enzyme penicillinase. A visual inspection of the data from constant-current measurements with liquid samples containing distinct concentrations of penicillin, glucose, or a buffer indicated a possible cross talk between units that contained penicillinase and those that did not. With the use of multidimensional data projection techniques, normally employed in information Visualization methods, we managed to distinguish the results from the modified LAPS, even in cases where the units were adjacent to each other. Furthermore, the plots generated with the interactive document map (IDMAP) projection technique enabled the distinction of the different concentrations of penicillin, from 5 mmol L(-1) down to 0.5 mmol L(-1). Data visualization also confirmed the enhanced performance of the sensing units containing carbon nanotubes, consistent with the analysis of results for LAPS sensors. The use of visual analytics, as with projection methods, may be essential to handle a large amount of data generated in multiple sensor arrays to achieve high performance in miniaturized systems.