Eigengalaxies: Galaxy Morphology as a Linear Image Space and its Applications
In this thesis I contextualise the history of morphology as underpinned by Hubble's scheme, discrete in nature, and deeply connected to theories of galaxy formation history. I set out in contrast, to describe a purely empirical morphology, continuous in nature, in which surveys become image spaces and galaxies become points, the meaning of which is sought by the quantifiable differences of their relative spatial positions. I show how an image space can be robustly constructed and then build upon it to illustrate important applications such as approximating surveys with small samples, detecting outliers, clustering, similarity search and missing data prediction. The thesis proceeds as follows. Section 1 briefly surveys the importance, genesis and recent history of galaxy morphology. It also lays out the objectives of the thesis and information about the survey data which I have used. Section 2 describes how galaxy images can be processed and projected to a defensible low dimensional space in a morphology preserving way. Several analyses are then performed to test the fidelity of the projection. It is also shown how the image space can be given a probabilistic interpretation. Section 3 discusses methods for approximating surveys by reducing the number of objects under consideration. The section starts by describing simple random sampling and its limitations. It then shows how means and covariances can be used to summarise image spaces and how differences between image spaces can be quantified using the Kullback-Leibler divergence. This concept is then used to apply “leverage scores" sampling as a means to use information from the galaxy population to create a weighted sampling scheme which preserves mean and covariance better than random sampling and therefore enables much smaller representative samples. I also motivate and describe a cutting edge “coresets" methodology which I intend to more fully explore in future work. Section 4 demonstrates parsimonious applications of the image space framework to common use cases such as clustering, similarity search and outlier detection. It is a modified and abridged version of a paper to be published in MNRAS with some modification. Finally, section 5 draws summary conclusions and highlights important directions for the future.
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