This report proposes a model to predict the location of the most deprived areas in a city using data from the census. A census data is very high dimensional and needs to be simplified. We use a novel algorithm to reduce dimensionality and find patterns: The diffusion map. Features are defined by eigenvectors of the Laplacian matrix that defines the diffusion map. Eigenvectors corresponding to the smallest eigenvalues indicate specific population features. Previous work has found qualitatively that the second most important dimension for describing the census data in Bristol is linked to deprivation. In this report, we analyse how good this dimension is as a model for predicting deprivation by comparing with the recognised measures. The Pearson correlation coefficient was found to be over 0.7. The top 10 per cent of deprived areas in the UK which also locate in Bristol are extracted to test the accuracy of the model. There are 52 most deprived areas, and 38 areas are correctly identified by comparing to the model. The influence of scores of IMD domains that do not correlate with the models, Eigenvector 2 entries of non-deprived OAs and orthogonality of Eigenvectors cause the model to fail the prediction of 14 deprived areas. However, overall, the model shows a high performance to predict the future deprivation of overall areas where the project considers. This project is expected to support the government to allocate resources and funding.

We apply a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors, to study the diversity of galaxies. This technique permits us to characterize empirically the natural variations in observed spectra data, and we illustrate how this approach can be used in an exploratory manner to highlight both large-scale global as well as small-scale local structure in Sloan Digital Sky Survey (SDSS) data. We use this method in a way that simultaneously takes into account the measurements of spectral lines as well as the continuum shape. Unlike Principal Component Analysis, this method does not assume that the Euclidean distance between galaxy spectra is a good global measure of similarity between all spectra, but instead it only assumes that local difference information between similar spectra is reliable. Moreover, unlike other nonlinear dimensionality methods, this method can be used to characterize very finely both small-scale local as well as large-scale global properties of realistic noisy data. The power of the method is demonstrated on the SDSS Main Galaxy Sample by illustrating that the derived embeddings of spectra carry an unprecedented amount of information. By using a straightforward global or unsupervised variant, we observe that the main features correlate strongly with star formation rate and that they clearly separate active galactic nuclei. Computed parameters of the method can be used to describe line strengths and their interdependencies. By using a locally-biased or semi-supervised variant, we are able to focus on typical variations around specific objects of astronomical interest. We present several examples illustrating that this approach can enable new discoveries in the data as well as a detailed understanding of very fine local structure that would otherwise be overwhelmed by large-scale noise and global trends in the data.