Jonathan T. Purnell

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We present a maximum likelihood method for determining the spatial properties of tidal debris and of the Galactic spheroid. With this method we characterize Sagittarius debris using stars with the colors of blue F turnoff stars in SDSS stripe 82. The debris is located at (α, δ, R) = (31.37 • ± 0.26 • , 0.0 • , 29.22 ± 0.20 kpc), with a (spatial) direction(More)
Data from the Sloan Digital Sky Survey has given evidence of structures within the Milky Way halo from other nearby galaxies. Both the halo and these structures are approximated by densities based on geometric objects. A model of the data is formed by a mixture of geometric densities. By using an EM-style algorithm, we optimize the parameters of our model(More)
Clustering social networks is vital to understanding online interactions and influence. This task becomes more difficult when communities overlap, and when the social networks become extremely large. We present an efficient algorithm for constructing overlapping clusters, roughly linear in the size of the network. The algorithm first embeds the graph and(More)
— Clustering social networks is vital to understanding online interactions and influence. This task becomes more difficult when communities overlap, and when the social networks become extremely large. We present an efficient algorithm for constructing overlapping clusters, (approximately linear). The algorithm first embeds the graph and then performs a(More)
Covariance matrices capture correlations that are invaluable in modeling real-life datasets. Using all d 2 elements of the covariance (in d dimensions) is costly and could result in over-fitting; and the simple diagonal approximation can be over-restrictive. In this work, we present a new model, the Low-Rank Gaussian Mixture Model (LRGMM), for modeling data(More)
Covariance matrices capture correlations that are invaluable in mod-eling real-life datasets. Using all d 2 elements of the covariance (in d dimensions) is costly and could result in over-fitting; and the simple diagonal approximation can be over-restrictive. We present an algorithm that improves upon the diagonal matrix by allowing a low rank perturbation.(More)
Accent identification has grown over the past decade. There has been decent success when a priori knowledge about the accents is available. A typical approach entails detection of certain syllables and phonemes, which in turn requires phoneme-based models. Recently, Gaussian Mixture Models (GMMs) have been used as an unsupervised alternative to these(More)
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