Spatial and Temporal Methods Spatial data and time-varying, or sequential data pose unique modeling challenges. fastlab Big Ideas People Stuff FuncICA for Time Series Pattern Discovery Nishant Mehta and Alexander Gray SIAM International Conference on Data Mining (SDM) 2009 An Independent Component Analysis (ICA) for data where each point is a function, such as a time series. [pdf] Abstract: We introduce FuncICA, a new independent component analysis method for pattern discovery in inherently functional data, such as time series data. FuncICA can be considered an analog to functional principal component analysis, where instead of extracting components to minimize L2 reconstruction error, we maximize independence of the components over the functional observations. We develop an algorithm for extracting independent component curves and offer a method for optimizing a smoothing parameter. Results for synthetic, gene expression, and event-related potential data indicate that FuncICA can recover well-known phenomena and improve classification accuracy, highlighting the utility of FuncICA for unsupervised learning in temporal data. @Inproceedings{mehta2009funcica, Author = "Nishant Mehta and Alexander Gray", Title = "{FuncICA for Time Series Pattern Discovery}", Booktitle = "{SIAM International Conference on Data Mining (SDM)}, Year = "2009" } Fast Algorithms and Efficient Statistics: n-Point Correlation Functions Andrew W. Moore, Andy J. Connolly, Chris Genovese, Alexander G. Gray, Larry Grone, Nick Kanidoris II, Robert C. Nichol, Jeff Schneider, Alex S. Szalay, Istvan Szapudi, and Larry Wasserman Mining the Sky, 2001 The paper which introduced our fast algorithm for n-point correlation functions to astronomy, and explained our algorithm in more detail. [pdf] Abstract: We present here a new algorithm for the fast computation of N-Point correlation functions in large astronomical data sets. The algorithm is based on kdtrees which are decorated with cached sufficient statistics thus allowing for orders of magnitude speed-ups over the naive non-tree-based implementation of correlation functions. We further discuss the use of controlled approximations within the computation which allows for further acceleration. In summary, our algorithm now makes it possible to compute exact, all-pairs, measurements of the 2, 3 and 4-Point correlation functions for cosmological data sets like the Sloan Digital Sky Survey (SDSS; York et al. 2000) and the next generation of Cosmic Microwave Background experiments (see Szapudi et al. 2000). @inproceedings{moore2000npt, author = "A. Moore and A. Connolly and C. Genovese and Alexander G. Gray and L. Grone and N. Kanidoris and R. Nichol and J. Schneider and A. Szalay and I. Szapudi and L. Wasserman", Title = "{Fast Algorithms and Efficient Statistics: $n$-point Correlation Functions}", Booktitle = "{Proceedings of MPA/MPE/ESO Conference Mining the Sky}", Year = "2000" } Isee elsewhere Fast n-point Correlations The n-point correlation functions, which constitute the foundation of spatial statistics, are a special case of generalized N-body problem. This is the context in which our fast algorithms for n-point functions were first introduced. [see full entry here] Iin progress Fast Hidden Markov Model Learning A new approach to learning HMMs, which is very efficient for massive time series.