Regularized Non-Negative Matrix Factorization for Dynamic and Relational Data

نویسندگان

  • Shawn Mankad
  • George Michailidis
چکیده

Data involving repeated measurements of several variables over different factors, experimental conditions or time may exhibit correlations among variables, as well as between factors. The discovery of these underlying, meaningful relations is important to a wide variety of areas such as psychology, signal processing, finance, among others. Common methods such as independent component analysis, factor analysis, tensor decomposition and others provide a great deal of flexibility, but may not contain any model information and hence are susceptible to noise. We discuss the development and application of a novel regularization framework for non-negative matrix factorization for feature extraction and latent source separation of dynamic and relational data. Our framework allows for the incorporation of expert knowledge and model information, resulting in decompositions that are more interpretable and robust to noise. To fit our modeling framework, we develop two algorithms that have received extensive focus in the NMF literature: multiplicative and alternating least squares. We also provide a systematic approach to parameter selection through cross-validation. To illustrate our modeling framework, we discuss multidimensional time-series data and apply our framework to a time-course fMRI study.

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تاریخ انتشار 2011