Statistics – Machine Learning
Scientific paper
2012-02-11
Statistics
Machine Learning
Scientific paper
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include flattening the data and applying matrix factorizations such as principal components analysis (PCA) or employing tensor decompositions such as the CANDECOMP / PARAFAC (CP) and Tucker decompositions. The former can lose important structure in the data, while the latter Higher-Order PCA (HOPCA) methods can be problematic in high-dimensions with many irrelevant features. We introduce frameworks for sparse tensor factorizations or Sparse HOPCA based on heuristic algorithmic approaches and by solving penalized optimization problems related to the CP decomposition. Extensions of these approaches lead to methods for general regularized tensor factorizations, multi-way Functional HOPCA and generalizations of HOPCA for structured data. We illustrate the utility of our methods for dimension reduction, feature selection, and signal recovery on simulated data and multi-dimensional microarrays and functional MRIs.
No associations
LandOfFree
Regularized Tensor Factorizations and Higher-Order Principal Components Analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Regularized Tensor Factorizations and Higher-Order Principal Components Analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularized Tensor Factorizations and Higher-Order Principal Components Analysis will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-371374