We propose a face difference model that decomposes face difference into three components, intrinsic difference, transformation difference, and noise. Using the face difference model and a detailed subspace analysis on the three components we develop a unified framework for subspace analysis. Using this framework we discover the inherent relationship among different subspace methods and their un...

The work presented in this paper employs multiscale subspace grids for pattern recognition applications. The proposed approach addresses the curse of dimensionality problem often associated with this task. The paper uses a multi-scale approach where coarse scale, being stable and generic in nature, suits well for small sample sizes, and fine scales, being more specialized in nature, enhance cla...

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In this paper a generalization of Post Nonlinear Independent Component Analysis (PNL-ICA) to Post Nonlinear Independent Subspace Analysis (PNL-ISA) is presented. In this framework sources to be identified can be multidimensional as well. For this generalization we prove a separability theorem: the ambiguities of this problem are essentially the same as for the linear Independent Subspace Analys...

Generalized Canonical Correlation Analysis (GCCA) is an important tool that finds numerous applications in data mining, machine learning, and artificial intelligence. It aims at finding `common' random variables are strongly correlated across multiple feature representations (views) of the same set entities. CCA to a lesser extent GCCA have been studied from statistical algorithmic points view,...

The increasing use of multiple sensors, which produce a large amount multi-dimensional data, requires efficient representation and classification methods. In this paper, we present new method for data that relies on two premises: (1) are usually represented by tensors, since brings benefits from multilinear algebra established tensor factorization methods; (2) can be described subspace vector s...

In many real-world applications data exhibits non-stationarity, i.e., its distribution changes over time. One approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain computer interface (BCI) data analysis this is sometimes achieved using stationary subspace analysis (SSA). The classic SSA method finds a matrix that project...