The recent paper (Cheung 2001) has studied the blind identification of Gaussian source process through a general temporal independent component analysis (ICA) approach named dual autoregressive modelling. It is actually a temporal extension of the classical principal component analysis without considering the principal order of the components. In this paper, we will further show the identifiabl...

We consider the dimensionality-reduction problem for a contaminated data set in a very high dimensional space, i.e., the problem of finding a subspace approximation of observed data, where the number of observations is of the same magnitude as the number of variables of each observation, and the data set contains some outlying observations. We propose a High-dimension Robust Principal Component...

Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduction approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, the existing robust PCA methods incorrectly center the data using the `2-norm distance to calculate the mean, which actually is not the optimal mean due to the `1-norm used in ...

Safeguarding the energy security is an important energy policy goal of every country. Assuring sufficient and reliable resources of energy at affordable prices is the main objective of energy security. Due to such reasons as special geopolitical position, terrorist attacks and other unrest in the Middle East, securing Iran’s energy demand and increasing her natural gas exports have turned into ...

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, it is difficult to develop an effective multilinear PCA method with the orthog...

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly orthogonal to the true eigenvector. A sparse structure is then commonly assumed along with a low rank structure. Recently, minimax estimation rates of sparse PCA ...

In the presence of outliers, the existing self-organizing rules for Principal Component Analysis (PCA) perform poorly. Using statistical physics techniques including the Gibbs distribution, binary decision fields and effective energies, we propose self-organizing PCA rules which are capable of resisting outliers while fulfilling various PCA-related tasks such as obtaining the first principal co...