let s be a locally compact foundation semigroup with identity and                          be its semigroup algebra. let x be a weak*-closed left translation invariant subspace of    in this paper, we prove that  x  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. we also prove that a foundation semigroup with identity s is left amenab...

We design an on-line algorithm for Principal Component Analysis. The instances are projected into a probabilistically chosen low dimensional subspace. The total expected quadratic approximation error equals the total quadratic approximation error of the best subspace chosen in hindsight plus some additional term that grows linearly in dimension of the subspace but logarithmically in the dimensi...

The paper deals with robust direction of arrival (DOA) estimation based on independent component analysis (ICA) in the presence of sensor gain perturbation and unknown noise fields. It has been shown that the noise subspace based estimator suffers from the drawback of being very sensitivity to orthogonality between the estimated noise subspace and true signal subspace. However, no single subspa...

It is a common practice that a matrix, the de facto image representation, is first converted into a vector before fed into subspace analysis or kernel method; however, the conversion ruins the spatial structure of the pixels that defines the image. In this paper, we propose two kernel subspace methods that are directly based on the matrix representation, namely matrix-based kernel principal com...

Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with having high input dimensionality, estimation becomes a daunting task. A popular approach to overcome the problem associated time-consuming and expensive evaluations building surrogate model. However, these efficient models suffer from curse of dimensionality. Hence, training m...

Using Joint Factor Analysis (JFA) supervector for subspace analysis has many problems, such as high processing complexity and over-fitting. We propose an analysis framework based on random subspace sampling to address these problems. In this framework, JFA supervectors are first partitioned equally and each partitioned subvector is projected on to a subspace by PCA. All projected subvectors are...