This paper presents a novel algorithm for analysis of stochastic processes. The algorithm can be used to nd the required solutions in the cases of principal component analysis (PCA), partial least squares (PLS), canonical correlation analysis (CCA) or multiple linear regression (MLR). The algorithm is iterative and sequential in its structure and uses on-line stochastic approximation to reach a...

This paper addresses the development of a new algorithm for parameter estimation of ordinary differential equations. Here, we show that (1) the simultaneous approach combined with orthogonal cyclic reduction can be used to reduce the estimation problem to an optimization problem subject to a fixed number of equality constraints without the need for structural information to devise a stable embe...

The connected vertex cover problem is a variant of the vertex cover problem, in which a vertex cover is additional required to induce a connected subgraph in a given connected graph. The problem is known to be NP-hard and to be at least as hard to approximate as the vertex cover problem is. While several 2-approximation NC algorithms are known for vertex cover, whether unweighted or weighted, n...

It is a well known fact that sequential algorithms which exhibit a strong ”local” nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number of colors. Surprisingly, this well known idea was never formally stated as a unified framework. In this paper we aim to define a robust family of local seque...

This paper presents a new indiscernibility-based rough agglomerative hierarchical clustering algorithm for sequential data. In this approach, the indiscernibility relation has been extended to a tolerance relation with the transitivity property being relaxed. Initial clusters are formed using a similarity upper approximation. Subsequent clusters are formed using the concept of constrained-simil...

We consider the problem of high-dimensional filtering state-space models (SSMs) at discrete times. This is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can have a cost that scales exponentially with dimension hidden state. Inspired by lag-approximation for smoothing [G. Kitagawa S. Sato, Monte Carlo self-organising model, ...

Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a science until this day. This paper proposes a sequential approach to adding new clusters of nodes and their interactions (i.e. “regions”) to the approximation. We...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...