6533b873fe1ef96bd12d5570

RESEARCH PRODUCT

JOINT TOPOLOGY LEARNING AND GRAPH SIGNAL RECOVERY VIA KALMAN FILTER IN CAUSAL DATA PROCESSES

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In this paper, a joint graph-signal recovery approach is investigated when we have a set of noisy graph signals generated based on a causal graph process. By leveraging the Kalman filter framework, a three steps iterative algorithm is utilized to predict and update signal estimation as well as graph topology learning, called Topological Kalman Filter or TKF. Similar to the regular Kalman filter, we first predict the a posterior signal state based on the prior available data and then this prediction is updated and corrected based on the recently arrived measurement. But contrary to the conventional Kalman filter algorithm, we have no information of the transition matrix and hence we relate this matrix to the graph weight matrix which can be extracted by graph topology estimation. Thus, given the set of updated graph signals, we update the graph topology estimate so as the graph weight and the state transition matrices. Since the proposed method is recursive and can update estimates online, it can keep track of changes in the underlying graph topology and signals based on the sequential arrival of new data and moreover, it suits for non-stationary processes. The experimental results show that for different scenarios, TKF has a lower mean squared error of the signal estimation when we compare it with the error of an available batch approach. Moreover, the proposed TKF has a low normalized mean squared error in terms of the graph topology inference and achieves the error associated to the batch method rapidly when the number of measurements increases.