Single Bit and Reduced Dimension Diffusion Strategies Over Distributed Networks

We introduce novel diffusion based adaptive estimation strategies for distributed networks that have significantly less communication load and achieve comparable performance to the full information exchange configurations. After local estimates of the desired data is produced in each node, a single bit of information (or a reduced dimensional data vector) is generated using certain random projections of the local estimates. This newly generated data is diffused and then used in neighboring nodes to recover the original full information. We provide the complete state-space description and the mean stability analysis of our algorithms.Comment: Submitted to the IEEE Signal Processing Letter

Compressive Diffusion Strategies Over Distributed Networks for Reduced Communication Load

We study the compressive diffusion strategies over distributed networks based on the diffusion implementation and adaptive extraction of the information from the compressed diffusion data. We demonstrate that one can achieve a comparable performance with the full information exchange configurations, even if the diffused information is compressed into a scalar or a single bit. To this end, we provide a complete performance analysis for the compressive diffusion strategies. We analyze the transient, steady-state and tracking performance of the configurations in which the diffused data is compressed into a scalar or a single-bit. We propose a new adaptive combination method improving the convergence performance of the compressive diffusion strategies further. In the new method, we introduce one more freedom-of-dimension in the combination matrix and adapt it by using the conventional mixture approach in order to enhance the convergence performance for any possible combination rule used for the full diffusion configuration. We demonstrate that our theoretical analysis closely follow the ensemble averaged results in our simulations. We provide numerical examples showing the improved convergence performance with the new adaptive combination method.Comment: Submitted to IEEE Transactions on Signal Processin

Data Imputation through the Identification of Local Anomalies

We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework, we propose i) a novel algorithm to efficiently separate, i.e., detect and localize, possible corruptions from a given suspicious data instance and ii) a Maximum A Posteriori (MAP) estimator to impute the corrupted data. As a generalization to Euclidean distance, we also propose a novel distance measure, which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions. Our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted (clean) reference data set. Once each part is labeled as anomalous vs normal, the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed. Under a certain conditional independency structure assumed for the binary patterns, we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning. The proposed framework is tested over several well-known machine learning data sets with synthetically generated corruptions; and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities. Our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions