A new algorithmic framework called denoising source separation (DSS) is introduced. The main benefit of this framework is that it allows for easy development of new source separation algorithms which are optimised for specific problems. In this framework, source separation algorithms are constucted around denoising procedures. The resulting algorithms can range from almost blind to highly specialised source separation algorithms. Both simple linear and more complex nonlinear or adaptive denoising schemes are considered. Some existing independent component analysis algorithms are reinterpreted within DSS framework and new, robust blind source separation algorithms are suggested. Although DSS algorithms need not be explicitly based on objective functions, there is often an implicit objective function that is optimised. The exact relation between the denoising procedure and the objective function is derived and a useful approximation of the objective function is presented. In the experimental section, various DSS schemes are applied extensively to artificial data, to real magnetoencephalograms and to simulated CDMA mobile network signals. Finally, various extensions to the proposed DSS algorithms are considered. These include nonlinear observation mappings, hierarchical models and overcomplete, nonorthogonal feature spaces. With these extensions, DSS appears to have relevance to many existing models of neural information processing.

Abstract—Many of the industrial and research databases are plagued by the problem of missing values. Some evident examples include databases associated with instrument maintenance, medical applications, and surveys. One of the common ways to cope with missing values is to complete their imputation (filling in). Given the rapid growth of sizes of databases, it becomes imperative to come up with a new imputation methodology along with efficient algorithms. The main objective of this paper is to develop a unified framework supporting a host of imputation methods. In the development of this framework, we require that its usage should (on average) lead to the significant improvement of accuracy of imputation while maintaining the same asymptotic computational complexity of the individual methods. Our intent is to provide a comprehensive review of the representative imputation techniques. It is noticeable that the use of the framework in the case of a low-quality single-imputation method has resulted in the imputation accuracy that is comparable to the one achieved when dealing with some other advanced imputation techniques. We also demonstrate, both theoretically and experimentally, that the application of the proposed framework leads to a linear computational complexity and, therefore, does not affect the asymptotic complexity of the associated imputation method. Index Terms—Accuracy, databases, missing values, multiple imputation (MI), single imputation. I.

Abstract. The goal of this paper is to search for independent multidimensional processes subject to missing and mixed observations. The corresponding cocktail-party problem has a number of successful applications, however, the case of missing observations has been worked out only for the simplest Independent Component Analysis (ICA) task, where the hidden processes (i) are one-dimensional, and (ii) signal generation in time is independent and identically distributed (i.i.d.). Here, the missing observation situation is extended to processes with (i) autoregressive (AR) dynamics and (ii) multidimensional driving sources. Performance of the solution method is illustrated by numerical examples. 1