Weighting filter

Abstract: Due to its simplicity, efficiency, and efficacy, naive Bayes (NB) has continued to be one of the top 10 algorithms in the data mining and machine learning community. Of numerous approaches to alleviating its conditional independence assumption, feature weighting has placed more emphasis on highly predictive features than those that are less predictive. In this paper, we argue that for NB highly predictive features should be highly correlated with the class (maximum mutual relevance), yet uncorrelated with other features (minimum mutual redundancy). Based on this premise, we propose a correlation-based feature weighting (CFW) filter for NB. In CFW, the weight for a feature is a sigmoid transformation of the difference between the feature-class correlation (mutual relevance) and the average feature-feature intercorrelation (average mutual redundancy). Experimental results show that NB with CFW significantly outperforms NB and all the other existing state-of-the-art feature weighting filters used to compare. Compared to feature weighting wrappers for improving NB, the main advantages of CFW are its low computational complexity (no search involved) and the fact that it maintains the simplicity of the final model. Besides, we apply CFW to text classification and have achieved remarkable improvements.

Abstract: A new expression for the output moments of weighted median filtered data is derived. The noise attenuation capability of a weighted median filter can now be assessed using the L-vector and M-vector parameters in the new expression. The second major contribution of the paper is the development of a new optimality theory for weighted median filters. This theory is based on the new expression for the output moments, and combines the noise attenuation and some structural constraints on the filter's behavior. In certain special cases, the optimal weighted median filter can be obtained by merely solving a set of linear inequalities. This leads in some cases to closed form solutions for optimal weighted median filters. Some applications of the theory developed in this paper, in 1-D signal processing and image processing are discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filters. >

Abstract: A new generalized cross correlator (GCC) for the passive time delay estimation problem is presented. The interpretation of this GCC is that of estimating the cross-correlation function by cross correlating the least mean-square estimates of the signal component in each of the observed waveforms. The implementation is simply a GCC with the weighting filter equal to the magnitude coherency squared. Numerical evaluation of the performance of this processor and a robust version indicate that they compare favorably to some of the well-known GCC procedures.