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In this paper, we present a novel exponentially embedded families (EEF) based classification method, in which the probability density function (PDF) on raw data is estimated from the PDF on features. With the PDF construction, we show that class-specific features can be used in the proposed classification method, instead of a common feature subset for all classes as used in conventional approaches. We apply the proposed EEF classifier for text categorization as a case study and derive an optimal Bayesian classification rule with class-specific feature selection based on the Information Gain score. The promising performance on real-life data sets demonstrates the effectiveness of the proposed approach and indicates its wide potential applications. [ABSTRACT FROM PUBLISHER]

It usually suffers from long observing time and interference sensitivity when a radar transmits the high-range-resolution stepped-frequency chirp signal. Motivated by this, only partial pulses of the stepped-frequency chirp are utilized. For the obtained incomplete frequency data, a Bayesian model based on transfer learning is proposed to reconstruct the corresponding full-band frequency data. In the training phase, a complex beta process factor analysis (CBPFA) model is utilized to statistically model each aspect-frame from a set of given full-band frequency data, whose probability density function (pdf) can be learned from this CBPFA model. It is important to note that the numbers of factors and dictionaries are automatically learned from the data. The inference of CBPFA can be performed via the variational Bayesian (VB) method. In the reconstruction phase for the incomplete frequency data that “related” to the training samples, its corresponding full-band frequency data can be analytically reconstructed via the compressive sensing (CS) method and Bayesian criterion based on the transfer knowledge of the previous pdfs learned from the training phase. About the “relatedness” between each training frame and the incomplete test frequency data, we utilize the frame condition distribution of incomplete test frequency data to represent. The proposed method is validated on the measured high range resolution (HRR) data. [ABSTRACT FROM PUBLISHER]

In this communication, we address a numerical method to efficiently calculate a non-zero optimal threshold value for the performance improvement of a natural frequency-based radar target recognition. From the probability of correct classification with respect to a varying threshold value, we define a function, denoted by f(z) in this communication, so that one of the roots of f(z)=0 corresponds to the optimal threshold. The final optimal threshold value is obtained via the Newton iteration. The scheme is validated by comparing the threshold obtained from the Newton iteration with that using the probability density function. [ABSTRACT FROM PUBLISHER]

The use of the histogram to characterize the random component in raw measurements is widely known, applied and applauded. However, its correct use to show the features hidden in the data may require some caution and insight. The most important degree of freedom specified by the user is the binwidth. Although standard rules for binwidth selection exist, they offer no guarantees that the histogram reveals all the desired features. Furthermore, the histogram is a discontinuous representation of the underlying probability density function (pdf) of the data but measured data are usually continuous. Smooth alternatives to the histogram have been developed since the 1970s but still require significant user interaction and insight into the true data probability density. In this paper, we investigate a novel technique that offers a smooth estimate of the pdf without any necessary interaction of the user. The method is fully blind and adaptive such that the best graphical representation of the probability density is ensured. [ABSTRACT FROM PUBLISHER]

The GUM and its supplements one and two have come to be regarded as de facto standards for evaluating measurement uncertainty. The latter documents have stressed the benefits of deriving probability density functions (PDFs) for the output quantities instead of just evaluating the standard and expanded uncertainties associated with their best estimates. Those supplements, however, present a brute force numerical method for obtaining the output PDFs. In this paper, we rely instead on the use of the change-of-variables theorem as a way of obtaining analytical expressions for PDFs in the form of integrals that, at least in principle, can be numerically evaluated. But more importantly, the GUM supplements do not include situations in which the available information is more than enough, in the sense that by separately considering its various components one may arrive at concurrent PDFs for the quantity or quantities of interest. In some situations these PDFs will be largely similar, so that implementing some form of merging method would perhaps be reasonable. But it may also happen that significant discrepancies between those PDFs are apparent, in which case a modification of the measurement model might make all information appear to be consistent. Herein we review two procedures for merging concurrent and not too dissimilar PDFs. We also discuss some elements to be considered if extending the measurement model appears to be a better alternative. [ABSTRACT FROM PUBLISHER]