### Table 1: Bregman divergences generated from some convex functions.

2004

"... In PAGE 5: ... The Bregman divergence between F (ej ) and G(ej ) (the power spectrum of another signal g(t)) is given by d (F; G) = 1 2 Z log(F (ej )) + log(G(ej )) (F (ej ) G(ej )) 1 G(ej ) d = 1 2 Z log F (ej ) G(ej ) + F (ej ) G(ej ) 1 d ; which is exactly the Itakura-Saito distance between the power spectra F (ej ) and G(ej ) and can also be interpreted as the I-divergence (Csisz ar, 1991) between the generating processes under the assumption that they are equal mean, stationary Gaussian processes (Kazakos and Kazakos, 1980). Table1 contains a list of some common convex functions and their corresponding Bregman divergences. Bregman divergences have several interesting and useful properties, such as non-negativity, convexity in the rst argument, etc.... ..."

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### Table 1: A list of Bregman divergences and the corresponding convex functions.

"... In PAGE 4: ...(2) under all the Bregman divergences. Table1 shows a list of Bregman divergences and their corresponding Bregman convex functions. Note that Bregman divergences are non- negative.... In PAGE 7: ...uction. In [21], the model is based on Euclidean distance. Euclidean distance function has very wide applicability, since it implies the normal distribution and most data with a large sample size tend to have a normal distribution. However, since Bernoulli distribution is a more intuitive choice for the binary data, RSN-BD directly provides a new algorithm for clustering binary data with feature reduction by using lo- gistic distance function (see Table1 ), which corresponds to Bernoulli distribution. 5.... ..."

### Table 1: List of nonconvex and convex potential functions that have been used.

1998

"... In PAGE 6: ... Depending on the choice of the potential function, (2) includes many common MRF models that have been proposed in the literature. Table1 lists a variety of such potential functions. Notice that only the GGMRF model depends on p through the potential function.... In PAGE 10: ...4 ML Estimate of and p for Non-scalable Priors In this section, we derive methods to compute the joint ML estimates of and p when the potential function is not scalable. This includes all the potential functions of Table1 except the Gaussian, Laplacian, and GGMRF. Notice that u(x; p) is not a function of p for any of the non-scalable potential functions.... ..."

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### TABLE I LIST OF NONCONVEX AND CONVEX POTENTIAL FUNCTIONS THAT HAVE BEEN USED

1998

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### Table 1: Results for Quadratic Non-Convex Functions Number of Number of Precision Time of

1999

"... In PAGE 14: ... We chose a xed initial value of p which was increased if the optimal solution was not found after a given number of iterations. In Table1 - Table 2 (Appendix I) the computational results for quadratic and nonsmooth functions are presented, respectively. The space dimension for the test examples varied between 2 and 20 variables.... ..."

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