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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Venkatesan, R.C. Plastino, A. |
| Copyright Year | 2009 |
| Description | Author affiliation: Systems Research Corporation, Aundh, Pune 411007, India (Venkatesan, R.C.) || IFLP, National University La Plata & National Research Council (CONICET), C. C., 727 1900, La Plata, Argentina (Plastino, A.) |
| Abstract | The theoretical basis for a candidate variational principle for the information bottleneck (IB) method is formulated within the ambit of the generalized nonadditive statistics of Tsallis. Given a nonadditivity parameter q, the role of the additive duality of nonadditive statistics (q* = 2 - q ) in relating Tsallis entropies for ranges of the nonadditivity parameter q ≪ 1 and q ≫ 1 is described. Defining X, X̃, and Y to be the source alphabet, the compressed reproduction alphabet, and, the relevance variable respectively, it is demonstrated that minimization of a generalized IB (gIB) Lagrangian defined in terms of the nonadditivity parameter q* self-consistently yields the nonadditive effective distortion measure to be the q-deformed generalized Kullback-Leibler divergence: $DK-L^{q}[p(Y$ | X)∥p(Y | X̃)]. This result is achieved without enforcing any a-priori assumptions. Next, it is proven that the q*-deformed nonadditive free energy of the system is non-negative and convex. Finally, the update equations for the gIB method are derived. These results generalize critical features of the IB method to the case of Tsallis statistics. |
| Starting Page | 1323 |
| Ending Page | 1327 |
| File Size | 817242 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781424443123 |
| DOI | 10.1109/ISIT.2009.5205932 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2009-06-28 |
| Publisher Place | South Korea |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Statistics Data compression Entropy Lagrangian functions Distortion measurement Physics Councils Q measurement Equations Rate-distortion |
| Content Type | Text |
| Resource Type | Article |
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