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The diffusion based distributed learning approaches have been found to be aviable solution for learning over linearly separable datasets over a network.However, approaches till date are suitable for linearly separable datasets andneed to be extended to scenarios in which we need to learn a non-linearity. Insuch scenarios, the recently proposed diffusion kernel least mean squares(KLMS) has been found to be performing better than diffusion least mean squares(LMS). The drawback of diffusion KLMS is that it requires infinite storage forobservations (also called dictionary). This paper formulates the diffusion KLMSin a fixed budget setting such that the storage requirement is curtailed whilemaintaining appreciable performance in terms of convergence. Simulations havebeen carried out to validate the two newly proposed algorithms named asquantised diffusion KLMS (QDKLMS) and fixed budget diffusion KLMS (FBDKLMS)against KLMS, which indicate that both the proposed algorithms deliver betterperformance as compared to the KLMS while reducing the dictionary size storagerequirement.

Finite Dictionary Variants of the Diffusion KLMS Algorithm