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Machine Learning by Sergios Theodoridis

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5.6 The Affine Projection Algorithm

As it will soon be verified in the simulations section, a major drawback of the basic LMS scheme is its fairly slow convergence speed. In an attempt to improve upon it, a number of variants have been proposed over the years. The affine projection algorithm (APA) belongs to the so-called data-reusing family, where, at each time instant, past data are reused. Such a rationale helps the algorithm to “learn faster” and improve the convergence speed. However, besides the increased complexity, the faster convergence speed is achieved at the expense of an increased misadjustment level.

The APA was proposed originally in Ref. [48] and later on in Ref. [72]. Let the currently available estimate be θn−1. According ...

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