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Additional info for An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics)
Although RLS also embodies the concept of state, the state in RLS is time invariant. 2. 2. Signal-ﬂow graph representation of a linear dynamic system. 2 is deﬁned as the minimal set of data that is sufﬁcient to describe the unforced dynamic behavior of the system uniquely. In other words, the state comprises the fewest data on the past of the system that are needed to predict its future behavior. Typically, the state x(i) is unknown and we need to use a set of observations to estimate it. 2 embodies the following pair of equations: 1.
The adaptive resonance theory architecture [Grossberg, 1987, Carpenter and Grossberg, 1987] is one of the ﬁrst growing neural networks. It is a biologically inspired approach rather than a computational design. However, it is often inefﬁcient and the convergence of the iterative processing is not guaranteed. The cascade-correlation learning architecture [Fahlman and Lebiere, 1990] is another example of the network-growing approach. The procedure begins with a minimal network that has some input and one or more output nodes as indicated by input–output considerations, but no hidden nodes.
We present, in detail, the kernel least-mean-square algorithm, the kernel afﬁne projection algorithms, the kernel recursive least-squares algorithm, and the extended kernel recursive least-squares algorithm. 5, will become clear when we present them in the subsequent chapters. Kernel adaptive ﬁlters provide a generalization of linear adaptive ﬁlters because these become a special case of the former when expressed in the dual space. Kernel adaptive ﬁlters exhibit a growing memory structure embedded in the ﬁlter weights.