The Bayesian solution is known to be optimal for symbol-by-symbol equalizers: however, its computational complexity is usually very high. The signal space partitioning technique has been proposed to reduce complexity. It was shown that the decision boundary of the equalizer consists of a set of hyperplanes. The disadvantage of existing approaches is that the number of hyperplanes cannot be controlled. In addition, a state-search process, that is not efficient for time-varying channels, is required to find these hyperplanes. In this paper, we propose a new algorithm to remedy these problems. We propose an approximate Bayesian criterion that allows the number of hyperplanes to be arbitrarily set. As a consequence, a tradeoff can be made between performance and computational complexity. In many cases, the resulting performance loss is small, whereas the computational complexity reduction can be large. The proposed equalizer consists of a set of parallel linear discriminant functions and a maximum operation. An adaptive method using stochastic gradient descent has been developed to identify the functions. The proposed algorithm is thus inherently applicable to time-varying channels. The computational complexity of this adaptive algorithm is low and suitable for real-world implementation.