This work is aimed to study experimental and theoretical approaches for searching effective local training rules for unsupervised pattern recognition by high-performance memristor-based Spiking Neural Networks (SNNs). First, the possibility of weight change using Spike-Timing-Dependent Plasticity (STDP) is demonstrated with a pair of hardware analog neurons connected through a (CoFeB)_x(LiNbO₃)_1−x nanocomposite memristor. Next, the learning convergence to a solution of binary clusterization task is analyzed in a wide range of memristive STDP parameters for a single-layer fully connected feedforward SNN. The memristive STDP behavior supplying convergence in this simple task is shown also to provide it in the handwritten digit recognition domain by the more complex SNN architecture with a Winner-Take-All competition between neurons. To investigate basic conditions necessary for training convergence, an original probabilistic generative model of a rate-based single-layer network with independent or competing neurons is built and thoroughly analyzed. The main result is a statement of “correlation growth-anticorrelation decay” principle which prompts near-optimal policy to configure model parameters. This principle is in line with requiring the binary clusterization convergence which can be defined as the necessary condition for optimal learning and used as the simple benchmark for tuning parameters of various neural network realizations with population-rate information coding. At last, a heuristic algorithm is described to experimentally find out the convergence conditions in a memristive SNN, including robustness to a device variability. Due to the generality of the proposed approach, it can be applied to a wide range of memristors and neurons of software- or hardware-based rate-coding single-layer SNNs when searching for local rules that ensure their unsupervised learning convergence in a pattern recognition task domain.