A novel approach to the convergence of unsupervised learning algorithms

Unlike the conventional stochastic approach, an unsupervised learning algorithm is viewed as a deterministic system. A new concept of time-average invariance is introduced, which is a property of deterministic signals, but plays the role of stochastic signals that are stationary and ergodic. As such, deterministic-based analysis can be used for stochastic-like signals. Consequently, the complexity of convergence analysis is significantly reduced. The simplicity of the main theorem also suggests the possibility for the design of unsupervised learning algorithms. Two examples are given for illustration.