Neighborhood Mixture Model for Non-Linear Regression

The patent segments the high-dimensional feature space by introducing a neighborhood mixture model that decomposes the complex metric learning problem into multiple local neighborhood relationships. Each neighborhood is characterized by a local metric, avoiding the need to compute and optimize a single global metric across all high-dimensional features, thereby reducing computational complexity while maintaining prediction accuracy.

The patent applies local quality by allowing different regions of the feature space to have different metric properties through the neighborhood mixture model. Each component of the mixture model learns a local metric that is optimized for its specific neighborhood, enabling accurate local geometric structure capture without the computational burden of a global metric in high-dimensional space.

The patent makes the metric dynamic by using a mixture model where the metric choice is not fixed but adapts to each data point based on its neighborhood membership. The model dynamically selects and combines multiple local metrics according to the probability distribution of neighborhoods, allowing the metric to adapt to local geometric structures without being overly sensitive to any single metric choice.

The patent creates a composite metric structure by combining multiple local metrics into a neighborhood mixture model. Each metric in the mixture serves as a 'component material' that captures different aspects of the local geometry, and their weighted combination creates a robust composite metric that is less sensitive to the limitations of any individual metric while maintaining high measurement precision.