Clustering Process for Analyzing Pressure Gradient Data

A measurement clustering system, comprising:

• a memory for storing measurements of an environment, each measurement being multi-dimensional consisting of a plurality of variables in the environment;
• and
• a processor operatively coupled to the memory and configured to:
• assign each of the measurements in one or more clusters to one of the one or more prototypes for predicting the one or more physical properties of the environment;
• determine that at least one of the clusters of the measurements violates an error constraint with respect to its original prototype and reassign the measurements of the at least one cluster to new prototypes;
• recursively repeat the determination and reassignment based on the error constraint determination;
• fit each of the prototypes to its cluster of assigned measurements;
• and
• predict the one or more physical properties of the environment based on the characteristics of the one or more cluster-fitted prototypes relating the variables in the environment.

A measurement clustering method, comprising:

• obtaining measurements in an environment, each of the measurements being multi-dimensional and consisting of a plurality of variables in the environment;
• obtaining prototypes defining expected relationships between the variables for predicting one or more physical properties of the environment;
• restricting the prototypes with at least one mathematical constraint dictated by the physics of the environment;
• assigning each of the measurements to the one prototype for which a least error exists;
• fitting each of the prototypes to the measurements assigned thereto;
• and
• predict the one or more physical properties of the environment based on the characteristics of the one or more cluster-fitted prototypes relating the variables in the environment.

A measurement clustering method, comprising:

• obtaining measurements of an environment, each measurement being multi-dimensional consisting of a plurality of variables in the environment;
• obtaining prototypes defining expected relationships between the variables for predicting one or more physical properties of the environment;
• assigning each of the measurements in one or more clusters to one of the prototypes for which a least error exists;
• fitting each of the prototypes to the cluster of its assigned measurements;
• determining that at least two of the prototypes intersect one another at an intersection and that each have the assigned measurements present in each portion of the intersecting prototype around the intersection;
• reassigning the one or more measurements assigned to one of the portions of one of the intersecting prototypes to one of the other prototypes for which a least error exists;
• repeating the acts of fitting, determining, and reassigning;
• and
• predicting the one or more physical properties of the environment based on the characteristics of the one or more cluster-fitted prototypes relating the variables in the environment.

A measurement clustering method, comprising:

• obtaining measurements of an environment in real-time with a measurement device, each of the measurements being multi-dimensional consisting of a plurality of variables in the environment;
• obtaining prototypes defining expected relationships between the variables for predicting one or more physical properties of the environment;
• assigning, incrementally as each of the measurements is obtained in real-time, each of the measurements to one of the prototypes for which a least error exists;
• fitting, incrementally as each of the measurements is assigned, each of the prototypes to their assigned measurements;
• repeating the acts of reassigning and fitting until convergence;
• and
• predicting the one or more physical properties of the environment based on the characteristics of the cluster-fitted prototypes relating the variables in the environment.