Detection of Anomaly Trends in Dynamically Evolving Systems

We propose a learning framework, which is based on diffusionmethodology, that performs data fusion and anomalydetection in multi-dimensional time series data. Real lifeapplications and processes usually contain a large numberof sensors that generate parameters (features), where eachsensor collects partial information about the running process.These input sensors are fused to describe the behaviorof the whole process. The proposed data fusing algorithmis done in an hierarchial fashion: first it re-scales the inputsensors. Then, the re-formulated inputs are fused togetherby the application of the diffusion maps to reveal the nonlinearrelationships among them. This process constructsby embedding a low-dimensional description of the system.The embedding separates between sensors (parameters) thatcause stable and instable behavior of the system.This unsupervised algorithm first studies the system’sprofile from a training dataset by reducing its dimensions.Then, the coordinates of newly arrived data points are determinedby the application of multi-scale Gaussian approximation.To achieve this, an hierarchial processing of theincoming data is introduced.