Detection of anomaly trends in dynamically evolving systems

We propose a learning framework, which is based on diffusion methodology, that performs data fusion and anomaly detection in multi-dimensional time series data. Real life applications and processes usually contain a large number of sensors that generate parameters (features), where each sensor collects partial information about the running process. These input sensors are fused to describe the behavior of the whole process. The proposed data fusing algorithm is done in an hierarchial fashion: first it re-scales the input sensors. Then, the re-formulated inputs are fused together by the application of the diffusion maps to reveal the nonlinear relationships among them. This process constructs by embedding a low-dimensional description of the system. The embedding separates between sensors (parameters) that cause stable and instable behavior of the system. This unsupervised algorithm first studies the system's profile from a training dataset by reducing its dimensions. Then, the coordinates of newly arrived data points are determined by the application of multi-scale Gaussian approximation. To achieve this, an hierarchial processing of the incoming data is introduced.