Abstract: Methods for anomaly detection using dictionary based projection (DBP), and system for implementing such methods. In an embodiment, a method comprises receiving input data including a plurality n of multidimensional data points (MDDPs) with dimension m, applying DBP iteratively to the input data to construct a dictionary D, receiving a newly arrived MDDP (NAMDDP), calculating a score S associated with the NAMDDP as a distance of the NAMDDP from dictionary D, and classifying the NAMDDP as normal or as an anomaly based on score S, wherein classification of the NAMDDP as an anomaly is indicative of detection of an unknown undesirable event.

Abstract: A method for classification of a newly arrived multidimensional data point (MDP) in a dynamic data uses multi-scale extension (MSE). The multi-scale out-of-sample extension (OOSE) uses a coarse-to-fine hierarchy of the multi-scale decomposition of a Gaussian kernel that established the distances between MDPs in a training set to find the coordinates of newly arrived MDPs in an embedded space. A well-conditioned basis is first generated in a source matrix of MDPs. A single-scale out-of-sample extension (OOSE) is applied to the newly arrived MDP on the well-conditioned basis to provide coordinates of an approximate location of the newly arrived MDP in an embedded space. A multi-scale OOSE is then applied to the newly arrived MDP to provide improved coordinates of the newly arrived MDP location in the embedded space.

Abstract: A method for classification of a newly arrived multidimensional data point (MDP) in a dynamic data uses multi-scale extension (MSE). The multi-scale out-of-sample extension (OOSE) uses a coarse-to-fine hierarchy of the multi-scale decomposition of a Gaussian kernel that established the distances between MDPs in a training set to find the coordinates of newly arrived MDPs in an embedded space. A well-conditioned basis is first generated in a source matrix of MDPs. A single-scale out-of-sample extension (OOSE) is applied to the newly arrived MDP on the well-conditioned basis to provide coordinates of an approximate location of the newly arrived MDP in an embedded space. A multi-scale OOSE is then applied to the newly arrived MDP to provide improved coordinates of the newly arrived MDP location in the embedded space.