We introduce new methods for training an autoencoder (AE) as an unsupervised hyperspectral anomaly detector. We detail a new percentile loss (PL) that reliably constructs an accurate background model while limiting the erroneous inclusion of anomalous pixels. We also improve detection performance and reliability by introducing a cumulative detection score that incorporates statistics calculated from the ensemble of AE models generated over the history of the training process. We show improved detection performance on two data sets relative to two baseline algorithms.

We have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved k-sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a "path," or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. Two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.

Appropriately identifying outlier data is a critical requirement in the decision-making process of many expert and intelligent systems deployed in a variety of fields including finance, medicine, and defense. Classical outlier detection schemes typically rely on the assumption that normal/background data of interest are distributed according to an assumed statistical model and search for data that deviate from that assumption. However, it is frequently the case that performance is reduced because the underlying distribution does not follow the assumed model. Manifold learning techniques offer improved performance by learning better models of the background but can be too computationally expensive due to the need to calculate a distance measure between all data points. Here, we study a general framework that allows manifold learning techniques to be used for unsupervised anomaly detection by reducing computational expense via a uniform random sampling of a small fraction of the data. A background manifold is learned from the sample and then an out-of-sample extension is used to project unsampled data into the learned manifold space and construct an anomaly detection statistic based on the prediction error of the learned manifold. The method works well for unsupervised anomaly detection because, by definition, the ratio of anomalous to non-anomalous data points is small and the sampling will be dominated by background points. However, a variety of parameters that affect detection performance are introduced so we use here a low-dimensional toy problem to investigate their effect on the performance of four learning algorithms (kernel PCA, two versions of diffusion map, and the Parzen density estimator). We then apply the methods to the detection of watercraft in an ensemble of 22 infrared maritime scenes where we find kernel PCA to be superior and show that it outperforms a commonly employed baseline algorithm. The framework is not limited to the tested image processing example and can be used for any unsupervised anomaly detection task.

Many chaotic dynamical systems can produce time series with a wide range of temporal and spectral properties as a function of only a few fixed parameters. This malleability invites their use as tools for shaping or designing inputs used to drive a separate dynamical system of interest. By specifying an objective function and employing an evolutionary algorithm to manipulate the parameters governing the dynamics of the forcing system, the output of the driven system is made to approach an optimal response subject to desired constraints. The technique's versatility is demonstrated for two different applications: damage detection in structures and phase-locked loop disruption.

Differential evolution is used to search the parameter space of a system of ordinary differential equations (ODEs). For each tested parameter set, one time series resulting from integration of the ODE system is used to drive a dynamic system of interest. A fitness function is designed such that the response of the driven system is forced to have properties that are desirable to the practitioner. The dynamic versatility of a nonlinear ODE system coupled with an evolutionary algorithm search of its parameter space allows for significant improvement in excitation fitness. This input tailoring technique is generally applicable to a number of problems and is shown in this work to generate a chaotic modulation that reduces the power required to disrupt normal operation of a phase-locked loop.