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Our work is based on a recently introduced mathematical theory of deep convolutional neural networks (DCNNs).
It was shown that DCNNs are stable with respect to deformations of bandlimited input functions.
In the present paper, we generalize this result: We prove deformation stability on Sobolev spaces.
Further, we show a weak form of deformation stability for the whole input space L2.
The basic components of DCNNs are semi-discrete frames.
For practical applications, a concrete choice is necessary.

This paper presents a novel problem of detection and localization of anomalous events due to a certain class of objects in video data with applications to smart surveillance. A baseline system is proposed that uses a convolutional neural network (CNN) to generate pixel level masks corresponding to objects of a class of interest. A Restricted Boltzmann Machine (RBM) is then trained on the mask to learn patterns of normal behavior. The free energy of the RBM is used to detect the presence of an anomaly while the reconstruction error is used to localize the anomaly.

We present a new approach for detecting related crime series, by unsupervised learning of the latent feature embeddings from narratives of crime record via the Gaussian-Bernoulli Restricted Boltzmann Machines (RBM). This is a drastically different approach from prior work on crime analysis, which typically considers only time and location and at most category information.

The rapid rise of IoT and Big Data can facilitate the use of data to enhance our quality of life. However, the omnipresent and sensitive nature of data can simultaneously generate privacy concerns. Hence, there is a strong need to develop techniques that ensure the data serve the intended purposes, but not for prying into one’s sensitive information. We address this challenge via utility maximizing lossy compression of data.

Pattern recognition on big data can be challenging for kernel machines as the complexity grows with the squared number of training samples. In this work, we overcome this hurdle via the outlying data sample removal pre-processing step. This approach removes less informative data samples and trains the kernel machines only with the remaining data, and hence, directly reduces the complexity by reducing the number of training samples. To enhance the classification performance, the outlier removal process is done such that the discriminant information of the data is mostly intact.