Neighborhood Selection for Thresholding-based Subspace Clustering

Subspace clustering refers to the problem of clustering high-dimensional data points into a union of low-dimensional linear subspaces, where the number of subspaces, their dimensions and orientations are all unknown. In this paper, we propose a variation of the recently introduced thresholding-based subspace clustering (TSC) algorithm, which applies spectral clustering to an adjacency matrix constructed from the nearest neighbors of each data point with respect to the spherical distance measure. The new element resides in an individual and data-driven choice of the number of nearest neighbors. Previous performance results for TSC, as well as for other subspace clustering algorithms based on spectral clustering, come in terms of an intermediate performance measure, which does not address the clustering error directly. Our main analytical contribution is a performance analysis of the modified TSC algorithm (as well as the original TSC algorithm) in terms of the clustering error directly.Comment: ICASSP 201

Practical Full Resolution Learned Lossless Image Compression

We propose the first practical learned lossless image compression system, L3C, and show that it outperforms the popular engineered codecs, PNG, WebP and JPEG 2000. At the core of our method is a fully parallelizable hierarchical probabilistic model for adaptive entropy coding which is optimized end-to-end for the compression task. In contrast to recent autoregressive discrete probabilistic models such as PixelCNN, our method i) models the image distribution jointly with learned auxiliary representations instead of exclusively modeling the image distribution in RGB space, and ii) only requires three forward-passes to predict all pixel probabilities instead of one for each pixel. As a result, L3C obtains over two orders of magnitude speedups when sampling compared to the fastest PixelCNN variant (Multiscale-PixelCNN). Furthermore, we find that learning the auxiliary representation is crucial and outperforms predefined auxiliary representations such as an RGB pyramid significantly.Comment: Updated preprocessing and Table 1, see A.1 in supplementary. Code and models: https://github.com/fab-jul/L3C-PyTorc

The Possibility of Transfer(?): A Comprehensive Approach to the International Criminal Tribunal for Rwanda’s Rule 11bis To Permit Transfer to Rwandan Domestic Courts

We present a learned image compression system based on GANs, operating at extremely low bitrates. Our proposed framework combines an encoder, decoder/generator and a multi-scale discriminator, which we train jointly for a generative learned compression objective. The model synthesizes details it cannot afford to store, obtaining visually pleasing results at bitrates where previous methods fail and show strong artifacts. Furthermore, if a semantic label map of the original image is available, our method can fully synthesize unimportant regions in the decoded image such as streets and trees from the label map, proportionally reducing the storage cost. A user study confirms that for low bitrates, our approach is preferred to state-of-the-art methods, even when they use more than double the bits.Comment: E. Agustsson, M. Tschannen, and F. Mentzer contributed equally to this work. ICCV 2019 camera ready versio