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Our understanding of the structure of the brain and its relationships with human traits is largely determined by how we represent the structural connectome. Standard practice divides the brain into regions of interest (ROIs) and represents the connectome as an adjacency matrix having cells measuring connectivity between pairs of ROIs. Statistical analyses are then heavily driven by the (largely arbitrary) choice of ROIs. In this article, we propose a novel tractography-based representation of brain connectomes, which clusters fiber endpoints to define a data adaptive parcellation targeted to explain variation among individuals and predict human traits. This representation leads to Principal Parcellation Analysis (PPA), representing individual brain connectomes by compositional vectors building on a basis system of fiber bundles that captures the connectivity at the population level. PPA reduces subjectivity and facilitates statistical analyses. We illustrate the proposed approach through applications to data from the Human Connectome Project (HCP) and show that PPA connectomes improve power in predicting human traits over state-of-the-art methods based on classical connectomes, while dramatically improving parsimony and maintaining interpretability. Our PPA package is publicly available on GitHub, and can be implemented routinely for diffusion image data.

Fast and effective image compression for multi-dimensional images has become increasingly important for efficient storage and transfer of massive amounts of high-resolution images and videos. Desirable properties in compression methods include (1) high reconstruction quality at a wide range of compression rates while preserving key local details, (2) computational scalability, (3) applicability to a variety of different image/video types and of different dimensions, (4) progressive transmission, and (5) ease of tuning. We present such a method for multi-dimensional image compression called Compression via Adaptive Recursive Partitioning (CARP). CARP uses an optimal permutation of the image pixels inferred from a Bayesian probabilistic model on recursive partitions of the image to reduce its effective dimensionality, achieving a parsimonious representation that preserves information. CARP uses a multi-layer Bayesian hierarchical model to achieve in-situ compression along with self-tuning and regularization, with just one single parameter to be specified by the user to achieve the desired compression rate. Extensive numerical experiments using a variety of datasets including 2D still images, real-life YouTube videos, and surveillance videos show that CARP dominates the state-of-the-art image/video compression approaches---including JPEG, JPEG2000, BPG, MPEG4, HEVC and a neural network-based method---for all of these different image types and on nearly all of the individual images and videos over some methods., Comment: 20 pages, 11 figures