TensorCodec: Compact Lossy Compression of Tensors without Strong Data Assumptions

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor compression algorithms are available, many of them rely on strong data assumptions regarding its order, sparsity, rank, and smoothness. In this work, we propose TENSORCODEC, a lossy compression algorithm for general tensors that do not necessarily adhere to strong input data assumptions. TENSORCODEC incorporates three key ideas. The first idea is Neural Tensor-Train Decomposition (NTTD) where we integrate a recurrent neural network into Tensor-Train Decomposition to enhance its expressive power and alleviate the limitations imposed by the low-rank assumption. Another idea is to fold the input tensor into a higher-order tensor to reduce the space required by NTTD. Finally, the mode indices of the input tensor are reordered to reveal patterns that can be exploited by NTTD for improved approximation. Our analysis and experiments on 8 real-world datasets demonstrate that TENSORCODEC is (a) Concise: it gives up to 7.38x more compact compression than the best competitor with similar reconstruction error, (b) Accurate: given the same budget for compressed size, it yields up to 3.33x more accurate reconstruction than the best competitor, (c) Scalable: its empirical compression time is linear in the number of tensor entries, and it reconstructs each entry in logarithmic time. Our code and datasets are available at https://github.com/kbrother/TensorCodec.Comment: Accepted to ICDM 2023 - IEEE International Conference on Data Mining 202

NeuKron: Constant-Size Lossy Compression of Sparse Reorderable Matrices and Tensors

Many real-world data are naturally represented as a sparse reorderable matrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacency matrix of a bipartite graph). Storing a sparse matrix in conventional ways requires an amount of space linear in the number of non-zeros, and lossy compression of sparse matrices (e.g., Truncated SVD) typically requires an amount of space linear in the number of rows and columns. In this work, we propose NeuKron for compressing a sparse reorderable matrix into a constant-size space. NeuKron generalizes Kronecker products using a recurrent neural network with a constant number of parameters. NeuKron updates the parameters so that a given matrix is approximated by the product and reorders the rows and columns of the matrix to facilitate the approximation. The updates take time linear in the number of non-zeros in the input matrix, and the approximation of each entry can be retrieved in logarithmic time. We also extend NeuKron to compress sparse reorderable tensors (e.g. multi-layer graphs), which generalize matrices. Through experiments on ten real-world datasets, we show that NeuKron is (a) Compact: requiring up to five orders of magnitude less space than its best competitor with similar approximation errors, (b) Accurate: giving up to 10x smaller approximation error than its best competitors with similar size outputs, and (c) Scalable: successfully compressing a matrix with over 230 million non-zero entries.Comment: Accepted to WWW 2023 - The Web Conference 202

Learning and Practicing Data Analytics using SAP In-Memory Computing

The analysis and organization of Big Data is becoming important in the business industry. Using and understanding ERP (Enterprise Resource Planning) software to interpret Big Data is essential to the evolution of Information System Technology. This research on SAP HANA and SAP Lumira allows us the opportunity to explore

How disability severity is associated with changes in physical activity and inactivity from adolescence to young adulthood

Background Disabilities may play a different role in determining peoples physical activity (PA) and physical inactivity (PI) levels when they go through multiple lifetime transitions (e.g., graduation, marriage) between adolescence and young adulthood. This study investigates how disability severity is associated with changes in PA and PI engagement levels, focusing on adolescence and young adulthood, when the patterns of PA and PI are usually formed. Methods The study employed data from Waves 1 (adolescence) and 4 (young adulthood) of the National Longitudinal Study of Adolescent Health, which covers a total of 15,701 subjects. We first categorized subjects into 4 disability groups: no, minimal, mild, or moderate/severe disability and/or limitation. We then calculated the differences in PA and PI engagement levels between Waves 1 and 4 at the individual level to measure how much the PA and PI levels of individuals changed between adolescence and young adulthood. Finally, we used two separate multinomial logistic regression models for PA and PI to investigate the relationships between disability severity and the changes in PA and PI engagement levels between the two periods after controlling for multiple demographic (age, race, sex) and socioeconomic (household income level, education level) variables. Results We showed that individuals with minimal disabilities were more likely to decrease their PA levels during transitions from adolescence to young adulthood than those without disabilities. Our findings also revealed that individuals with moderate to severe disabilities tended to have higher PI levels than individuals without disabilities when they were young adults. Furthermore, we found that people above the poverty level were more likely to increase their PA levels to a certain degree compared to people in the group below or near the poverty level. Conclusions Our study partially indicates that individuals with disabilities are more vulnerable to unhealthy lifestyles due to a lack of PA engagement and increased PI time compared to people without disabilities. We recommend that health agencies at the state and federal levels allocate more resources for individuals with disabilities to mitigate health disparities between those with and without disabilities

Ultrathin, polarization-independent, and focus-tunable liquid crystal diffractive lens for augmented reality

Despite the recent advances in augmented reality (AR), which has shown the potential to significantly impact on our daily lives by offering a new way to manipulate and interact with virtual information, minimizing visual discomfort due to the vergence-accommodation conflict remains a challenge. Emerging AR technologies often exploit focus-tunable optics to address this problem. Although they demonstrated improved depth perception by enabling proper focus cues, a bulky form factor of focus-tunable optics prevents their use in the form of a pair of eyeglasses. Herein, we describe an ultrathin, focus-tunable liquid crystal (LC) diffractive lens with a large aperture, a low weight, and a low operating voltage. In addition, we show that the polarization dependence of the lens, which is an inherent optical property of LC lenses, can be eliminated using birefringent thin films as substrates and by aligning the optical axes of the birefringent substrates and LC at a specific angle. The polarization independence eliminates the need for a polarizer, thus further reducing the form factor of the optical system. Next, we demonstrate a prototype of AR glasses with addressable focal planes using the ultrathin lens. The prototype AR glasses can adjust the accommodation distance of the virtual image, mitigating the vergence-accommodation conflict without substantially compromising the form factor or image quality. This research on ultrathin lens technology shows promising potential for developing compact optical displays in various applications.Comment: 23 pages, 9 figure