Vector quantization is a nearest neighbor representation based compression technique for vector data. It creates a collection of codewords to represent the entire vector space. Each vector data is then represented by its nearest neighbor codeword, where the distance between them is the compression error. To improve nearest neighbor representation for vector quantization, we propose to apply sorting transformation to vector data such that members within each vector are sorted. We show that among all permutation transformations, the sorting transformation minimizes L2 distance and maximizes similarity measures such as cosine similarity and Pearson correlation for vector data. Applying sorting transformation with vector quantization can substantially reduce compression errors. Meanwhile, it incurs storage overhead for saving the sorting permutation for each compressed vector. Through experimental validation on compression and nearest neighbor retrieval, we show that this is a beneficial trade-off for vector quantization on low dimensional vectors, a common scenario for vector quantization applications.

Nature-based carbon sequestration is currently the most viable solutions to extract CO2from the atmosphere and convert it into carbon. Oceans, soils and forests have the potential to capture and store large amount of carbon for decades. There is an ongoing debate about the permanence of the carbon sequestered by nature-based processes and the precise techniques required to monitor these carbon pools. Remote sensing plays a crucial role in the large scale observations of the Earth surface and provides a scalable method to monitor land use that can affect carbon sequestration. Optical spectral information and radar signals are the best candidates as proxy data to quantify and monitor the change in carbon sequestered. Here we outline the design of an AI enabled framework to monitor, verify, and quantify carbon sequestration in nature-based carbon sequestration processes.