Visualization of Big Spatial Data using Coresets for Kernel Density Estimates

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for subsampling of spatial data suitable for creating kernel density estimates from very large data and demonstrate that it results in less error than random sampling. We also introduce a method to ensure that thresholding of low values based on sampled data does not omit any regions above the desired threshold when working with sampled data. We demonstrate the effectiveness of our approach using both, artificial and real-world large geospatial datasets

Doctor of Philosophy

dissertationKernel smoothing provides a simple way of finding structures in data sets without the imposition of a parametric model, for example, nonparametric regression and density estimates. However, in many data-intensive applications, the data set could be large. Thus, evaluating a kernel density estimate or kernel regression over the data set directly can be prohibitively expensive in big data. This dissertation is working on how to efficiently find a smaller data set that can approximate the original data set with a theoretical guarantee in the kernel smoothing setting and how to extend it to more general smooth range spaces. For kernel density estimates, we propose randomized and deterministic algorithms with quality guarantees that are orders of magnitude more efficient than previous algorithms, which do not require knowledge of the kernel or its bandwidth parameter and are easily parallelizable. Our algorithms are applicable to any large-scale data processing framework. We then further investigate how to measure the error between two kernel density estimates, which is usually measured either in L1 or L2 error. In this dissertation, we investigate the challenges in using a stronger error, L ∞ (or worst case) error. We present efficient solutions for how to estimate the L∞ error and how to choose the bandwidth parameter for a kernel density estimate built on a subsample of a large data set. We next extend smoothed versions of geometric range spaces from kernel range spaces to more general types of ranges, so that an element of the ground set can be contained in a range with a non-binary value in [0,1]. We investigate the approximation of these range spaces through ϵ-nets and ϵ-samples. Finally, we study coresets algorithms for kernel regression. The size of the coresets are independent of the size of the data set, rather they only depend on the error guarantee, and in some cases the size of domain and amount of smoothing. We evaluate our methods on very large time series and spatial data, demonstrate that they can be constructed extremely efficiently, and allow for great computational gains

BETULA: Numerically Stable CF-Trees for BIRCH Clustering

BIRCH clustering is a widely known approach for clustering, that has influenced much subsequent research and commercial products. The key contribution of BIRCH is the Clustering Feature tree (CF-Tree), which is a compressed representation of the input data. As new data arrives, the tree is eventually rebuilt to increase the compression. Afterward, the leaves of the tree are used for clustering. Because of the data compression, this method is very scalable. The idea has been adopted for example for k-means, data stream, and density-based clustering. Clustering features used by BIRCH are simple summary statistics that can easily be updated with new data: the number of points, the linear sums, and the sum of squared values. Unfortunately, how the sum of squares is then used in BIRCH is prone to catastrophic cancellation. We introduce a replacement cluster feature that does not have this numeric problem, that is not much more expensive to maintain, and which makes many computations simpler and hence more efficient. These cluster features can also easily be used in other work derived from BIRCH, such as algorithms for streaming data. In the experiments, we demonstrate the numerical problem and compare the performance of the original algorithm compared to the improved cluster features

Applied Randomized Algorithms for Efficient Genomic Analysis

The scope and scale of biological data continues to grow at an exponential clip, driven by advances in genetic sequencing, annotation and widespread adoption of surveillance efforts. For instance, the Sequence Read Archive (SRA) now contains more than 25 petabases of public data, while RefSeq, a collection of reference genomes, recently surpassed 100,000 complete genomes. In the process, it has outgrown the practical reach of many traditional algorithmic approaches in both time and space. Motivated by this extreme scale, this thesis details efficient methods for clustering and summarizing large collections of sequence data. While our primary area of interest is biological sequences, these approaches largely apply to sequence collections of any type, including natural language, software source code, and graph structured data. We applied recent advances in randomized algorithms to practical problems. We used MinHash and HyperLogLog, both examples of Locality- Sensitive Hashing, as well as coresets, which are approximate representations for finite sum problems, to build methods capable of scaling to billions of items. Ultimately, these are all derived from variations on sampling. We combined these advances with hardware-based optimizations and incorporated into free and open-source software libraries (sketch, frp, lib- simdsampling) and practical software tools built on these libraries (Dashing, Minicore, Dashing 2), empowering users to interact practically with colossal datasets on commodity hardware

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Community Sense and Response Systems

The proliferation of smartphones and other internet-enabled, sensor-equipped consumer devices enables us to sense and act upon the physical environment in unprecedented ways. This thesis considers Community Sense-and-Response (CSR) systems, a new class of web application for acting on sensory data gathered from participants' personal smart devices. The thesis describes how rare events can be reliably detected using a decentralized anomaly detection architecture that performs client-side anomaly detection and server-side event detection. After analyzing this decentralized anomaly detection approach, the thesis describes how weak but spatially structured events can be detected, despite significant noise, when the events have a sparse representation in an alternative basis. Finally, the thesis describes how the statistical models needed for client-side anomaly detection may be learned efficiently, using limited space, via coresets. The Caltech Community Seismic Network (CSN) is a prototypical example of a CSR system that harnesses accelerometers in volunteers' smartphones and consumer electronics. Using CSN, this thesis presents the systems and algorithmic techniques to design, build and evaluate a scalable network for real-time awareness of spatial phenomena such as dangerous earthquakes.</p

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Deep Active Learning in the Presence of Label Noise: A Survey

Deep active learning has emerged as a powerful tool for training deep learning models within a predefined labeling budget. These models have achieved performances comparable to those trained in an offline setting. However, deep active learning faces substantial issues when dealing with classification datasets containing noisy labels. In this literature review, we discuss the current state of deep active learning in the presence of label noise, highlighting unique approaches, their strengths, and weaknesses. With the recent success of vision transformers in image classification tasks, we provide a brief overview and consider how the transformer layers and attention mechanisms can be used to enhance diversity, importance, and uncertainty-based selection in queries sent to an oracle for labeling. We further propose exploring contrastive learning methods to derive good image representations that can aid in selecting high-value samples for labeling in an active learning setting. We also highlight the need for creating unified benchmarks and standardized datasets for deep active learning in the presence of label noise for image classification to promote the reproducibility of research. The review concludes by suggesting avenues for future research in this area.Comment: 20 pages, PhD literature revie