Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means

We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix and therefore subsequent processing, such as PCA or K-means, is significantly faster, especially in a distributed-data setting. Furthermore, the sampling is single-pass and applicable to streaming data. The sampling mechanism is a variant of previous methods proposed in the literature combined with a randomized preconditioning to smooth the data. We provide guarantees for PCA in terms of the covariance matrix, and guarantees for K-means in terms of the error in the center estimators at a given step. We present numerical evidence to show both that our bounds are nearly tight and that our algorithms provide a real benefit when applied to standard test data sets, as well as providing certain benefits over related sampling approaches.Comment: 28 pages, 10 figure

Towards Probabilistic and Partially-Supervised Structural Health Monitoring

One of the most significant challenges for signal processing in data-based structural health monitoring (SHM) is a lack of comprehensive data; in particular, recording labels to describe what each of the measured signals represent. For example, consider an offshore wind-turbine, monitored by an SHM strategy. It is infeasible to artificially damage such a high-value asset to collect signals that might relate to the damaged structure in situ; additionally, signals that correspond to abnormal wave-loading, or unusually low-temperatures, could take several years to be recorded. Regular inspections of the turbine in operation, to describe (and label) what measured data represent, would also prove impracticable -- conventionally, it is only possible to check various components (such as the turbine blades) following manual inspection; this involves travelling to a remote, offshore location, which is a high-cost procedure. Therefore, the collection of labelled data is generally limited by some expense incurred when investigating the signals; this might include direct costs, or loss of income due to down-time. Conventionally, incomplete label information forces a dependence on unsupervised machine learning, limiting SHM strategies to damage (i.e. novelty) detection. However, while comprehensive and fully labelled data can be rare, it is often possible to provide labels for a limited subset of data, given a label budget. In this scenario, partially-supervised machine learning should become relevant. The associated algorithms offer an alternative approach to monitor measured data, as they can utilise both labelled and unlabelled signals, within a unifying training scheme. In consequence, this work introduces (and adapts) partially-supervised algorithms for SHM; specifically, semi-supervised and active learning methods. Through applications to experimental data, semi-supervised learning is shown to utilise information in the unlabelled signals, alongside a limited set of labelled data, to further update a predictive-model. On the other hand, active learning improves the predictive performance by querying specific signals to investigate, which are assumed the most informative. Both discriminative and generative methods are investigated, leading towards a novel, probabilistic framework, to classify, investigate, and label signals for online SHM. The findings indicate that, through partially-supervised learning, the cost associated with labelling data can be managed, as the information in a selected subset of labelled signals can be combined with larger sets of unlabelled data -- increasing the potential scope and predictive performance for data-driven SHM

Aesthetic preference for art emerges from a weighted integration over hierarchically structured visual features in the brain

It is an open question whether preferences for visual art can be lawfully predicted from the basic constituent elements of a visual image. Moreover, little is known about how such preferences are actually constructed in the brain. Here we developed and tested a computational framework to gain an understanding of how the human brain constructs aesthetic value. We show that it is possible to explain human preferences for a piece of art based on an analysis of features present in the image. This was achieved by analyzing the visual properties of drawings and photographs by multiple means, ranging from image statistics extracted by computer vision tools, subjective human ratings about attributes, to a deep convolutional neural network. Crucially, it is possible to predict subjective value ratings not only within but also across individuals, speaking to the possibility that much of the variance in human visual preference is shared across individuals. Neuroimaging data revealed that preference computations occur in the brain by means of a graded hierarchical representation of lower and higher level features in the visual system. These features are in turn integrated to compute an overall subjective preference in the parietal and prefrontal cortex. Our findings suggest that rather than being idiosyncratic, human preferences for art can be explained at least in part as a product of a systematic neural integration over underlying visual features of an image. This work not only advances our understanding of the brain-wide computations underlying value construction but also brings new mechanistic insights to the study of visual aesthetics and art appreciation