Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue by assessing DNNs’ ability to estimate conditional probabilities and propose a framework for systematic uncertainty characterization. Denoting the input sample as x and the category as y, the classification task of assigning a category y to a given input x can be reduced to the task of estimating the conditional probabilities p(y|x), as approximated by the DNN at its last layer using the softmax function. Since softmax yields a vector whose elements all fall in the interval (0, 1) and sum to 1, it suggests a probabilistic interpretation to the DNN’s outcome. Using synthetic and real-world datasets, we look into the impact of various factors, e.g., probability density f(x) and inter-categorical sparsity, on the precision of DNNs’ estimations of p(y|x), and find that the likelihood probability density and the inter-categorical sparsity have greater impacts than the prior probability to DNNs’ classification uncertainty.

Scaling up volume and variety in Big Earth Science Data is particularly difficult when combining low-level, ungridded data, such as swath observations obtained with, for example, Moderate Resolution Imaging Spectroradiometers (MODIS). A unified way to index and combine data with different geo-spatiotemporal layouts and incomparable native array formatting is required for scalable integrative analyses based on data at its full instrument resolution, that is, without extra interpolation (or extrapolation) onto a common grid. The SpatioTemporal Adaptive Resolution Encoding (STARE) uses the Hierarchical Triangular Mesh (HTM) and the Hierarchical Calendrical Partitioning (HCP), recursive partitionings of solid angle and time into tree data structures, to encode spatiotemporal neighborhoods as sets of integers. Regions sharing common paths through the STARE tree hierarchy have similar index values, which can then serve as keys in algorithms and data structures supporting scalable integrative analyses. Thus, STARE co-aligns data in both physical (spatiotemporal) and cyber (memory) spaces, providing a means for marshalling computing resources and conducting analysis with minimum data movement, addressing volume scalability while simultaneously unifying diverse data for variety scaling. In this paper, we demonstrate how easy it is to use the Python STARE API (PySTARE) and the parallel programming platform Dask to integrate MODIS and Geostationary Operational Environmental Satellite (GOES) data, datasets with very different geo-spatiotemporal characteristics.

We have devised and implemented a key technology, SpatioTemporal Adaptive-Resolution Encoding (STARE), in an array database management system, i.e. SciDB, to achieve unparalleled variety scaling for Big Earth Data, enabling rapid-response visual analytics. STARE not only serves as a unifying data representation homogenizing diverse varieties of Earth Science Datasets, but also supports spatiotemporal data placement alignment of these datasets to optimize a major class of Earth Science data analyses, i.e. those requiring spatiotemporal coincidence. Using STARE, we tailor a data partitioning and distribution strategy for the data access patterns of our scientific analysis, leading to optimal use of distributed resources. With STARE, rapid-response visual analytics are made possible through a high-level query interface, allowing geoscientists to perform data exploration visually, intuitively and interactively. We envision a system based on these innovations to relieve geoscientists of most laborious data management chores so that they may focus better on scientific issues and investigations. A significant boost in scientific productivity may thus be expected. We demonstrate these advantages with a prototypical system including comparisons to alternatives.

We investigate the impact of data placement on two Big Data technologies, Spark and SciDB, with a use case from Earth Science where data arrays are multidimensional. Simultaneously, this investigation provides an opportunity to evaluate the performance of the technologies involved. Two datastores, HDFS and Cassandra, are used with Spark for our comparison. It is found that Spark with Cassandra performs better than with HDFS, but SciDB performs better yet than Spark with either datastore. The investigation also underscores the value of having data aligned for the most common analysis scenarios in advance on a shared nothing architecture. Otherwise, repartitioning needs to be carried out on the fly, degrading overall performance.

We have implemented a flexible User Defined Operator (UDO) for labeling connected components of a binary mask expressed as an array in SciDB, a parallel distributed database management system based on the array data model. This UDO is able to process very large multidimensional arrays by exploiting SciDB's memory management mechanism that efficiently manipulates arrays whose memory requirements far exceed available physical memory. The UDO takes as primary inputs a binary mask array and a binary stencil array that specifies the connectivity of a given cell to its neighbors. The UDO returns an array of the same shape as the input mask array with each foreground cell containing the label of the component it belongs to. By default, dimensions are treated as non-periodic, but the UDO also accepts optional input parameters to specify periodicity in any of the array dimensions. The UDO requires four stages to completely label connected components. In the first stage, labels are computed for each subarray or chunk of the mask array in parallel across SciDB instances using the weighted quick union (WQU) with half-path compression algorithm. In the second stage, labels around chunk boundaries from the first stage are stored in a temporary SciDB array that is then replicated across all SciDB instances. Equivalences are resolved by again applying the WQU algorithm to these boundary labels. In the third stage, relabeling is done for each chunk using the resolved equivalences. In the fourth stage, the resolved labels, which so far are “flattened” coordinates of the original binary mask array, are renamed with sequential integers for legibility. The UDO is demonstrated on a 3-D mask of 0(10n) elements, with 0(108) foreground cells and o(106) connected components. The operator completes in 19 minutes using 84 SciDB instances.

We have implemented an updated Hierarchical Triangular Mesh (HTM) as the basis for a unified data model and an indexing scheme for geoscience data to address the variety challenge of Big Earth Data. In the absence of variety, the volume challenge of Big Data is relatively easily addressable with parallel processing. The more important challenge in achieving optimal value with a Big Data solution for Earth Science (ES) data analysis, however, is being able to achieve good scalability with variety. With HTM unifying at least the three popular data models, i.e. Grid, Swath, and Point, used by current ES data products, data preparation time for integrative analysis of diverse datasets can be drastically reduced and better variety scaling can be achieved. HTM is also an indexing scheme, and when applied to all ES datasets, data placement alignment (or co-location) on the shared nothing architecture, which most Big Data systems are based on, is guaranteed and better performance is ensured. With HTM most geospatial set operations become integer interval operations with further performance advantages.