Statistics for Spatial Data.

IEEE Transactions on Pattern Analysis and Machine Intelligence

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Remote Sensing And Image Interpretation

Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to leverage the wealth of scientific knowledge for improving the effectiveness of data science models in enabling scientific discovery. The overarching vision of TGDS is to introduce scientific consistency as an essential component for learning generalizable models. Further, by producing scientifically interpretable models, TGDS aims to advance our scientific understanding by discovering novel domain insights. Indeed, the paradigm of TGDS has started to gain prominence in a number of scientific disciplines such as turbulence modeling, material discovery, quantum chemistry, bio-medical science, bio-marker discovery, climate science, and hydrology. In this paper, we formally conceptualize the paradigm of TGDS and present a taxonomy of research themes in TGDS. We describe several approaches for integrating domain knowledge in different research themes using illustrative examples from different disciplines. We also highlight some of the promising avenues of novel research for realizing the full potential of theory-guided data science.

Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data

Being newly immersed in the upstream part of the oil business, I just recently had my first work session with data in ARC–GIS®. The project involves subsurface geographical modeling. Obviously I had considerable interest in discovering if the methodology in this book would enhance my modeling capabilities. The book is for social scientists, but I had no difficulty imagining my own important oil exploration application within the framework of geographically weighted regression (GWR). The first chapter nicely explains what is unique in this book. A standard regression model using geographically oriented data (the example is housing prices across all of England) is a global representation of a spatial relationship, an average that does not account for any local differences. In y = f (x), imagine a whole family of f ’s that are indexed by spatial location. That is the focus of this book. It is about one form of local spatial modeling, which is GWR. A more general resource for this topic is the earlier book by Fotheringham and Wegener (2000), which escaped the notice of Technometrics. Imagine a display of model parameters in a geographical information system (GIS) and you will understand the focus for this book. The authors note, “only where there is no significant spatial variation in a measured relationship can global models be accepted” (p. 10). The second chapter develops the basis of GWR. It analyzes the housing sales prices versus the 33 boroughs in London and begins by fitting a conventional multiple regression model versus housing characteristics. The GWR is motivated by differences in the regression models fitted separately by borough. The GWR is a spatial moving-window approach with all data distances weighted versus a specific data point using a weighting function and a bandwidth. A GIS can then be used to evaluate the spatial dependency of the parameters. As in kriging, local standard errors also are calculated. The chapter also provides all the math. Chapter 3 comprises several further considerations: parameters that are globally constant, outliers, and spatial heteroscedasticity. The first issue leads to hypothesis tests for model comparison using an Akaike information criterion (AIC). Local outliers are hard to detect. Studentized (deletion) residuals are recommended. The outliers can be plotted geographically. Robust regression is suggested as a less computationally intensive alternative. Hetereoscedasticity is harder to handle. Chapter 4 adds statistical inference to the capabilities of GWR: both a confidence interval approach using local likelihood and an AIC method. Four additional methodology chapters present various extensions of GWR. Chapter 5 considers the relationship between GWR and spatial autocorrelation, and includes a combined version of GWR and spatial regression using some complex hybrid models. Chapter 6 examines the relationship of scale and zoning problems in spatial analysis to GWR. Chapter 7 introduces the use of initial exploratory data analysis using geographically weighted statistics, which are based on the idea of using a kernel around each data point to create weights. Univariate statistics and correlation coefficients are defined for exploring local patterns in data. A final set of extensions in Chapter 8 discusses regression models with non-Gaussian errors, logistic regression, local principal components analysis, and local probability density estimation. The methods all use some kind of distributional model. The million-dollar question for me is always, “What about software?” The authors have a stand-alone program, GWR 3, available in CD–ROM by contacting the authors. Basically the drill with GWR 3 is to gather your data, use Excel to transform and reformat the data for GWR 3, use GWR 3 to produce a set of coefficients, and feed those coefficients to your favorite GIS to produce your maps. Forty pages of discussion about using the software are provided. A final epilogue chapter also discusses embedding GWR in R or Matlab and includes some references to people who have done that type of work. I probably would not have read this book if I had not happened to have had it in my briefcase on a visit with the exploration technologists. Though inclusive of appropriate mathematical development, this material is readily approachable because of the many illustrations and the pages and pages of GIS displays. The authors unabashedly present much of the material as their developmental work, so GWR offers a lot of opportunity for research and further development through novel applications and extensions.

Geographically Weighted Regression

Explosive growth in geospatial and temporal data as well as the emergence of new technologies emphasize the need for automated discovery of spatiotemporal knowledge. Spatiotemporal data mining studies the process of discovering interesting and previously unknown, but potentially useful patterns from large spatiotemporal databases. It has broad application domains including ecology and environmental management, public safety, transportation, earth science, epidemiology, and climatology. The complexity of spatiotemporal data and intrinsic relationships limits the usefulness of conventional data science techniques for extracting spatiotemporal patterns. In this survey, we review recent computational techniques and tools in spatiotemporal data mining, focusing on several major pattern families: spatiotemporal outlier, spatiotemporal coupling and tele-coupling, spatiotemporal prediction, spatiotemporal partitioning and summarization, spatiotemporal hotspots, and change detection. Compared with other surveys in the literature, this paper emphasizes the statistical foundations of spatiotemporal data mining and provides comprehensive coverage of computational approaches for various pattern families. ISPRS Int. J. Geo-Inf. 2015, 4 2307 We also list popular software tools for spatiotemporal data analysis. The survey concludes with a look at future research needs.

https://www.mdpi.com/2220-9964/4/4/2306/pdf

Spatiotemporal Data Mining: A Computational Perspective

Monitoring land-cover changes is of prime importance for the effective planning and management of critical, natural and man-made resources. The growing availability of remote sensing data provides ample opportunities for monitoring land-cover changes on a global scale using machine-learning techniques. However, remote sensing data sets exhibit unique domain-specific properties that limit the usefulness of traditional machine-learning methods. This article presents a brief overview of these challenges from the perspective of machine learning and discusses some of the recent advances in machine learning that are relevant for addressing them. These approaches show promise for future research in the detection of land-cover change using machine-learning algorithms.

Monitoring Land-Cover Changes: A Machine-Learning Perspective

Regional co-location patterns (RCPs) represent collections of feature types frequently located together in certain localities. For example, RCP suggests that a co-location pattern involving alcohol-related crimes and bars is often localized to downtown regions. Given a set of Boolean feature types, their geo-located instances, a spatial neighbor relation, and a prevalence threshold, the RCP discovery problem finds all prevalent RCPs (pairs of co-locations and their prevalence localities). RCP discovery is important in many societal applications, including public safety, public health, climate science and ecology. The RCP discovery problem involves three major challenges: (a) an exponential number of subsets of feature types, (b) an exponential number of candidate localities and (c) a tradeoff between accurately modeling pattern locality and achieving computational efficiency. Related work does not provide computationally efficient methods to discover all interesting RCPs with their natural prevalence localities. To address these limitations, this paper proposes a neighborhood graph based approach that discovers all interesting RCPs and is aware of a pattern's prevalence localities. We identify partitions based on the pattern instances and neighbor graph. We introduce two new interest measures, a regional participation ratio and a regional participation index to quantify the strength of RCPs. We present two new algorithms, Pattern Space (PS) enumeration and Maximal Locality (ML) enumeration and show that they are correct and complete. Experiments using real crime datasets show that ML pruning outperforms PS enumeration.

A neighborhood graph based approach to regional co-location pattern discovery: a summary of results

With the advancement of GPS and remote sensing technologies, large amounts of geospatial data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data samples with explanatory features and targeted responses (categorical or continuous) at a set of locations, the spatial prediction problem aims to learn a model that can predict the response variable based on explanatory features. The problem is important with broad applications in earth science, urban informatics, geosocial media analytics, and public health, but is challenging due to the unique characteristics of spatial data, including spatial autocorrelation, heterogeneity, limited ground truth, and multiple scales and resolutions. This paper provides a systematic review on principles and methods in spatial prediction. We provide a taxonomy of methods categorized by the key challenge they address. For each method, we introduce its underlying assumption, theoretical foundation, and discuss its advantages and disadvantages. We also discuss spatiotemporal extensions of methods. Our goal is to help interdisciplinary domain scientists choose techniques to solve their problems, and more importantly, to help data mining researchers to understand the main principles and methods in spatial prediction and identify future research opportunities.

A Survey on Spatial Prediction Methods

Given learning samples from a raster data set, spatial decision tree learning aims to find a decision tree classifier that minimizes classification errors as well as salt-and-pepper noise. The problem has important societal applications such as land cover classification for natural resource management. However, the problem is challenging due to the fact that learning samples show spatial autocorrelation in class labels, instead of being independently identically distributed. Related work relies on local tests (i.e., testing feature information of a location) and cannot adequately model the spatial autocorrelation effect, resulting in salt-and-pepper noise. In contrast, we recently proposed a focal-test-based spatial decision tree (FTSDT), in which the tree traversal direction of a sample is based on both local and focal (neighborhood) information. Preliminary results showed that FTSDT reduces classification errors and salt-and-pepper noise. This paper extends our recent work by introducing a new focal test approach with adaptive neighborhoods that avoids over-smoothing in wedge-shaped areas. We also conduct computational refinement on the FTSDT training algorithm by reusing focal values across candidate thresholds. Theoretical analysis shows that the refined training algorithm is correct and more scalable. Experiment results on real world data sets show that new FTSDT with adaptive neighborhoods improves classification accuracy, and that our computational refinement significantly reduces training time.

Zhe Jiang

Papers

Spatiotemporal Data Mining: A Computational Perspective

Monitoring Land-Cover Changes: A Machine-Learning Perspective

A neighborhood graph based approach to regional co-location pattern discovery: a summary of results

A Survey on Spatial Prediction Methods

Focal-Test-Based Spatial Decision Tree Learning