SpatEntropy: Spatial Entropy Measures in R

This article illustrates how to measure the heterogeneity of spatial data presenting a finite number of categories via computation of spatial entropy. The R package SpatEntropy contains functions for the computation of entropy and spatial entropy measures. The extension to spatial entropy measures is a unique feature of SpatEntropy. In addition to the traditional version of Shannon's entropy, the package includes Batty's spatial entropy, O'Neill's entropy, Li and Reynolds' contagion index, Karlstrom and Ceccato's entropy, Leibovici's entropy, Parresol and Edwards' entropy and Altieri's entropy. The package is able to work with both areal and point data. This paper is a general description of SpatEntropy, as well as its necessary theoretical background, and an introduction for new users.Comment: 24 pages, 6 figure

Characterizing Clustering Models of High-dimensional Remotely Sensed Data Using Subsampled Field-subfield Spatial Cross-validated Random Forests

Clustering models are regularly used to construct meaningful groups of observations within complex datasets, and they are an exceptional tool for spatial exploratory analysis. The clusters detected in a recent spatio-temporal cluster analysis of leaf area index (LAI) in the Columbia River Basin (CRB) require further investigation since they are only derived using a single greenness metric. It is of great interest to further understand how greening indices can be used to determine separation of sites across an array of remotely sensed environmental attributes. In this prior work, there are highly localized minority clusters that were detected to be most dissimilar from the remaining clusters as determined by annual variation in remotely sensed LAI. The objective of this study is to discern what other environmental factors are important predictors of cluster allocation from the mentioned cluster analysis, and secondarily, to construct a predictive model that prioritizes minority clusters. A random forest classification is considered to examine the importance of various site attributes in predicting cluster allocation. To satisfy these objectives, I propose an application-specific process that integrates spatial sub-sampling and cross-validation to improve the interpretability and utility of random forests for spatially autocorrelated, highly-localized, and unbalanced class-size response variables. The final random forest model identifies that the cluster allocation, using only LAI, separates sites significantly across many other environmental attributes, and further that elevation, slope, and water storage potential are the most important predictors of cluster allocation. Most importantly, the class errors rates for the clusters that are most dissimilar, as detected by the cluster model, have the best misclassification rates which fulfills the secondary objective of aligning the priorities of a predictive model with a prior cluster model

Measuring heterogeneity in urban expansion via spatial entropy

The lack of efficiency in urban diffusion is a debated issue, important for biologists, urban specialists, planners and statisticians, both in developed and new developing countries. Many approaches have been considered to measure urban sprawl, i.e. chaotic urban expansion; such idea of chaos is here linked to the concept of entropy. Entropy, firstly introduced in information theory, rapidly became a standard tool in ecology, biology and geography to measure the degree of heterogeneity among observations; in these contexts, entropy measures should include spatial information. The aim of this paper is to employ a rigorous spatial entropy based approach to measure urban sprawl associated to the diffusion of metropolitan cities. In order to assess the performance of the considered measures, a comparative study is run over alternative urban scenarios; afterwards, measures are used to quantify the degree of disorder in the urban expansion of three cities in Europe. Results are easily interpretable and can be used both as an absolute measure of urban sprawl and for comparison over space and time.Comment: 23 pages, 7 figure

The Emergence of Urban Land Use Patterns Driven by Dispersion and Aggregation Mechanisms

Abstract We employ a cellular-automata to reconstruct the land use patterns of cities that we characterize by two measures of spatial heterogeneity: (a) a variant of spatial entropy, which measures the spread of residential, business, and industrial activity sectors, and (b) an index of dissimilarity, which quantifies the degree of spatial mixing of these land use activity parcels. A minimalist and bottom-up approach is adopted that utilizes a limited set of three parameters which represent the forces which determine the extent to which each of these sectors spatially aggregate into clusters. The dispersion degrees of the land uses are governed by a fixed pre-specified power-law distribution based on empirical observations in other cities. Our method is then used to reconstruct land use patterns for the city state of Singapore and a selection of North American cities. We demonstrate the emergence of land use patterns that exhibit comparable visual features to the actual city maps defining our case studies whilst sharing similar spatial characteristics. Our work provides a complementary approach to other measures of urban spatial structure that differentiate cities by their land use patterns resulting from bottom-up dispersion and aggregation processes

Evaluation of pixel based and object based classification methods for land cover mapping with high spatial resolution satellite imagery, in the Amazonas, Brazil

In the state of Acre, Brazil, there is ongoing land use change, where inhabitants of this part of the Amazonian rainforest practice shifting agriculture. Practicing this type of agriculture is, according to the SKY Rainforest Rescue organization, damaging to forest ecosystems. This organization aims to educate people in how to maintain sustainable agriculture. By monitoring this shift in agricultural practices with the use of remotely sensed data, the organization can follow the development. In this thesis, an image with high spatial resolution from the SPOT-5 satellite is used to evaluate which classification method is most appropriate for monitoring land use change in this specific area. Three methods are tested; two pixels based and one object based. The pixel based methods are the Support Vector Machine (SVM) with a Radial Basis Function (RBF) kernel and the Maximum Likelihood Classifier (MLC), and the object based method is segmented with Multi Resolution Segmentation (MRS) and classified with the k-Nearest Neighbor (kNN). The parameters gamma and penalty parameter C in the SVM with an RBF kernel were estimated by a k-fold cross validation and grid search method; and for the MLC, an assumption that each class had an equal probability distribution was made. For the object based approach the first step was segmentation; for the MRS there are three parameters: scale, shape and compactness. The scale parameter was set by using an algorithm that was based on comparing local variance; shape and compactness were defined based on previous studies and visual evaluation of the segments. All three methods will produce two classified maps each; one where the feature space consists of the three original wavebands (green, red and NIR) and one where the feature space is of six dimensions that include the original three wavebands and three texture derivations, one from each original band. The texture is derived from the co-occurrence GLCM method, which can be used to calculate 14 different texture measures. The three most suitable texture derivations were the contrast texture measure from the green and NIR band, and an entropy texture derived from the red band. When combining these three texture derivations with the original bands, the classes were further separated. The original image was also lowered in resolution, from 2.5m to 25m in pixel size. However, this did not generate either higher or similar overall accuracy compared to any of the high spatial resolution classified images. The moderate spatial resolution classifications were only computed with the MLC and SVM due to the inefficiency of an object based image analysis method when used with moderate spatial resolution. Of these six classifications, only two exceeded the 85% threshold of an acceptable overall accuracy. These were the SVM (86.8%) and OB-kNN (86.2%), which included the texture analysis. None of those classifications with only the three original bands exceeded this threshold. In conclusion, the object based method is the most suitable approach for this dataset because: 1) the parameter optimization is less subjective, 2) computational time is relatively lower, 3) the classes in the image are more cohesive and 4) there is less need for post-classification filtering.Människor boende i Brasiliens regnskogar livnär sig på svedjebruk, vilket är en jordbruksmetod där en först hugger ned skogen för att sen bränna resterande stubbar och annan vegetation. Jordbruksmetoden är, enligt SKY Rainforest Rescue, en ohållbar metod som kan försämra regnskogens ekosystem och därmed dess ekosystemtjänster som människan har kommit att bli beroende av. Organisationen arbetar för att invånarna ska lära sig att bruka en mer hållbar metod och för att övervaka utvecklingen av projektet använder sig SKY Rainforest Rescue av fjärranalys. Med hjälp av satellitbilder kan jordens yta studeras från ett avstånd vilket genererar en god överblick av ett större område vilket kan vara att föredra i den här studien. Analyserna utgår från bilder tagna av sensorer som är placerade på satelliter, vilka kretsar kring jorden i en omloppsbana och samtidigt registrerar bilder. Varje bild består av ett visst antal band där varje band representerar ett spektralt intervall t.ex. synligt ljus som grön, röd och blå, i det elektromagnetiska spektrumet. Högupplösta bilder är ett resultat av ny teknik som kommit ut på marknaden och det har med den utvecklingen uppstått frågor om hur en ska behandla satellitbilder i framtiden. Därför är det viktigt att utvärdera och utveckla metoder för bildbehandling. I den här studien används satellitbilder som är högupplösta, där en pixel motsvarar 2.5x2.5m på jordytan. Tre olika metoder används för att framställa markanvändningskartor för att finna den mest optimala metoden för just den plasten och typ av bild. Metoderna är klassificeringsmetoder som grundar sig på pixlars digitala nummer, en pixel kan ha ett värde mellan 0-255 där varje nummer representerar en färg. Två av dessa är baserade på varje pixels enskilda spektrala värden, den tredje segmenterar ihop närliggande pixlar med liknande värden till objekt och beräknar ett spektralt medelvärde av pixlarna tillhörande objekten. En stor skillnad mellan de två metoderna är att i den objektbaserade spelar en pixels intilliggande pixlar en stor roll, medan en pixelbaserad metod behandlar varje pixel enskilt oberoende utav grannpixlar. I och med högupplösta bilder kan intill liggande pixlar spela en större roll eftersom objekt t.ex. ett träd kan bestå av flera pixlar med varierande spektrala värden. En metod som kan minska det problem som uppstår är att analysera en bilds textur, alltså variationen av gråtoner i en bild. En markanvändningskarta måste valideras innan den kan accepteras som riktig. Validering är baserad på att jämföra stickprov från kartan med den faktiska marken och på det viset skatta hur bra kartan stämmer överens med verkligheten. Enligt tidigare studier ska den generella procenten av korrekt karterade punkter överstiga 85 % för att kartan i fråga ska accepteras som riktig och representativ för området. I studien framställs sex kartor, baserat på olika metoder från en högupplöst satellitbild och två kartor från samma bild men med lägre upplösning. Endast två av de åtta kartorna hade högre än 85 % korrekt karterade markanvändningsklasser. Den ena är baserad på enskilda pixlar (86.8%) och den andra är baserad på segmenterade pixlar (86.2%), vad metoderna har gemensamt är att de både inkluderar en texturanalys. Den objektbaserad är dock att föredra på grund av mindre komplex algoritm, mindre tidskrävande och ser visuellt bättre ut

Learning Social Links and Communities from Interaction, Topical, and Spatio-Temporal Information

The immense popularity of today's social networks has lead to the availability and accessibility of vast amounts of data created by users on a daily basis. Various types of information can be extracted from such data, for example, interactions among users, topics of user postings, and geographic locations of users. While most of the existing works on social network analysis, in particular those focusing on social links and communities, rely on explicit and static link structures among users, extracting knowledge from exploiting more features embedded in user-generated data is another important direction that only recently has gained more attention. Initial studies employing this approach show good results in terms of a better understanding latent interactions among users. In the context of this dissertation, multiple features embedded in user-generated data are investigated to develop new models and algorithms for (1) revealing hidden social links between users and (2) extracting and analyzing dynamic feature-based communities in social networks. We introduce two approaches for extracting and measuring interpretable and meaningful social links between users. One is based on the participation of users in threads of discussions. The other one relies on the social characteristics of users as reflected in their postings. A novel probabilistic model called rLinkTopic is developed to address the problem of extracting a new type of feature-based community called regional LinkTopic: a community of users that are geographically close to each other over time, have common interests indicated by the topical similarity of their postings, and are contextually linked to each other. Based on the rLinkTopic model, a comprehensive framework called ErLinkTopic is developed that allows to extract and capture complex changes in the features describing regional LinkTopic communities, for example, the community membership of users and topics of communities. Our framework provides a novel basis for important studies such as exploring social characteristics of users in geographic regions and predicting the evolution of user communities. For each approach developed in this dissertation, extensive comparative experiments are conducted using data from real-world social networks to validate the proposed models and algorithms in terms of effectiveness and efficiency. The experimental results are further discussed in detail to show improvements over existing approaches and the applicability and advantages of our models in terms of learning social links and communities from user-generated data