Identify one spatial pattern shown on the map.

II.D.1 Patterns of Recent Change

Spatial patterns of change are shown in Figs. 2 and Figs.3 for the two 25-year periods that show the strongest warming of the twentieth century (1920–1944 and 1975–1999). Patterns are shown seasonally and for the annual average. Even for the most recent period, coverage is not complete, with missing areas over most of the Southern mid to high-latitude oceans, parts of the Antarctic and central Arctic, and some continental interiors. Available data for the 1920–1944 period, however, only enables patterns to be shown for about half the earth's surface, compared with about three-quarters now. Both periods exhibit strong and highly significant warming in the hemispheric averages, but statistical significance is achieved in only relatively few areas on a local basis. More areas achieve significance in the recent period, but this is no more than would be expected, given the greater areas with data and the stronger warming (see Table I). Warming is not spread evenly across the seasons, although annually most regions indicate warming. The warming patterns of the two periods show different patterns, suggesting that they might be related to different combinations of causes.

3.4 Spatial Aspects of Gene-Expression

Spatial patterns of gene-expression can be recorded in text or images. Some currently available databases that store gene-expression information (e.g. the Xenopus Molecular Marker Resource and TBASE) use free text descriptions, whereas others (e.g. Flyview) use controlled vocabularies to describe sites of gene-expression. Controlled vocabularies include standard anatomical nomenclature systems and can be used consistently in different databases relating to the same organism. For Caenorhabditis elegans there is a unique means of identifying individual cells on the basis of lineage. A controlled vocabulary for Drosophila is given in Flybase; indeed, a subset of this vocabulary describes subcellular components and could form the basis for subcellular descriptions in other species. The MGEIR will include an anatomical description of the mouse embryo which is organized in an open-ended database to which finer detail can be added as required. The mouse anatomical nomenclature is being used, where appropriate, to help formulate descriptions of zebrafish and human embryos. It is to be hoped that, ultimately, the use of standard nomenclature systems will not only simplify the use of each of these databases, but will enable cross-database links.

A novel non-textual approach to recording gene-expression information is employed by the Tooth Database, in which gene-expression is assigned to tissues that are represented in diagrams of tooth primordia at successive stages of development. The use of diagrams removes the need for the user to identify the tissue by name and reduces confusion over the use of different names. Data cannot, however, be assigned to part of a defined tissue.

In addition to textual records, many databases hold images that illustrate the details of complex gene-expression patterns. A major distinction here is between databases that document the expression of different genes in a series of independent images and those in which different gene-expression patterns are spatially mapped onto a single set of standard reference images. Spatial mapping allows immediate comparison between different patterns and, in principle, allows purely spatial searches. The main advantage of spatially mapped data over textual descriptions is that many gene-expression patterns do not map 1 : 1 with an anatomical description, so that gene-expression data often cannot be translated simply into a list of anatomical terms. This is particularly true of genes involved in mechanisms that operate in a spatial, rather than tissue-specific, context during the early stages of development when the anatomy of the organism is being established. The spatial mapping approach has considerable potential because it can link gene-expression data to other spatially distributed information of relevance to gene function, for example cell lineage, cell proliferation and cell death. A disadvantage is that the data are transformed from their original form. This is more laborious than simply cataloguing original images; moreover, the mapping must be done carefully to ensure that significant features are not lost or spurious features introduced. The Drosophila database being developed at the University of California by Hartenstein and colleagues (Hartenstein et al., 1996), the Zebrafish Database and the MGEIR will employ spatial mapping.

As more gene-expression patterns are entered into databases it is likely that some will become established as reference patterns. These will be patterns that are clearly defined, invariant and dynamically stable, and for which probes or antibodies are readily available. These gene-expression domains will define a ‘molecular anatomy’ against which the expression of other genes can be described. Such a molecular anatomy may reflect a developmentally more profound subdivision of the embryo than the morphological subdivision that is presently recognized by classical anatomy.

3.2 Understanding Firms

Early studies focused on actual spatial patterns of industrial location, as well as optimal patterns, a theme that continues (see Location Theory). The object in geographers' study of firms is less the organizational or industrial form of these entities than their actual behavior. Understanding the mechanisms by which firms and industries operate and their impact on industrial location and regional development also is a central issue in Industrial Geography. Along these lines, of particular interest have been studies of vertical integration and disintegration, or what is inside a firm and what is obtained from other firms.

As companies became vertically integrated, absorbing necessary processes in-house, studies of large firms evolved into what was known as the ‘geography of enterprise.’ Globalization is an effect of the actions of large (multinational, transnational, global) companies, whether through trade, foreign direct investment (see Foreign Investment: Direct), or other arrangements (Cox 1997, Dicken 1998). This work has been complemented if not largely superseded by the view that large firms are less influential in their own right than merely taking advantage of divisions of labor, an interpretation that goes a long way toward explaining the geography of production (Massey 1995, Sayer and Walker 1992).

In addition to large firms, entrepreneurship and small firms are a central feature of both flexible accumulation and creative destruction, and therefore have received increasing attention as their significance in most economies has grown. This is most evident in the case of regions where new firms and new industries are common (see Technology Districts).

1.10.6 Conclusion

This article examines techniques for analyzing the spatial patterns of point and area features. The first three sections cover topics related to point features, and the next two sections introduce topics on area features. Section “Descriptive Measures of Point Features” provides some descriptive measures of point features in terms of central tendency and spatial dispersion. Central tendency measures include mean center, median center, and central feature, and spatial dispersion measures include standard distance and deviational ellipse. Section “Inferential Measures of One Type of Points” discusses inferential measures of one type of points such as quadrat analysis, ordered neighbor statistics, and Ripley’s K-function to assess whether an observed pattern is random, dispersed, or clustered. Section “Collocation Analysis of Two Types of Points” examines colocation of two types of points by cross K-function and CLQ in order to measure the extent that they are within the vicinity of each other. Section “Area-Based Analysis of Spatial Autocorrelation” analyzes spatial autocorrelation of areal features by popular indices such as the join-count statistic, Moran’s I, Geary Ratio, and Getis-G statistic. Section “Regionalization Methods” introduces several GIS-automated regionalization methods, such as REDCAP and MLR, to aggregate smaller and similar (and thus spatially autocorrelated) areal units into larger regions. All sections have some illustrative examples to explain the implementation process with sample data and programs to download.

1.14.2.3 Gaps and Challenges

Notwithstanding the prolific literature on metrics examining urban spatial patterns from distinct backgrounds, some important gaps still exist in terms of encompassing the dynamic urban processes. Landscape metrics are often criticized for relying too much on ecology principles and not being the most adequate to study some specific urban processes—in particular those occurring at smaller spatial scales—or processes involving population movements, socioeconomic variables, or governance structures (Herold et al., 2005; Schneider and Woodcock, 2008; Schwarz, 2010). Geospatial metrics usually focus on spatial patterns, or use the datasets specific to a particular case study, and are therefore not robust enough to transfer and adapt to different geographic contexts or to draw general conclusions.

The scarcity of metrics focusing on patterns of urban shrinkage is another important gap in the literature (Reis et al., 2015). Strong and enduring population decline, migration across different tier cities (i.e., in some cases from small to mid-size cities), and inter-metropolitan area movements of residents are all related to the changing demographic, cultural, and socioeconomic trends. Urban shrinkage is an increasing reality in many regions of the world, which has emerged as one of the most important research topics of urban and regional planning, particularly in Europe and North America (Pallagst, 2010; Wiechmann and Bontje, 2015). These processes are quite relevant at an intra-urban scale and, therefore, growing and shrinking areas can be found in most large cities regardless of overall metropolitan population trends. Although some metrics have been developed and used to study urban decline (e.g., residential vacancy and share of demolition), there is a clear lack of quantitative research on urban shrinkage, particularly in terms of development of metrics specifically aimed at assessing its spatial patterns.

An important challenge for the development and application of spatial metrics is related to the gaps in knowledge on the exact nature of spatial patterns intended to be quantified. The first step toward the development of metrics, therefore, is to identify the particular spatial features of an urban area that should be quantified. For example, the concept of “fragmentation” often addressed by landscape and geospatial metrics is not always clear and it is sometimes mixed with “shape irregularity” (Reis, 2015). Moreover, as mentioned above, the specific spatial features of urban sprawl are still not clear in the literature despite the high number of studies addressing this issue. More notably, the literature on spatial patterns associated with urban shrinkage is still much undeveloped. For instance, although “perforation” is commonly considered a spatial outcome of shrinkage, Reis (2015) found at least five different definitions of perforation in the literature, thus indicating a clear gap in standardizing the definitions of shrinkage-related terminologies.

In addition to the aforementioned challenges, scalability effects, types of data units and aggregation, and issues of subjective selection are some of the intrinsic limitations of empirical applications of spatial metrics. Spatial metrics use the data variables that are often aggregated into arbitrary units; however, since the boundaries of the data units affect the results of spatial data, the outcomes of an application of metrics are influenced by the quality of available data and the spatial scale used (Martínez et al., 2007; Martínez et al., 2009). Certainly, no application of spatial metrics can be considered completely objective as the results are always influenced by the quality and level of aggregation of data and the criteria for the definition of spatial units or the extent of the study area. These aspects are dependent on subjective choices made by the analyst, on specific characteristics, and research objectives of different case studies, and therefore limit the generalization of findings of a particular case study, and/or the extent to which the metrics can be replicated to other case studies.

Several authors argue that more effort is needed toward the development of new spatial metrics to achieve robust measures for assessing urban patterns (Aguilera et al., 2011; Huang et al., 2007, 2009; Liu and Yang, 2015). This is quite imperative for the study of urban shrinkage and comparative analyses of different cities. Furthermore, combining the spatial metrics—particularly those focusing on physical configuration of spatial structures—with demographic and socioeconomic variables would be a leap forward toward forming more robust mixed indicators, and to some extent overcoming the challenges of using diverse datasets and spatial aggregations.

3.4 Recognition

One important end point of the processing of spatial pattern is the visual recognition of objects, faces, and scenes. Object recognition can be specifically impaired (agnosia) by damage to the temporal lobe of the brain, and a specific loss of the ability to recognize faces (prosopagnosia) may also occur. Functional imaging studies shows an area that is selectively activated during the processing of faces (the fusiform face area), and another that is active in visual recognition of locations (the parahippocampal place area). Human studies cannot show how individual neurons are responding, but in the temporal lobe of the monkey, single neurons are found to respond specifically to faces. The pattern of activation over a group of such cells conveys sufficient information to distinguish one individual from another. In the inferotemporal region, cells respond to features that can define different types of object. In both cases, the response shows position generalization; that is, it is selective for a particular class of stimulus, irrespective of its position within a wide receptive field.

Thus, the principles of a sparse population code, found in the representation of local pattern in V1, appear to apply also to the higher level representation of visual identity. However, the hierarchy of neural transformations which connects the former with the latter is very poorly understood.

1.5 Succession

Initially ecologists were concerned primarily with trying to explain spatial patterns, i.e., plant and animal geographic distributions. Nevertheless, many observers had noted that temporal changes in vegetation or succession often occurred locally [Clements, 1916; Acot, 1998]. Clements [1916] reviewed the early literature on succession and found numerous descriptions of temporal changes going back to the seventeenth century. (See also Egerton [2009] for a recent review of succession studies.) A couple of examples will illustrate the character of these observations. The French writer Dureau de la Malle (1777-1857) in 1825 published a paper primarily on crop rotation that describes the succession of species in forests and meadows. He concludes that changes in plant species “est une loi générale de la nature” [Acot, 1998, p. 130]. Likewise, Henry David Thoreau (1817-1862) in 1860 gave an address on “The succession of forest trees” in which he describes changes in forest vegetation that he had observed in New England [Spurr, 1952]. Thoreau “recognized the effects of wind-throw and fire in the forests found by the original European settlers, and distinguished between successional trends in small clearings, following cutting, following single fires, and as a results of agricultural use” [Spurr 1952, p. 426]. Such observations, however, had little influence on early ecologists. Although Warming [1895, 1896] had previously described the phenomenon of succession and even postulated some rules that govern it, the studies of succession that most influenced the development of ecology were those of Henry Chandler Cowles (1869-1939). Cowles described succession, more correctly a chronosequence, in the sand dunes along the south shore of Lake Michigan in a series of papers published in 1899. (For a detailed account of Cowles life and works, see Cassidy [2007].) Cowles was able to place the vegetation types observed into a crude chronological sequence because the dunes became older as you moved inland from Lake Michigan. He interpreted this chronosequence as a putative successional sequence from pioneering dune to mature forest vegetation. Cowles describes the various kinds of vegetation found in the dunes in considerable detail, but he does not hypothesize much about the patterns observed beyond noting that physiographic (landscape) position and dune age are correlated with vegetation types. In short, Cowles’ study is transitional in that it focuses primarily on the distribution of vegetation types and only secondarily on temporal changes. It was the temporal dimensions of his studies, however, that were to have the most lasting influence on the development of ecology in the twentieth century [McIntosh, 1985; Cassidy, 2007]. Early animal ecologists, most notably, Victor Shelford (1877-1968) quickly picked up the concept of succession first from Cowles and later from Frederic E. Clements [Croker 1991].

In 1917, Frederic E. Clements (1874-1945) published a massive monograph on succession in which he proposed another defining hypothesis of ecology: succession is the development of a climax formation [Clements, 1916]. A climax formation (a vegetation type defined by the growth form of its dominant species, e.g., deciduous trees) was in equilibrium with its climate and thus was able to persist until the climate changed. A formation is for Clements an organism that “arises, grows, matures, and dies.” In short, a climax formation has both an ontogeny and phylogeny just like an individual plant. Like the ontogeny of a plant, succession is directional and irreversible (progressive in Clements’ words). Nevertheless, Clements also recognized that succession was much more “complex and obscure” than the development of an individual plant and his descriptions of specific vegetation changes are often highly mechanistic. In short, Clements’ novel hypothesis is that a climax formation is a “super-organism” and that its ontogeny is the result of succession. Clements makes the claim that there is a strong but not perfect analogy between an individual organism and a formation. Nevertheless, he seems to be making a metaphysical claim that there is a level of biological organization, the climax formation, above the species level and that formations have characteristics, e.g., an ontogeny, similar to those of individual organisms.

In Chapters 1 and 2 of Bio-Ecology [Clements and Shelford 1939], one of Clements’ last major works, Clements and Shelford review various hypotheses about the nature of communities and defend in considerable detail Clements’ hypothesis that communities are “complex” organisms (formerly superorganisms). In this work, Clements and Shelford now call the endpoint of succession a “climax community” rather than a climax formation. “One of the first consequences of regarding succession as the key to vegetation was the realization that the community … is more than the sum of its parts, that it is indeed an organism of a new order” [Clements and Shelford, 1939, p. 21]. They continue “… it is essential to bear in mind the significance of the word “complex” in this connection, since this expressly takes the community out of the category of organisms as represented by individual plants and animals” [p. 21]. They try to clarify their definition of complex organism again by analogy and state that it bears “something” of the same relation to the individual plant or animal that “each of these does to the one-celled protophyte or protozoan”. In other words, the formation is a real entity, but one that is not as integrated as a higher plant or higher animal. Not surprisingly, the exact metaphysical status of Clements’ complex or superorganism is still being debated [Eliot, 2007].

According to Clements, ecology is fundamentally a holistic science [Clements 1935]. The Möbius-Forbes hypothesis about communities tending toward equilibrium had holistic overtones, but it did not necessarily imply that communities are metaphysically distinct entities. Clements’ critics like Henry Gleason [1917], who saw communities as groups of overlapping populations of species, believed that Clements confused change [e.g., in species composition] with development. Nevertheless, Clements’ novel succession/super-organism hypothesis was to be one of the most important defining hypotheses in American ecology in the first half of the twentieth century [Worster [1977]; McIntosh, 1985; Kingsland, 2005].

4.2 User Behavior Understanding Through Spatial Big Data Analytics

Another typical application for spatial big data analytics in CC systems is user behavior detection, which includes single-user and multiuser cases. For the single-user case, an anomaly detection method is proposed in Karatepe and Zeydan [38]. This method is based on CDR data from a mobile service provider in Turkey. The main idea is to detect suspicious CITY ID and CELL ID pairs by analyzing the details of the user’s call activities through knowledge-based rules. For example, an abnormal trip can be detected due to a longer traveling time between two cities. The time stamps are collected through the call records of different cells.

Through understanding the behavior of multiusers in CC systems, it is possible to understand new communication or behavior trends, the spatial structure of a high-density city, and so on. For example, in Chen et al. [39], the urban spatial structure is identified through CDR data. The urban spatial structure often refers to the sets of human flows occurring from the regular interactions between different functional regions of an urban area, such as daily travel behaviors. The travel behaviors cause relatively frequently human flows, which can be considered as the hot lines between different functional regions. The study finally shows hot lines would be quantified as relatively popular channels that exist in two different functional regions.

Next, we further explore the possible application when adopting spatial pattern mining methods into an application as follows.

Spatial prediction: As discussed in Section 3.2.1, spatial prediction models discover nonspatial values at unknown locations through observation of values at surrounding areas, based on spatial dependencies retrieved from domain knowledge. However, when we consider applications to detect users’ behavior, the spatial dependency is unclear and too much of a contingency factor for modeling.

Spatial outlier detection: This is expected to be adopted in this kind of application, to detect hot points where the people have abnormal behaviors. For example, suppose CC systems provide CDR data with very precise geo-location information; then the frequency of people going through each location/point can be calculated and used as spatial objects in the spatial outlier detection method. The nonspatial values (i.e., frequency of visiting) can be modeled by attribute function f(x), and the neighboring effects are represented by the aggregated function FaggrN. Through further calculation, as shown in Section 3.2.2, spatial outliers can be detected. For example, a spatial outlier is a strange point with very few visits even when the surrounding locations are popular (i.e., high visiting frequency). The information behind the data could be a destroyed road, especially in a disaster scenario. The above detection can help users to find a better route.

Spatial co-location discovery: This discovers features/data that are frequently located in the same areas. Assume we have the same data (i.e., frequency of visiting). Then, assume we have another dataset (e.g., store information around the street). The spatial co-location can help us to find the spatial relation between the frequency of visiting and the type of store. A possible result could be that young people often visit fashion shops at lunch time.

Spatial clustering: This groups data with similar features together, and so this clustering has many applications considering multiuser behaviors. Spatial clustering supports a system to detect the areas where people often have similar specific behaviors and then discovers unobservable hidden information.

What is an example of a spatial pattern?

What are spatial patterns on a map?

How can spatial patterns be represented on maps?

What is global spatial pattern?