This article considers critically how one of the oldest and most widely applied statistical methods, principal components analysis (PCA), is employed with spatial data. We first provide a brief guide to how PCA works: This includes robust and compositional PCA variants, links to factor analysis, latent variable modeling, and multilevel PCA. We then present two different approaches to using PCA with spatial data. First we look at the nonspatial approach, which avoids challenges posed by spatial data by using a standard PCA on attribute space only. Within this approach we identify four main methodologies, which we define as (1) PCA applied to spatial objects, (2) PCA applied to raster data, (3) atmospheric science PCA, and (4) PCA on flows. In the second approach, we look at PCA adapted for effects in geographical space by looking at PCA methods adapted for first-order nonstationary effects (spatial heterogeneity) and second-order stationary effects (spatial autocorrelation). We also describe how PCA can be used to investigate multiple scales of spatial autocorrelation. Furthermore, we attempt to disambiguate a terminology confusion by clarifying which methods are specifically termed “spatial PCA” in the literature and how this term has different meanings in different areas. Finally, we look at a further three variations of PCA that have not been used in a spatial context but show considerable potential in this respect: simple PCA, sparse PCA, and multilinear PCA.

Visual analytics aims to combine the strengths of human and electronic data processing. Visualisation, whereby humans and computers cooperate through graphics, is the means through which this is achieved. Seamless and sophisticated synergies are required for analysing spatio-temporal data and solving spatio-temporal problems. In modern society, spatio-temporal analysis is not solely the business of professional analysts. Many citizens need or would be interested in undertaking analysis of information in time and space. Researchers should find approaches to deal with the complexities of the current data and problems and find ways to make analytical tools accessible and usable for the broad community of potential users to support spatio-temporal thinking and contribute to solving a large range of problems.

Human mobility is important for understanding the evolution of size and structure of urban areas, the spatial distribution of facilities, and the provision of transportation services. Until recently, exploring human mobility in detail was challenging because data collection methods consisted of cumbersome manual travel surveys, space-time diaries, or interviews. The development of location-aware sensors has significantly altered the possibilities for acquiring detailed data on human movements. Although this has spurred many methodological developments in identifying human movement patterns, many of these methods operate solely from the analytical perspective and ignore the environmental context within which the movement takes place. In this paper we attempt to widen this view and present an integrated approach to the analysis of human mobility using a combination of volunteered GPS trajectories and contextual spatial information. We propose a new framework for the identification of dynamic (travel modes) and static (significant places) behaviour using trajectory segmentation, data mining, and spatio-temporal analysis. We are interested in examining if and how travel modes depend on the residential location, age, or gender of the tracked individuals. Further, we explore theorised ‘third places’, which are spaces beyond main locations (home/work) where individuals spend time to socialise. Can these places be identified from GPS traces? We evaluate our framework using a collection of trajectories from 205 volunteers linked to contextual spatial information on the types of places visited and the transport routes they use. The result of this study is a contextually enriched data set that supports new possibilities for modelling human movement behaviour.

Modern positioning and identification technologies enable tracking of almost any type of moving object. A remarkable amount of new trajectory data is thus available for the analysis of various phenomena. In cartography, a typical way to visualise and explore such data is to use a space–time cube, where trajectories are shown as 3D polylines through space and time. With increasingly large movement datasets becoming available, this type of display quickly becomes cluttered and unclear. In this article, we introduce the concept of 3D space–time density of trajectories to solve the problem of cluttering in the space–time cube. The space–time density is a generalisation of standard 2D kernel density around 2D point data into 3D density around 3D polyline data (i.e. trajectories). We present the algorithm for space–time density, test it on simulated data, show some basic visualisations of the resulting density volume and observe particular types of spatio-temporal patterns in the density that are specific to trajectory data. We also present an application to real-time movement data, that is, vessel movement trajectories acquired using the Automatic Identification System (AIS) equipment on ships in the Gulf of Finland. Finally, we consider the wider ramifications to spatial analysis of using this novel type of spatio-temporal visualisation.