Summarizing large spatial datasets: Spatial principal components (original) (raw)
Related papers
We propose a method for spatial principal components analysis that has two important advantages over the method that Wartenberg (1985) proposed. The first advantage is that, contrary to Wartenberg’s method, our method has a clear and exact interpretation: it produces a summary measure (component) that itself has maximum spatial correlation. Second, an easy and intuitive link can be made to canonical correlation analysis. Our spatial canonical correlation analysis produces summary measures of two datasets (e.g., each measuring a different phenomenon), and these summary measures maximize the spatial correlation between themselves. This provides an alternative weighting scheme as compared to spatial principal components analysis. We provide example applications of the methods and show that our variant of spatial canonical correlation analysis may produce rather different results than spatial principal components analysis using Wartenberg’s method. We also illustrate how spatial canonical correlation analysis may produce different results than spatial principal components analysis.
Principal Component Analysis on Spatial Data: An Overview
Annals of The Association of American Geographers, 2012
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. Este artículo considera críticamente la manera de utilizar con datos espaciales uno de los métodos estadísticos más viejos y de aplicación generalizada, el análisis de componentes principales (ACP). Antes de todo, suministramos una breve guía sobre cómo trabaja el ACP: Esto incluye variantes del ACP robustas y composicionales, vínculos con el análisis factorial, modelización de variable latente, y ACP de nivel múltiple. Luego presentamos dos enfoques diferentes para utilizar el ACP con datos espaciales. Primero, dirigimos nuestra atención al enfoque no espacial, que evita los problemas que surgen cuando los datos espaciales se utilizan con un ACP estándar de solo el espacio como atributo. Dentro de este enfoque identificamos cuatro metodologías principales, las cuales definimos como (1) el ACP aplicado a objetos espaciales, (2) el ACP aplicado a datos raster, (3) el ACP para ciencia atmosférica, y (4) el ACP para flujos. En el segundo enfoque, tratamos al ACP adaptado para efectos en el espacio geográfico, examinando métodos de ACP adaptados para efectos no estacionarios de primer orden (heterogeneidad espacial) y efectos estacionarios de segundo orden (autocorrelación espacial). También describimos la manera de utilizar el ACP para investigar múltiples escalas de autocorrelación espacial. Adicionalmente, intentamos desambiguar una confusión de terminología aclarando qué métodos son específicamente denominados “ACP espacial” en la literatura y cómo esta expresión tiene significados diferentes en áreas distintas. Por último, dirigimos nuestra atención a tres variaciones adicionales del ACP que no han sido usadas en un contexto espacial pero que muestran considerable potencial en este respecto: ACP simple, ACP ralo y ACP multilineal.
Evaluating Principal Components Analysis of Particular Spatial Statistical Models
This work is based on an analysis of the main components derived from particular patterns of spatial statistical data. The reference models of spatial statistical analysis are extracted only from the data of bi-temporal aerial photographs. This methodological approach introduces a significant improvement in the evaluation of changes in the territorial scenery, providing a wider interpretation of the problems of the area studied and encouraging a more analytical reading of complex environmental phenomena. In order to improve reading and analysis of the territorial changes it is necessary to compare the same geographical space in two different moments that enclose a well-defined period of time.
Canonical correlation approach to common spatial patterns
2013 6th International IEEE/EMBS Conference on Neural Engineering (NER), 2013
Common spatial patterns (CSPs) are a way of spatially filtering EEG signals to increase the discriminability between the filtered variance/power between the two classes. The proposed canonical correlation approach to CSP (CCACSP) utilizes temporal information in the time series, in addition to exploiting the covariance structure of the different classes, to find filters which maximize the bandpower difference between the classes. We show with simulated data, that the unsupervised canonical correlation analysis (CCA) algorithm is better able to extract the original class-discriminative sources than the CSP algorithm in the presence of large amounts of additive Gaussian noise (while the CSP algorithm is better at very low noise levels) and that our CCACSP algorithm is a hybrid, yielding good performance at all noise levels. Finally, experiments on data from the BCI competitions confirm the effectiveness of the CCACSP algorithm and a merged CSP/CCACSP algorithm (mCCACSP).
Spatial decorrelation methods : beyond MAF and PCA
2012
In the geostatistical treatment of multivariate data sets the joint modelling of their spatial continuity is usually required. While it is possible to automate the inference of a suitable variogram model a transformation of the set of attributes into spatially uncorrelated factors that can be simulated independently, might be desirable. Standard methods used in geostatistics for this purpose are principal component analysis (PCA) and the method of minimum/maximum autocorrelation factors (MAF). Both methods have restrictions in their applicability and a more flexible approach may be more suitable such as that offered by approximate joint diagonalisation (AJD) methods common in Blind Source Separation. The application of two AJD methods to a family of experimental semivariogram matrices is explored here and the performance is assessed on a number of simulated data sets with different spatial characteristics. A comparison with MAF and PCA shows that the use of AJD algorithm results in ...
Structuring Complex Correlations: An Overview of Multivariate Spatial Approaches
Multivariate spatial data are increasingly encountered in many disciplines, obvious examples being in geology, ecology, agriculture, epidemiology and in the environmental and atmospheric sciences. The defining feature of such data is the availability of measurements on a set of different and potentially related response variables at each spatial location in the region studied. Often, there is also an associated vector of potential explanatory variables measured at each of these sites. Such multivariate spatial data may exhibit not only correlations between variables at each site, but also spatial autocorrelation within each variable, and spatial cross-correlation between variables, at neighbouring sites. Any analysis or modelling must therefore allow for dependency structures that are both complex and inevitably confounded in the observed data. Moreover, if repeat observations are present on the response vector, they often refer to different points in time and add temporal autocorrelations or cross-correlations into the already complex mix of potential correlation structures.
Local Measures of Spatial Association
Geographic information science & technology body of knowledge, 2020
A fundamental concern in analyzing a spatial data set is to identify the presence and nature of spatial autocorrelation. Global measures can be used to summarize the typical features of spatial autocorrelation for the entire data set. However, if the data set has large spatial coverage, it is likely that there will be one or more subareas, possibly of variable sizes and shapes, that are different from the typical situation. Further, unless prior information is available, we are unlikely to have strong expectations about the number, locations, sizes, and shapes of such anomalies. Local measures of spatial autocorrelation have been developed to provide a way of revealing such peculiarities. By identifying anomalous subareas, local measures provide information that is useful in modelling the spatial processes that are thought to give rise to the data, especially since they give an indication of the spatial scales at which such processes might be operating. In addition, the information they provide is of potential value in other activities such as identifying patches and delimiting boundaries. This paper reviews the development and use of local measures of spatial autocorrelation and presents a summary of the findings for all existing measures. It also explores unresolved issues in their application and considers likely directions for future work.
ELSA: a new local indicator for spatial association
2021
There are several local indicators of spatial association (LISA) that allow exploration of local patterns in spatial data. Despite numerous situations where categorical variables are encountered, few attempts have been devoted to the development of methods to explore the local spatial pattern in categorical data. To our knowledge, there is no indicator of local spatial association that can be used for both continuous and categorical data. We introduce ELSA, which can be used for exploring and testing local spatial association for continuous and categorical variables. We provide the R-package elsa for making these computations.