Measuring Subcompositional Incoherence   总被引：2，自引：0，他引：2  

Michael Greenacre 《Mathematical Geosciences》2011,43(6):681-693

Subcompositional coherence is a fundamental property of Aitchison’s approach to compositional data analysis and is the principal justification for using ratios of components. We maintain, however, that lack of subcompositional coherence (i.e., incoherence) can be measured in an attempt to evaluate whether any given technique is close enough, for all practical purposes, to being subcompositionally coherent. This opens up the field to alternative methods that might be better suited to cope with problems such as data zeros and outliers while being only slightly incoherent. The measure that we propose is based on the distance measure between components. We show that the two-part subcompositions, which appear to be the most sensitive to subcompositional incoherence, can be used to establish a distance matrix that can be directly compared with the pairwise distances in the full composition. The closeness of these two matrices can be quantified using a stress measure that is common in multidimensional scaling, providing a measure of subcompositional incoherence. The approach is illustrated using power-transformed correspondence analysis, which has already been shown to converge to log-ratio analysis as the power transform tends to zero.  相似文献   

Variable Selection in Compositional Data Analysis Using Pairwise Logratios     

Greenacre  Michael 《Mathematical Geosciences》2019,51(5):649-682

Mathematical Geosciences - In the approach to compositional data analysis originated by John Aitchison, a set of linearly independent logratios (i.e., ratios of compositional parts, logarithmically...  相似文献   

Distribution and population structure of deep‐dwelling red coral in the Northwest Mediterranean          下载免费PDF全文

Michela Angiolillo  Andrea Gori  Simonepietro Canese  Marzia Bo  Cristina Priori  Giorgio Bavestrello  Eva Salvati  Fabrizio Erra  Michael Greenacre  Giovanni Santangelo 《Marine Ecology》2016,37(2):294-310

Commercially harvested since ancient times, the highly valuable red coral Corallium rubrum (Linnaeus, 1758) is an octocoral endemic to the Mediterranean Sea and adjacent Eastern Atlantic Ocean, where it occurs on rocky bottoms over a wide bathymetric range. Current knowledge is restricted to its shallow populations (15–50 m depth), with comparably little attention given to the deeper populations (50–200 m) that are nowadays the main target of exploitation. In this study, red coral distribution and population structure were assessed in three historically exploited areas (Amalfi, Ischia Island and Elba Island) in the Tyrrhenian Sea (Western Mediterranean Sea) between 50 and 130 m depth by means of ROV during a cruise carried out in the summer of 2010. Red coral populations showed a maximum patch frequency of 0.20 ± 0.04 SD patches·m^?1 and a density ranging between 28 and 204 colonies·m^?2, with a fairly continuous bathymetric distribution. The highest red coral densities in the investigated areas were found on cliffs and boulders mainly exposed to the east, at the greatest depth, and characterized by medium percentage sediment cover. The study populations contained a high percentage (46% on average) of harvestable colonies (>7 mm basal diameter). Moreover, some colonies with fifth‐order branches were also observed, highlighting the probable older age of some components of these populations. The Ischia population showed the highest colony occupancy, density and size, suggesting a better conservation status than the populations at the other study locations. These results indicate that deep dwelling red coral populations in non‐stressed or less‐harvested areas may diverge from the inverse size‐density relationship previously observed in red coral populations with increasing depth.  相似文献   

Log-Ratio Analysis Is a Limiting Case of Correspondence Analysis     

Michael Greenacre 《Mathematical Geosciences》2010,42(1):129-134

It is common practice in compositional data analysis to perform the log-ratio transformation in order to preserve sub-compositional coherence in the analysis. Correspondence analysis is an alternative approach to analyzing ratio-scale data and is often contrasted with log-ratio analysis. It turns out that if one introduces a power transformation into the correspondence analysis algorithm, then the limit of the power-transformed correspondence analysis, as the power parameter tends to zero, is exactly the log-ratio analysis. Depending on how the power transformation is applied, we can obtain as limiting cases either Aitchison’s unweighted log-ratio analysis or the weighted form called “spectral mapping”. The upshot of this is that one can come as close as one likes to the log-ratio analysis, weighted or unweighted, using correspondence analysis.  相似文献