In this paper, we propose a Ward-like hierarchical clustering algorithm including spatial/geographical constraints. Two dissimilarity matrices D 0 and D 1 are inputted, along with a mixing parameter α ∈ [0, 1]. The dissimilarities can be non-Euclidean and the weights of the observations can be non-uniform. The first matrix gives the dissimilarities in the "feature space" and the second matrix gives the dissimilarities in the "constraint space". The criterion minimized at each stage is a convex combination of the homogeneity criterion calculated with D 0 and the homogeneity criterion calculated with D 1 . The idea is then to determine a value of α which increases the spatial contiguity without deteriorating too much the quality of the solution based on the variables of interest i.e. those of the feature space. This procedure is illustrated on a real dataset using the R package ClustGeo.

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International audienceThe purpose of this study is to propose a methodological essay for defining evolutionary trajectories of channel planforms and to examine the channel change in the middle Garonne River (southwest France) over a 130-year period. The study focuses on a reach of ~90 km situated downstream from the city of Toulouse. A set of four historical maps (1868, 1940s, 1970s, and 2000s) is used to build a geomorphometric diachronic database. Data processing through mixed multiple factor analysis (MFAmix) and hierarchical cluster analysis (HCA) allows distinction between four homogeneous zones within the study reach, depending on their evolutionary trajectories. Channel behavior in the upstream and median zones evolved as of the beginning of the study period (narrowing of the fluvial area, colonization by vegetation, and removal of alluvial bars), likely owing to punctual anthropogenic actions. The downstream zone is characterized by stabilization of the channel and alluvial bar removal over the second half of the twentieth century, coinciding with the campaign undertaken by French local authorities between 1960 and 1984 to protect river banks. The role of ACCEPTED MANUSCRIPT climate transition between the Little Ice Age (LIA) and the onset of the Global Warming period (GW) is also discussed. Results generally are consistent with the chronology established for most European rivers

Mixed data arise when observations are described by a mixture of numerical and categorical variables. The R package PCAmixdata extends standard multivariate analysis methods to incorporate this type of data. The key techniques/methods included in the package are principal component analysis for mixed data (PCAmix), varimax-like orthogonal rotation for PCAmix, and multiple factor analysis for mixed multi-table data. This paper gives a synthetic presentation of the three algorithms with details to help the user understand graphical and numerical outputs of the corresponding R functions. The three main methods are illustrated on a real dataset composed of four data tables characterizing living conditions in different municipalities in the Gironde region of southwest France.

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