Performs hard or fuzzy clustering of vegetation data
vegclust(x, mobileCenters, fixedCenters = NULL, method="NC", m = 2, dnoise = NULL, eta = NULL, alpha=0.001, iter.max=100, nstart=1, maxminJ = 10, seeds=NULL, verbose=FALSE) vegclustdist(x, mobileMemb, fixedDistToCenters = NULL, method="NC", m = 2, dnoise = NULL, eta = NULL, alpha=0.001, iter.max=100, nstart=1, seeds=NULL, verbose=FALSE)
Returns an object of type
vegclust with the following items:
raw for function
dist for function
The clustering model used
The fuzziness exponent used (
m=1 in case of kmeans)
The distance to the noise cluster used for noise clustering (NC, HNC, NCdd or HNCdd). This is set to
NULL for other models.
The reference distance vector used for possibilistic clustering (PCM or PCMdd). This is set to
NULL for other models.
The fuzzy membership matrix. Columns starting with "M" indicate mobile clusters, whereas columns starting with "F" indicate fixed clusters.
vegclust is used, this contains a data frame with the coordinates of the mobile centers (centroids or medoids). If
vegclustdist is used, it will contain the indices of mobile medoids for models KMdd, FCMdd, HNCdd, NCdd and PCMdd; or
vegclust is used, this contains a data frame with the coordinates of the fixed centers (centroids or medoids). If
vegclustdist is used, it will contain the indices of fixed medoids for models KMdd, FCMdd, HNCdd, NCdd and PCMdd; or
The matrix of object distances to cluster centers. Columns starting with "M" indicate mobile clusters, whereas columns starting with "F" indicate fixed clusters.
In the case of methods KM, FCM, NC, PCM and HNC it contains the within-cluster sum of squares for each cluster (squared distances to cluster center weighted by membership). In the case of methods KMdd, FCMdd, NCdd, HNCdd and PCMdd it contains the sum of distances to each cluster (weighted by membership).
The number of objects belonging to each cluster. In case of fuzzy clusters the sum of memberships is given.
The objective function value (the minimum value attained after all iterations).
Community data. A site-by-species matrix or data frame (for
vegclust) or a site-by-site dissimilarity matrix or
dist object (for
A number, a vector of seeds, or coordinates for mobile clusters.
A matrix or data frame with coordinates for fixed (non-mobile) clusters.
A number, a vector of seeds, or starting memberships for mobile clusters.
A matrix or data frame with the distances to fixed cluster centers.
A clustering model. Current accepted models are:
"KM": K-means or hard c-means (MacQueen 1967)
"KMdd": Hard c-medoids (Krishnapuram et al. 1999)
"FCM": Fuzzy c-means (Bezdek 1981)
"FCMdd": Fuzzy c-medoids (Krishnapuram et al. 1999)
"NC": Noise clustering (Dave and Krishnapuram 1997)
"NCdd": Noise clustering with medoids
"HNC": Hard noise clustering
"HNCdd": Hard noise clustering with medoids
"PCM": Possibilistic c-means (Krishnapuram and Keller 1993)
"PCMdd": Possibilistic c-medoids
The fuzziness exponent to be used (this is relevant for all models except for kmeans)
The distance to the noise cluster, relevant for noise clustering (NC).
A vector of reference distances, relevant for possibilistic C-means (PCM).
Threshold used to stop iterations. The maximum difference in the membership matrix of the current vs. the previous iteration will be compared to this value.
The maximum number of iterations allowed.
mobileMemb is a number, how many random sets should be chosen?
When random starts are used, these will stop if at least
maxminJ runs ended up in the same functional value.
mobileMemb is a number, a vector indicating which objects are potential initial centers. If
NULL all objects are valid seeds.
Flag to print extra output.
Miquel De Cáceres, CREAF
vegclustdist try to generalize the
kmeans function in
stats in three ways.
Firstly, they allows different clustering models. Clustering models can be divided in (a) fuzzy or hard; (b) centroid-based or medoid-based; (c) Partitioning (KM and FCM family), noise clustering (NC family), and possibilistic clustering (PCM and PCMdd). The reader should refer to the original publications to better understand the differences between models.
Secondly, users can specify fixed clusters (that is, centroids that do not change their positions during iterations). Fixed clusters are intended to be used when some clusters were previously defined and new data has been collected. One may allow some of these new data points to form new clusters, while some other points will be assigned to the original clusters. In the case of models with cluster repulsion (such as KM, FCM or NC) the new (mobile) clusters are not allowed to 'push' the fixed ones. As a result, mobile clusters will occupy new regions of the reference space.
vegclustdist implements the distance-based equivalent of
vegclust. The results of
vegclustdist will be the same (if seeds are equal) if the distance matrix is calculated using the Euclidean distance (see function
dist). Otherwise, the equivalence holds by resorting on principal coordinates analysis.
Note that all data frames or matrices used as input of
vegclust should be defined on the same space of species (see
kmeans, which allows different specific algorithms, here updates of prototypes (centroids or medoids) are done after all objects have been reassigned (Forgy 1965). In order to obtain hard cluster definitions, users can apply the function
defuzzify to the
Forgy, E. W. (1965) Cluster analysis of multivariate data: efficiency vs interpretability of classifications. Biometrics 21, 768-769.
MacQueen, J. (1967) Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, eds L. M. Le Cam and J. Neyman, 1, pp. 281-297. Berkeley, CA: University of California Press.
Davé, R. N. and R. Krishnapuram (1997) Robust clustering methods: a unified view. IEEE Transactions on Fuzzy Systems 5, 270-293.
Bezdek, J. C. (1981) Pattern recognition with fuzzy objective functions. Plenum Press, New York.
Krishnapuram, R., Joshi, A., & Yi, L. (1999). A Fuzzy relative of the k-medoids algorithm with application to web document and snippet clustering. IEEE International Fuzzy Systems (pp. 1281–1286).
Krishnapuram, R. and J. M. Keller. (1993) A possibilistic approach to clustering. IEEE transactions on fuzzy systems 1, 98-110.
De Cáceres, M., Font, X, Oliva, F. (2010) The management of numerical vegetation classifications with fuzzy clustering methods. Journal of Vegetation Science 21 (6): 1138-1151.
## Loads data data(wetland) ## This equals the chord transformation ## (see also 'decostand' in package vegan) wetland.chord = as.data.frame(sweep(as.matrix(wetland), 1, sqrt(rowSums(as.matrix(wetland)^2)), "/")) ## Create noise clustering with 3 clusters. Perform 10 starts from random seeds ## and keep the best solution wetland.nc = vegclust(wetland.chord, mobileCenters=3, m = 1.2, dnoise=0.75, method="NC", nstart=10) ## Fuzzy membership matrix wetland.nc$memb ## Cardinality of fuzzy clusters (i.e., the number of objects belonging to each cluster) wetland.nc$size ## Obtains hard membership vector, with 'N' for objects that are unclassified defuzzify(wetland.nc$memb)$cluster ## The same result is obtained with a matrix of chord distances wetland.d = dist(wetland.chord) wetland.d.nc = vegclustdist(wetland.d, mobileMemb=3, m = 1.2, dnoise=0.75, method="NC", nstart=10)
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