Search results
Results from the WOW.Com Content Network
Fuzzy clustering (also referred to as soft clustering or soft k-means) is a form of clustering in which each data point can belong to more than one cluster.. Clustering or cluster analysis involves assigning data points to clusters such that items in the same cluster are as similar as possible, while items belonging to different clusters are as dissimilar as possible.
Centroid-based clustering problems such as k-means and k-medoids are special cases of the uncapacitated, metric facility location problem, a canonical problem in the operations research and computational geometry communities. In a basic facility location problem (of which there are numerous variants that model more elaborate settings), the task ...
c is an involution, which means that c(c(a)) = a for each a ∈ [0,1] c is a strong negator (aka fuzzy complement). A function c satisfying axioms c1 and c3 has at least one fixpoint a * with c(a *) = a *, and if axiom c2 is fulfilled as well there is exactly one such fixpoint. For the standard negator c(x) = 1-x the unique fixpoint is a * = 0. ...
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
Examples for fuzzy intersection/union pairs with standard negator can be derived from samples provided in the article about t-norms. The fuzzy intersection is not idempotent in general, because the standard t-norm min is the only one which has this property. Indeed, if the arithmetic multiplication is used as the t-norm, the resulting fuzzy ...
The starting point for this new version of the validation index is the result of a given soft clustering algorithm (e.g. fuzzy c-means), shaped with the computed clustering partitions and membership values associating the elements with the clusters. In the soft domain, each element of the system belongs to every classes, given the membership ...
Let (G, *) be a group and A a fuzzy subset of G. Then A is a fuzzy subgroup of G if for all x, y in G, A(x*y −1) ≥ min(A(x), A(y −1)). A similar generalization principle is used, for example, for fuzzification of the transitivity property. Let R be a fuzzy relation on X, i.e. R is a fuzzy subset of X × X.
For example, given data that actually consist of k labeled groups – for example, k points sampled with noise – clustering with more than k clusters will "explain" more of the variation (since it can use smaller, tighter clusters), but this is over-fitting, since it is subdividing the labeled groups into multiple clusters. The idea is that ...