# Cosine similarity measure - External Measure, Cluster Stability Similarity index based on dot product is the measure which estimates how those two different partitionings, that comming from one dataset, are different from each other. ```r dot.product(clust1, clust2) ``` ## Arguments - `clust1`: integer `vector` with information about cluster id the object is assigned to. If vector is not integer type, it will be coerced with warning. - `clust2`: integer `vector` with information about cluster id the object is assigned to. If vector is not integer type, it will be coerced with warning. ## Details Two input `vectors` keep information about two different partitionings of the same subset comming from one data set. For each partitioning (let say P and P') its matrix representation is created. Let P[i,j] and P'[i,j] each defines as: P[i,j] = 1 when object i and j belongs to the same cluster and i != j P[i,j] = 0 in other case Two matrices are needed to compute **dot product** using formula: = sum(forall i and j) P[i,j]*P'[i,j] This **dot product** satisfy Cauchy-Schwartz inequality <= *. As result we get **cosine similarity measure**: /sqrt(*) ## Returns `dot.product` returns a **cosine similarity measure** of two partitionings. `NaN` is returned when in any partitioning each cluster contains only one object. ## See Also Other external measures: `std.ext`, `similarity.index` ## References A. Ben-Hur and I. Guyon **Detecting stable clusters using principal component analysis**, [http://citeseer.ist.psu.edu/528061.html](http://citeseer.ist.psu.edu/528061.html) T. Lange, V. Roth, M. L. Braun and J. M. Buhmann **Stability-Based Validation of Clustering Solutions**, tools:::Rd_expr_doi("10.1162/089976604773717621") ## Examples ```r # dot.product function(and also similarity.index) is used to compute # cluster stability, additional stability functions will be # defined - as its arguments some additional functions (wrappers) # will be needed # define wrappers pam.wrapp <-function(data) { return( as.integer(data$clustering) ) } identity <- function(data) { return( as.integer(data) ) } agnes.average <- function(data, clust.num) { return( cutree( agnes(data,method="average"), clust.num ) ) } # define cluster stability function - cls.stabb # cls.stabb arguments description: # data - data to be clustered # clust.num - number of clusters to which data will be clustered # sample.num - number of pairs of data subsets to be clustered, # each clustered pair will be given as argument for # dot.product and similarity.index functions # ratio - value comming from (0,1) section: # 0 - means sample emtpy subset, # 1 - means chose all "data" objects # method - cluster method (see wrapper functions) # wrapp - function which extract information about cluster id assigned # to each clustered object # as a result mean of dot.product (and similarity.index) results, # computed for subsampled pairs of subsets is given cls.stabb <- function( data, clust.num, sample.num , ratio, method, wrapp ) { dot.pr = 0 sim.ind = 0 obj.num = dim(data)[1] for( j in 1:sample.num ) { smp1 = sort( sample( 1:obj.num, ratio*obj.num ) ) smp2 = sort( sample( 1:obj.num, ratio*obj.num ) ) d1 = data[smp1,] cls1 = wrapp( method(d1,clust.num) ) d2 = data[smp2,] cls2 = wrapp( method(d2,clust.num) ) clsm1 = t(rbind(smp1,cls1)) clsm2 = t(rbind(smp2,cls2)) m = cls.set.section(clsm1, clsm2) cls1 = as.integer(m[,2]) cls2 = as.integer(m[,3]) cnf.mx = confusion.matrix(cls1,cls2) std.ms = std.ext(cls1,cls2) # external measures - compare partitioning dt = dot.product(cls1,cls2) si = similarity.index(cnf.mx) if( !is.nan(dt) ) dot.pr = dot.pr + dt/sample.num sim.ind = sim.ind + si/sample.num } return( c(dot.pr, sim.ind) ) } # load and prepare data library(clv) data(iris) iris.data <- iris[,1:4] # fix arguments for cls.stabb function iter = c(2,3,4,5,6,7,9,12,15) smp.num = 5 sub.smp.ratio = 0.8 # cluster stability for PAM print("PAM method:") for( i in iter ) { result = cls.stabb(iris.data, clust.num=i, sample.num=smp.num, ratio=sub.smp.ratio, method=pam, wrapp=pam.wrapp) print(result) } # cluster stability for Agnes (average-link) print("Agnes (single) method:") for( i in iter ) { result = cls.stabb(iris.data, clust.num=i, sample.num=smp.num, ratio=sub.smp.ratio, method=agnes.average, wrapp=identity) print(result) } ``` ## Author(s) Lukasz Nieweglowski

dot_product function