I have a large matrix of 500K observations to cluster using hierarchical clustering. Due to the large size, i do not have the computing power to calculate the distance matrix.
To overcome this problem I chose to aggregate my matrix to merge those observations which were identical to reduce my matrix to about 10K observations. I have the frequency for each of the rows in this aggregated matrix. I now need to incorporate this frequency as a weight in my hierarchical clustering.
The data is a mixture of numerical and categorical variables for the 500K observations so i have used the daisy package to calculate the gower dissimilarity for my aggregated dataset. I want to use hclust in the stats package for the aggregated dataset however i want to take into account the frequency of each observation. From the help information for hclust the arguments are as follows:
hclust(d, method = "complete", members = NULL)
The information for the members argument is:, NULL or a vector with length size of d. See the ‘Details’ section. When you look at the details section you get: If members != NULL, then d is taken to be a dissimilarity matrix between clusters instead of dissimilarities between singletons and members gives the number of observations per cluster. This way the hierarchical cluster algorithm can be ‘started in the middle of the dendrogram’, e.g., in order to reconstruct the part of the tree above a cut (see examples). Dissimilarities between clusters can be efficiently computed (i.e., without hclust itself) only for a limited number of distance/linkage combinations, the simplest one being squared Euclidean distance and centroid linkage. In this case the dissimilarities between the clusters are the squared Euclidean distances between cluster means.
From the above description, i am unsure if i can assign my frequency weights to the members arguments as it is not clear if this is the purpose of this argument. I would like to use it like this:
hclust(d, method = "complete", members = df$freq)
Where df$freq is the frequency of each row in the aggregated matrix. So if a row is duplicated 10 times this value would be 10.
If anyone can help me that would be great,
Thanks
Yes, this should work fine for most linkages, in particular single, group average and complete linkage. For ward etc. you need to correctly take the weights into account yourself.
But even that part is not hard. Just make sure to use the cluster sizes, because you need to pass the distance of two clusters, not two points. So the matrix should contain the distance of n1 points at location x and n2 points at location y. For min/max/mean this n disappears or cancels out. For ward, you should get a SSQ like formula.
Related
I'm performing hierarchical cluster analysis using Ward's method on a dataset containing 1000 observations and 37 variables (all are 5-point likert-scales).
First, I ran the analysis in SPSS via
CLUSTER Var01 to Var37
/METHOD WARD
/MEASURE=SEUCLID
/ID=ID
/PRINT CLUSTER(2,10) SCHEDULE
/PLOT DENDROGRAM
/SAVE CLUSTER(2,10).
FREQUENCIES CLU2_1.
I additionaly performed the analysis in R:
datA <- subset(dat, select = Var01:Var37)
dist <- dist(datA, method = "euclidean")
hc <- hclust(d = dist, method = "ward.D2")
table(cutree(hc, k = 2))
The resulting cluster sizes are:
1 2
SPSS 712 288
R 610 390
These results are obviously confusing to me, as they differ substentially (which becomes highly visible when observing the dendrograms; also applies for the 3-10 clusters solutions). "ward.D2" takes into account the squared distance, if I'm not mistaken, so I included the simple distance matrix here. However, I tried several (combinations) of distance and clustering methods, e.g. EUCLID instead of SEUCLID, squaring the distance matrix in R, applying "ward.D" method,.... I also looked at the distance matrices generated by SPSS and R, which are identical (when applying the same method). Ultimately, I excluded duplicate cases (N=29) from my data, guessing that those might have caused differences when being allocated (randomly) at a certain point. All this did not result in matching outputs in R and SPSS.
I tried running the analysis with the agnes() function from the cluster package, which resulted in - again - different results compared to SPSS and even hclust() (But that's a topic for another post, I guess).
Are the underlying clustering procedures that different between the programs/packages? Or did I overlook a crucial detail? Is there a "correct" procedure that replicates the results yielded in SPSS?
If the distance matrices are identical and the merging methods are identical, the only thing that should create different outcomes is having tied distances handled differently in two algorithms. Tied distances might be present with the original full distance matrix, or might occur during the joining process. If one program searches the matrix and finds two or more distances tied at the minimum value at that step, and it selects the first one, while another program selects the last one, or one or both select one at random from among the ties, different results could occur.
I'd suggest starting with a small example with some data with randomness added to values to make tied distances unlikely and see if the two programs produce matching results on those data. If not, there's a deeper problem. If so, then tie handling might be the issue.
I am currently working with some forest inventory data.
The data were collected on sample plots whose positions are available as point data (spatial data).
I have two datasets:
dataset dat.1 with n sample plots of species A
dataset dat.2 with k sample plots of species B
with n < k
What I want to do is to match every point of dat.1 with a point of dat.2. The result should be n pairs of points. So n of k plots from dat.2 should be selected.
The criteria for matching are:
spatial distance between a pair of points is as close as possible
one point of dat.2 can only be matched with one point in dat.1 and vice versa. So if there is a pair of points, these points should not be used in any other pair, even if it would be useful in terms of shortest distance. The "occupied" points should not be replaced and should not be used in the further matching process.
I have been looking for a very long time for ways to perform this analysis. There are functions like st_nn from 'nngeo' or nn2 from 'RANN' which give out the k nearest neighbours of a point. However, it is not possible to exclude the possibility of a replacement with these functions.
In the package 'matchIt' there are possibilites to perform a nearest neighbour matching without replacement. Yet these functions are adapted to find the closest distance between control variables and not between spatial locations.
Could anyone come up with an idea for a possibility to match my requirements?
I would really appreciate any hints or suggestions for packages and / or functions that could help me with this issue.
The first thing you should do is create your own distance matrix. The rows should correspond to those in dat.1 and the columns to those in dat.2, and each entry in the matrix is the distance between the plot in the row and the plot in the column. You can do this manually by looping through your datasets and computing the Euclidean (or other) distance between the points. You can also use the match_on function in the optmatch package to do this with the following code:
d <- rbind(dat.1, dat.2)
d$dat <- c(rep(1, nrow(dat.1)), rep(0, nrow(dat.2))
dist <- optmatch::match_on(dat ~ x.coor + y.coord, data = d,
method = "euclidean")
Once you have a distance matrix in this form, you can supply it to pairmatch in the optmatch package. pairmatch performs K:1 optimal matching without replacement. The matching is optimal in that the sum of the absolute distances between matched pairs in the matched sample is as low as possible. It doesn't guarantee that any one unit will get its nearest neighbor, but it does yield matched samples that ensure no units are matched to other units too far apart from them. You can specify an argument to controls to choose how many dat.2 units you want to be matched to each dat.1 unit. For example, to match 2 plots from dat.2 to each unit in dat.1, you can use
d$pairs <- optmatch::pairmatch(dist)
The output is a factor containing pair membership for each unit. Unmatched units will have a value of NA.
You can also do this in one single step with
d$pairs <- optmatch::pairmatch(dat ~ x.coor + y.coord, data = d,
method = "euclidean")
Then you can subset your dataset so only matched plots remain:
matched <- d[!is.na(d$pairs),]
I'm trying to conduct a hierarchical agglomerative cluster analysis in R by using the Weighted Cluster package. Before doing so, I calculated the distances between state sequences by leveraging the TraMineR package (see pp. 4-6 here).
Following the vignette hyperlinked above, I fed my distance matrix into hclust while adding a vector of weights as follows (datadist is the distance matrix; dataframe is my data frame featuring time series data; and weight is an all-waves longitudinal survey weight):
Cluster <- hclust(as.dist(datadist), method = "ward", members = dataframe$weight)
Then, after arriving at a specific cluster solution (four subgroups), I used the cutree function to determine the relative frequency of each cluster and assign cases:
subgroups <- cutree(Cluster, k = 4)
However, I somehow generated more than four groups after executing the code above (over 30, in fact). When I removed the vector of weights, I was able to produce frequencies for four clusters, but unweighted results are sub-optimal.
If anyone out there can help me understand what's going on (and how I can address or treat the problem), it would be greatly appreciated.
my aim is to cluster 126 time-series concerning 26 weeks (so each time-series has 26 observation). I used pam{cluster} = partitioning around medoids to cluster these time-series.
Before clustering I wanted to compare which distance measure is the most appropriate: euclidean, manhattan or dynamic time warping. I used each distance to cluster and compare by silhouette plot. Is there any way I can compare different distance measure?
For example I know that procedure clValid {clValid} to validate cluster results, however I cannot implement dtw to calculate indexes.
So how can I compare different distance metrics (not only by silhouette)?
Additional question: is GAP statistic enough to decide how many clusters choose? Or should I evaluate number of clusters with different methods or compare two or three ways how to do it?
I would be grateful for any suggestions.
I have just read the book "cluster analysis, fifth edition" by Brian S. Everitt, etc. And currently, I adopt the following strategy to select method to calculate distance matrix, clustering and validation:
for distance: using cmdscale{stats} function to calculate multidimentional scaling, and plot the scatterplot of the two scaling dimensions with density information. As expected, if there is distinct clusters or nested clusters, the scatterplot will give some hints.
for clustering: for every clustering method, calculate cophenetic correlation between clustering results and the distance, this can be calculated using cophenetic{stats} function. The best clustering method will give higher correlation. However, this is only working for hierarchical clustering. I haven't idea for other clustering methods, like pam, or kmeans.
for partition evaluation: package {clusterSim} give several function to calculate the index to evaluate the clustering quality. Another package {NbClust} also calculate so many as 30 index to evaluate the combination of "distance", "clustering" and "number of clusters". However, this package partition the hierarchical tree using {cutree}, which is not suitable for nested clustering structure. Another method provided by {dynamicTreeCut} give reasonable results.
for cluster number determination: will added later.
Cluster data for which you have class labels, and use the RAND index to measure cluster quality.
50 such datasets are at the UCR time series archive
This paper does something similar
http://www.cs.ucr.edu/~eamonn/ClusteringTimeSeriesUsingUnsupervised-Shapelets.pdf
I have an R matrix which dimensions are ~20,000,000 rows by 1,000 columns. The first column represents counts and the rest of the columns represent the probabilities of a multinomial distribution of these counts. So in other words, in each row the first column is n and the rest of the k columns are the probabilities of the k categories. Another point is that the matrix is sparse, meaning that in each row there are many columns with value of 0.
Here's a toy matrix I created:
mat=rbind(c(5,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1),c(2,0.2,0.2,0.2,0.2,0.2,0,0,0,0,0),c(22,0.4,0.6,0,0,0,0,0,0,0,0),c(5,0.5,0.2,0,0.1,0.2,0,0,0,0,0),c(4,0.4,0.15,0.15,0.15,0.15,0,0,0,0,0),c(10,0.6,0.1,0.1,0.1,0.1,0,0,0,0,0))
What I'd like to do is obtain an empirical measure of the variance of the counts for each category. The natural thing that comes to mind is to obtain random draws and then compute the variances over them. Something like:
draws = apply(mat,1,function(x) rmultinom(samples,x[1],x[2:ncol(mat)]))
Where say samples=100000
Then I can run an apply over draws to compute the variances.
However, for my real data dimensions this will become prohibitive at least in terms of RAM. Is whether a more efficient solution in R to this problem?
If all you need is the variance of the counts, just compute it immediately instead of returning the intermediate simulated draws.
draws = apply(mat,1,function(x) var(rmultinom(samples,x[1],x[2:ncol(mat)])))