I am trying to cluster a Multidimensional Functional Object with the "kmeans" algorithms. What does it mean: So I don't have anymore a vector per each row or Individual, even more a 3x3 observation matrix per each Individual.For example: Individual = 1 has the following observations:
(x1, x2, x3),(y1,y2,y3),(z1,z2,z3).
The same structure of observations is also given for the other Individuals. So do you know how I can cluster with "kmeans" including all 3 observation vectors -and not only one observation vector how it is normal used for "kmeans" clustering?
Would you do it for each observation vector, f.e. (x1, x2, x3), separately and then combine the Information somehow together? I want to do this with the kmeans() Function in R.
Many thanks for your answers!
Using k-means you interpret each observation as a point in an N-dimensional vector space. Then you minimize the distances between your observations and the cluster centers.
Since, the data is viewed as dots in an N-dim space, the actual arrangement of the values does not matter.
You can, therefore, either tell your k-means routine to use a matrix norm, for example the Frobenius norm, to compute the distances. The other way would be to flatten your observations from 3 by 3 matrices to 1 by 9 vectors. The Frobenius norm of a NxN matrix is equivalent to the euclidean norm of a 1xN^2 vector.
Just give the argument to kmeans() with all the three columns it'll calculate the distances in 3 dimension, if that is what you are looking for.
Related
Im a begginer using R, and Im trying to apply a permutation process (statistical test) for two matrix comparison in order to assess if there is a real relation between spatial association and functional traits of forest tree species.
My first matrix is formed by indices of spatial interactions positive (+) and negative (-) between species. Positive interactions (+) were assigned with the value of 3 and negative interactions (-)
with the value of 1. The second matrix, include the mean euclidean distance of functional traits between species.
Theoretically, what I want to do, is to randomize or permute the trait matrix (incidence matrix) along the spatial matrix, without broken (or better said-retaining) the spatial structure of association among species. One permutation for positive ones (+) and other permutation for negative ones (-).
Can anybody help me to structure a script in R to test this previous relationship?
I just have the two csv species x species matrix files!.
I want to quantify the dissimilarity between two group. Each group has 5 observations, so there are 25 combinations.
For each combination, I have calculated their pairwise Euclidean distance (based on feature space). So I have had a vector of pairwise Euclidean distances as follows:
set.seed(1)
runif(n=25, min=50, max=90)
[1] 60.62035 64.88496 72.91413 86.32831 58.06728 85.93559 87.78701 76.43191 75.16456 52.47145 58.23898 57.06227 77.48091
[14] 65.36415 80.79366 69.90797 78.70474 89.67624 65.20141 81.09781 87.38821 58.48570 76.06695 55.02220 60.68883
I want to use Kernel function to assign weights to the 25 combinations based on the vector of pairwise Euclidean distances. Shorter distance, larger weight.
How can I do it in R?
I have limited knowledge about kernel. Thank you in advance for any suggestions!
I would really appreciated it even if you can give me some hints about the mathematical formula without any programming.
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.
Once again I have been set another programming task and to most of which I have done, so a quick run through: I've had to take n amount of samples of multivariate normal distribution with dimension p (called it X) then to put it into a matrix (Matx) where the first two values in each row were taken and summed a long with a value randomly drawn from the standard normal distribution. (Call this vector Y) Then we had to order Y numerically and split it up into H groups, and then I had to find out the mean of each row in the matrix and now having to order then in terms of which Y group they were associated. I've struggled a fair bit and have now hit a brick wall. Quite confusing I understand, if anyone could help it'd be greatly appreciated!
Task:Return the pxH matrix which has in the first column the mean of the observations in the first group and in the Hth column the mean in the observations in the Hth group.
Code:
library('MASS')
x<-mvrnorm(36,0,1)
Matx<-matrix(c(x), ncol=6, byrow=TRUE)
v<-rnorm(6)
y1<-sum(x[1:2],v[1])
y2<-sum(x[7:8],v[2])
y3<-sum(x[12:13],v[3])
y4<-sum(x[19:20],v[4])
y5<-sum(x[25:26],v[5])
y6<-sum(x[31:32],v[6])
y<-c(y1,y2,y3,y4,y5,y6)
out<-order(y)
h1<-c(out[1:2])
h2<-c(out[3:4])
h3<-c(out[5:6])
x1<-c(x[1:6])
x2<-c(x[7:12])
x3<-c(x[13:18])
x4<-c(x[19:24])
x5<-c(x[25:30])
x6<-c(x[31:36])
mx1<-mean(x1)
mx2<-mean(x2)
mx3<-mean(x3)
mx4<-mean(x4)
mx5<-mean(x5)
mx6<-mean(x6)
d<-c(mx1,mx2,mx3,mx4,mx5,mx6)[order(out)]
d
I would like to measure the hamming sequence similarity in which the substitution costs are not based on the substitution rates in the observed sequences but based on the spatial autocorrelation within the study area of the different states (states are thus not related to DNA but something else).
I divided my study area in grid cells of equal size (e.g. 1000m) and measured how often the same "state" is observed in a neighboring cell (Rook-case). Consequently the weight matrix indicates that from state A to A (to move within the same states) has a much higher probability than to go from A to B or B to C or A to C. This already indicates that states have a high spatial autocorrelation.
The problem is, if you want to measure sequence similarity the substitution matrix should be 0 at the diagonal. Therefore I was wondering whether there is a kind of transformation to go from an "autocorrelation matrix" to a substitution matrix, with 0 values along the diagonal. By means of this we would like to account for spatial autocorrelation in the study area in our sequence similarity measure. To do my analysis I am using the package TraMineR.
Example matrix in R for sequences consisting out of four states (A,B,C,D):
Sequence example: AAAAAABBBBCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDDDAAAAAAAAA
Autocorrelation matrix:
A = c(17.50,3.00,1.00,0.05)
B = c(3.00,10.00,2.00,1.00)
C = c(1.00,2.00,30.00,3.00)
D = c(0.05,1.00,3.00,20.00)
subm = rbind(A,B,C,D)
colnames(subm) = c("A","B","C","D")
how to transform this matrix to a substitution matrix?
First, TraMineR computes the Hamming distance, i.e., a dissimilarity, not a similarity.
The simple Hamming distance is just the count of mismatches between two sequences. For example, the Hamming distance between AABBCC and ABBBAC is 2, and between AAAAAA and AAAAAA it is 0 since there are no mismatches.
Generalized Hamming allows to weighting mismatches (not matches!) with substitution costs. For example if the substitution cost between A and B is 1.5, and is 2 between B and C, then the distance would be the weighted sum of mismatches, i.e., 3.5 between the first two sequences. It would still be zero between one sequence and itself.
From what I understand, the shown matrix is not the matrix of substitution costs. It is the matrix of what you call 'spatial autocorrelations', and you look for how you can turn this information into substitutions costs.
The idea is to assign high substitution cost (mismatch weight) when the autocorrelation (a rate in your case) is low, i.e., when there is a low probability to find say state B in the neighborhood of state A, and to assign a low substitution cost when the probability is high. Since your probability matrix is symmetric, a simple solution is to use $1 - p(A|B)$ for all off diagonal terms, and leave 0 on the diagonal for the reason explained above.
sm <- 1 - subm/100
diag(sm) <- 0
sm
For non symmetric probabilities, you could use a similar formula to the one used for deriving the costs from transition rates, i.e., $2 - p(A|B) - p(B|A)$.