# Category Archives: Clusters - Page 3

It's time to update the Harappa admixture dendrogram since the last time I created one we had only 40 participants.

Note that this is not a phylogeny. It just visualizes the closeness of your admixture results to others.

Also note that I am using Euclidean distance between admixture proportions which has problems and using complete linkage hierarchical clustering.

## Ref2 South Asian + Harappa Admixture

Using the reference II dataset of 548 South Asians and 38 Harappa Project South Asians that I have been working on, I ran Admixture.

The optimum number of ancestral components was 5-6. So I used K=6. The components are highest among the following groups:

C1 C2 Brahui, Makrani, Balochi TN Dalit, North Kannadi Irula Gujaratis Hazara Kalash

I consider the Irulas, a Scheduled tribe from Tamil Nadu, to be problematic in a similar way to the Kalash except that the Irulas are well-scattered in their own space in the PCA plot.

Also, note that all the European, West Asian, etc is being represented by C1. Similarly, all the East Asian ancestry is being collected in C5.

The spreadsheet showing the admixture results is here. The first sheet shows the individual results for the project participants.

The 2nd sheet shows the average (and standard deviation) for the reference populations.

The 3rd sheet shows the average and standard deviation for each cluster computed by MClust from PCA.

The 4th sheet shows the average and standard deviation for each cluster computed by MClust from MDS.

Also, take a look at the admixture percentage standard deviations. You'll notice that those are generally lower for the clusters compared to the population groups.

## Ref 2 South Asians + Harappa MDS Clusters

Why do MDS clusters when we already did PCA-based clustering for this data?

You guys probably know about Dienekes' Clusters Galore approach. The way it works is that varying the number of MDS dimensions used you compute the number of clusters inferred (done using Mclust) and use the number of MDS dimensions which give you the maximum number of clusters.

This sounded a little unsatisfactory for me. So I ran an experiment. I computed 100 MDS dimensions for the samples in this dataset which includes South Asians from Reference II as well as 38 Harappa participants. Then I kept 2,3,4,...,100 dimensions and ran NNClean (to get initial noise/outlier estimate) and Mclust on them.

This first graph shows the number of outliers NNclean computed from 586 samples.

Things go crazy with NNclean when 64 or more MDS dimensions are retained since it considers most of the samples to be noise then.

Now let's look at the number of outliers identified after Mclust's clustering procedure.

This shows us that probably somewhere between 8 and 65 MDS dimensions might be useful to keep.

Finally, a plot of the number of clusters inferred by Mclust versus the number of MDS dimensions used.

There are two big jumps here to consider. One is around 12 MDS dimensions and the other after 52. So we are looking at an optimum number of MDS dimensions between 12 and 52. However, in that range, the number of clusters computed is fairly noisy between 18 and 26. The only pattern I can discern with some smoothed fitting is that we should likely be looking at somewhere between 20 and 30 MDS dimensions.

But why choose the maximum number of clusters (26 clusters when 24 MDS dimensions are kept)? That could be the result of noise too.

Is there some other way to figure out what are the significant number of MDS dimensions to keep for population structure? It turns out there is. Patterson, Price and Reich proposed Tracy-Widom statistics for Principal Component Analysis in their paper "Population Structure and Eigenanalysis". We also know that the MDS analysis we are performing is the classical metric MDS which is in some ways equivalent to a PCA. Looking at the Tracy Widom stats then, we see that about 25 eigenvalues are significant. Thus, keeping 24 MDS dimensions to maximum the number of clusters seems defensible.

Finally, here are the clustering results.

## Ref 2 South Asians + Harappa PCA Clusters

Using the fifteen principal components shown before, I tried to use MClust to cluster the 573 individuals.

This time, I ran NNclean first to find out the outliers. NNClean pointed to the following as outliers:

HGDP00104 HGDP00100 HGDP00119 HGDP00112 HGDP00118 HGDP00279 HGDP00060 HGDP00029 HGDP00076 HGDP00041 HGDP00146 HGDP00163 HGDP00234 HGDP00412 HGDP00090 HGDP00148 HGDP00165 HGDP00068 HGDP00134 HGDP00149 HGDP00052 HGDP00074 HGDP00098 HGDP00153 HGDP00173 HGDP00376 HGDP00143 HGDP00158 HGDP00145 HGDP00161 HGDP00151 HGDP00243 HGDP00139 HGDP00140 HGDP00177 HGDP00224 GSM536497 GSM536806 GSM536807 GSM536808 I16 I3 I5 SS231506 HRP0001

As you can see, I am included in this list.

Then I used this list of outliers to initialize "noise" in the MClust procedure. The final list of outliers is as fllows:

HGDP00279 HGDP00029 HGDP00134 HGDP00151 GSM536806 GSM536807 GSM536808

These are 1 Kalash, 1 Brahui, 2 Makranis, and 3 Paniyas.

There are a bunch of interesting things in the results. For example, Pathans and Punjabis were mostly indistinguishable by this technique. But let me leave you with a caution: Some of these clusters are nice, tight ones and others are loose, long ones, so don't overread the results.

## Reference II PCA

I ran PCA on the Reference II dataset which includes 3.161 samples from various populations but with only 23,000 SNPs in common.

Here are the top ten eigenvalues:

• 219.225396
• 146.835968
• 20.719760
• 9.721733
• 7.552482
• 6.216977
• 3.991663
• 3.484690
• 3.106919
• 2.805874

While the first two eigenvalues are much bigger than the rest, the first explains 7.12% of the variation and the second 4.77%, the Tracy-Widom stats show that about 54 eigenvectors are significant.

Here are the plots for the first 10 principal components. Remember that the 1st eigenvector is 1.5 times the 2nd.

Here is a 3-D PCA plot (hat tip: Doug McDonald) showing the first three eigenvectors. The plot is rotating about the 1st eigenvector which is vertical. Also, I have stretched the principal components based on the corresponding eigenvalues.

I also ran MClust on the PCA data and got 17 clusters. The results are in a spreadsheet. I am sure with more principal components than the 10 I used, I would be able to deduce finer population structure.

Do take a look at the clusters assigned to the South Asian populations from Xing et al.

## Reference I PCA

I ran PCA on the Reference I dataset which includes 2,654 samples from various populations.

Here are the top ten eigenvalues:

• 178.727040
• 118.884690
• 15.014072
• 9.346602
• 5.983225
• 5.140090
• 3.322723
• 2.739313
• 2.559640
• 2.475389

While the first two eigenvalues are much bigger than the rest, the first explains 6.82% of the variation and the second 4.54%, the Tracy-Widom stats show that about 70-something eeigenvectors are significant.

Here are the plots for the first 10 principal components. Remember that the 1st eigenvector is 1.5 times the 2nd.

Here is a 3-D PCA plot (hat tip: Doug McDonald) showing the first three eigenvectors. The plot is rotating about the 1st eigenvector which is vertical. Also, I have stretched the principal components based on the corresponding eigenvalues.

I also ran MClust on the PCA data and got 16 clusters. The results are in a spreadsheet. I am sure with more principal components than the 10 I used, I would be able to deduce finer population structure.

Note that African Americans cluster with East Africans in CL1. That's because African Americans have some European ancestry (20% on average) and that pulls them away from West Africans and towards Europeans. East Africans also lie in that direction, so they cluster together in a PCA. However, that doesn't mean that African Americans have East African ancestry. If you look at the Admixture results for African Americans, you see that their East African ancestry is negligible.

## Ref1 South Asian + Harappa MDS MClust

Now I am going nuts on this dataset consisting of South Asians (minus Kalash and Hazara) from Reference I and some Harappa participants, but I promise this is the last item on this specific data. I will however do similar analyses some time after integrating all the new South Asian samples I have gotten (via project participation as well as from research data).

I ran MDS on the data in Plink and then retaining various number of MDS dimensions, ran MClust on it. This is what Dienekes calls Clusters Galore.

Here are the plots of the MDS, two dimensions at a time.

The graph of number of MDS dimensions retained versus optimum number of clusters computed by Mclust is as follows:

The maximum number of clusters (28) are inferred with 8 MDS dimensions. So I posted the clustering results for 8 MDS dimensions + 28 clusters.

Some observations on the clusters:

1. 56 of the 62 Gujaratis are in cluster CL1 and the remaining 6 are in CL5. Both are Gujarati-only clusters. Let's see where the Harappa Gujaratis fall next time I do this analysis,
2. CL2 has an Andhra Reddy, Caribbean Indians, a Keralan, a few Gujaratis-B, and a third of the Singapore Indians.
3. Gujaratis-B are a varied lot spread out into CL3, CL7, CL2, CL8, CL4, CL6, and CL15, but half are in CL3.
4. CL6 has a lot of the South Indian Brahmins
5. Burusho are isolated
6. Punjabis from the project seem to be divided among CL7, CL8 and CL15.

I also posted the results for 20 MDS dimensions resulting in 21 clusters.

## Ref1 South Asians + Harappa PCA Clusters II

Using the PCA data for Reference I South Asians plus project participants, Sriram computed a tree-based clustering called clique optimization. The result for that is a pdf file. Take a look!

Thanks, Sriram!Балки

## Ref1 South Asian + Harappa Admixture

Since I was working on this dataset consisting of South Asians (minus Kalash and Hazara) from Reference I and some Harappa participants, I thought I would run Admixture on it.

The optimum value for the number of ancestral populations K is 3 in this case. Roughly the three ancestral components correspond to South India, Balochistan and Gujarat.

The spreadsheet showing the admixture results is here. The first sheet shows the individual results for reference samples as well as project participants.

The 2nd sheet shows the average (and standard deviation) for the reference populations.

The 3rd sheet shows the average and standard deviation for each cluster computed by MClust. I included only the samples which had at least 90% probability of belonging to a cluster.

Note how clusters CL8, CL9 and CL13 have a lot more variation than the others. Of course, I am in CL9 along with some fairly eclectic samples.

## Ref1 South Asians + Harappa PCA Clusters

Using the PCA results of the South Asians in Reference I as well as Harappa participants, I ran a couple of clustering algorithms.

First, I scaled the principal components by the respective eigenvalues.

Using Euclidean distance for hierarchical clustering with complete linkage, here's the dendrogram for the Harappa Project participants.

You can compare this to the Admixture-based dendrogram:

The most obvious thing is that I (HRP0001) am an outlier by far.

We inferred three major clusters with the admixture results. Those are intact, though changed a little.

I also ran MClust on the PCA data. The optimum number of clusters was 14. The resulting cluster assignments can be seen in a spreadsheet.

For the Harappa Project participants, the numbers give the probability of assignment to a cluster. For example, for HRP0009 there is a 72% of belonging to cluster 4. For the reference populations, the numbers give the expected number of samples assigned to a cluster.