This is part (2/2) about my travel this past summer to Iceland and Israel:

In my previous blog post I discussed the genetics of Icelanders, and the fact that most Icelanders can trace their roots back dozens of generations, all the way to Vikings from ca. 900AD. The country is homogenous in many other ways as well (religion, income, etc.), and therefore presents a stark contrast to the other country I visited this summer: Israel. Even though I’ve been to Israel many times since I was a child, now that I am an adult the manifold ethnic, social and religious makeup of the society is much more evident to me. This was particularly true during my visit this past summer, during which political and military turmoil in the country served to accentuate differences. There are Armenians, Ashkenazi Jews, Bahai, Bedouin, Beta Israel, Christian Arabs, Circassians, Copts, Druze, Maronites, Muslim Arab, Sephardic Jews etc. etc. etc. , and additional “diversity” caused by political splits leading to West Bank Palestinians, Gaza Palestinians, Israelis inside vs. outside the Green Line, etc. etc. etc. (and of course many individuals fall into multiple categories). It’s fair to say that “it’s complicated”. Moreover, the complex fabric that makes up Israeli society is part of a larger web of intertwined threads in the Middle East. The “Arab countries” that neighbor Israel are also internally heterogeneous and complex, both in obvious ways (e.g. the Sunni vs. Shia division), but also in many more subtle ways (e.g. language).

The 2014 Israeli-Gaza conflict started on July 8th. Having been in Israel for 4 weeks I was interacting closely with many friends and colleagues who were deeply impacted by the events (e.g. their children were suddenly called up to a partake in a war), and among them I noticed almost immediately an extreme polarization that reflected a public relations battle being waged between Hamas and Israel that played out more intensely than in any previous conflict on news channels and social media. The polarization extended to friends and acquaintances outside of Israel. Everyone had a very strong opinion. One thing I noticed were graphic memes being passed around in which the conflict was projected onto a two-colored map. For example, the map below was passed around on Facebook showing the (“real democratic”) Israel surrounded by a sea of Arab green in the Middle East:

I started noticing other bifurcating maps as other Middle East issues came to the fore later in the summer. Here is a map from a website depicting the Sunni-Shia divide:

In many cases the images being passed around were explicitly encouraging a “one-dimensional” view of the conflict(s), whereas in other cases the “us” vs. “them” factor was more subliminal. The feeling that I was being programmed how to think made me uncomfortable.

Moreover, the Middle East memes that were flooding my inbox were distracting me. I had visited Israel to nurture and establish connections and collaborations with the large number of computational biologists in the country. During my trip I was kindly hosted by Yael Mandel-Gutfreund at the Technion, and also had the honor of being an invited speaker at the annual Israeli Bioinformatics Society meeting. The visit was not supposed to be a bootcamp in salon politics. In any case, I found myself thinking about the situation in the Middle East with a computational biology mindset, and I was struck by the following “Middle East Friendship Chart” published in July that showed data about the relationships of the various entities/countries/organizations:

As a (computational) biologist I was keen to understand the data in a visual way that would reveal the connections more clearly, and as a computational (biologist) faced with ordinal data I thought immediately of non-metric multi-dimensional scaling as a way to depict the information in the matrix. I have discussed classic multi-dimensional scaling (or MDS) in a previous blog post, where I explained its connection to principal component analysis. In the case of ordinal data, non-metric MDS seeks to find points in a low-dimensional Euclidean space so that the ranks of distances correspond to the input ordinal matrix. It has been used in computational biology, for example in the analysis of gene expression matrices. The idea originates with a classic paper by Kruskal,that remains a good reference for understanding non-metric MDS. The key idea is summarized in his Figure 4:

Formally, in Kruskal’s notation, given a dissimilarity map $\delta$ (symmetric matrix with zeroes on the diagonal and nonnegative entries), the goal is to find points x in $R^k$ so that their pairwise distance match in rank. In Kruskal’s Figure 4, points on the plot correspond to pairs of points in $R^k$ and $\delta$ is shown on the y-axis, while the Euclidean distance between the points, represented by $d$, is shown on the x-axis. Monotonically increasing values $\hat{d}$ are then chosen so that $S=\sum_{ij} \left( d_{ij}-\hat{d}_{ij} \right)^2$ is minimized. The function S is called the “stress” function and is further normalized so that the “stress” is invariant up to scaling of the points. An iterative procedure can then be used to optimize the points, although results depend on which starting configuration is chosen, and for this reason multiple starting positions are considered.

I converted the smiley/frowny faces into numbers 0,1 or 2 (for red, yellow and green faces respectively) and was able to easily experiment with non-metric MDS using an implementation in R. The results for a 2D scaling of the friendship matrix are shown in the figure below:

It is evident that, as expected from the friendship matrix, ISIS is an outlier. One also sees some of “the enemy of thine enemy is thy friend”. What is interesting is that in some cases the placements are clearly affected by shared allegiances and mutual dislikes that are complicated in nature. For example, the reason Saudi Arabia is placed between Israel and the United States is the friendship of the U.S. towards Iraq in contrast to Israel’s relationship to the country. One interesting question, that is not addressed by the non-metric MDS approach, is what the direct influences are. For example, it stands to reason that Israel is neutral to Saudi Arabia partly because of the U.S. friendship with the country- can this be inferred from the data in the same way that causative links are inferred for gene networks? In any case, I thought the scaling was illuminating and it seems like an interesting exercise to extend the analysis to more countries/organizations/entities but it may be necessary to deal with missing data and I don’t have the time to do it.

I did decide to look at the 1D non-metric MDS, to see whether there is a meaningful one-dimensional representation of the matrix, consistent with some of the maps I’d seen. As it turns out, this is not what the data suggests. The one-dimensional scaling described below places ISIS in the middle, i.e. as the “neutral” country!

Israel                -4.55606607
Saudi Arabia          -3.62249810
Turkey                -3.04579321
United States         -2.6429534
Egypt                 -1.12919328
Al-Qaida              -0.38125270
Hamas                  0.01629508
ISIS                   0.40101149
Palestinian Authority  1.55546030
Iraq                   2.23849150
Hezbollah              2.66933449
Iran                   3.29650784
Syria                  5.20065616


This failure of non-metric MDS is simply a reflection of the fact that the friendship matrix is not “one-dimensional”. The Middle East is not one-dimensional. The complex interplay of Sunni vs. Shia, terrorist vs. freedom fighter, muslim vs. infidel, and all the rest of what is going on make it incorrect to think of the conflict in terms of a single attribute. The complex pattern of alliances and conflicts is therefore not well explained by two-colored maps, and the computations described above provide some kind of a “proof” of this fact. The friendship matrix also explains why it’s difficult to have meaningful discussions about the Middle East in 140 characters, or in Facebook tirades, or with soundbites on cable news. But as complicated as the Middle East is, I have no doubt that the “friendship matrix” of my colleagues in computational biology would require even higher dimension…