Archive for December 2015
Enterprise architects are seldom (never?) given a blank canvas on which they can draw as they please. They invariably have to begin with an installed base of systems over which they have no control. As I wrote in a piece on the legacy of legacy systems:
An often unstated (but implicit) requirement [on new systems] is that [they] must maintain continuity between the past and present. This is true even for systems that claim to represent a clean break from the past; one never has the luxury of a completely blank slate, there are always arbitrary constraints placed by legacy systems.
Indeed the system landscape of any large organization is a palimpsest, always retaining traces of what came before. Those who actually maintain systems – usually not architects – are painfully aware of this simple truth.
The IT landscape of an organization is therefore a snapshot, a picture that begins to age the instant is taken. Practicing enterprise architects will say they know this “of course”, and pay due homage to it in their words…but often not their actions. The conflicts and contradictions between legacy and their aspirational architectures are hard to deal with and hence easier to ignore. In this post, I draw a parallel between this central conundrum of enterprise architecture and the process of biological evolution.
A Batesonian perspective on evolution
I’ve recently been re-reading Mind and Nature: A Necessary Unity, a book that Gregory Bateson wrote towards the end of his life of eclectic scholarship. Tucked away in the appendix of the book is an essay lamenting the fragmentation of knowledge and the lack of transdisciplinary thinking within universities. Central to the essay is the notion of obsolescence. Bateson argued that much of what was taught in universities lagged behind the practical skills and mindsets that were needed to tackle the problems of that time. Most people would agree that this is as true today as it was in Bateson’s time, perhaps even more so.
Bateson had a very specific idea of obsolescence in mind. He suggested that the educational system is lopsided because it invariably lags behind what is needed in the “real world”. Specifically, there is a lag between the typical university curriculum and the attitudes, dispositions, knowledge and skills needed to the problems of an ever-changing world. This lag is what Bateson referred to as obsolescence. Indeed, if the external world did not change there would be no lag and hence no obsolescence. As he noted:
I therefore propose to analyze the lopsided process called “obsolescence” which we might more precisely call “one-sided progress.” Clearly for obsolescence to occur there must be, in other parts of the system, other changes compared with which the obsolete is somehow lagging or left behind. In a static system, there would be no obsolescence…
This notion of obsolescence-as-lag has a direct connection with the contrasting process of developmental and evolutionary biology. The process of development of an embryo is inherently conservative – it develops according predetermined rules and is relatively robust to external stimuli. On the other hand, after birth, individuals are continually subject to a wide range of external factors (e.g. climate, stress etc.) that are unpredictable. If exposed to such factors over an extended period, they may change their characteristics in response to them (e.g. the tanning effect of sunlight, adaptability etc). However, these characteristics are not inheritable. They are passed on (if at all) by a much slower process of natural selection. As a consequence, there is a significant lag between external stimuli and the inheritability of the associated characteristics.
As Bateson puts it:
Survival depends upon two contrasting phenomena or processes, two ways of achieving adaptive action. Evolution must always, Janus-like, face in two directions: inward towards the developmental regularities and physiology of the living creature and outward towards the vagaries and demands of the environment. These two necessary components of life contrast in interesting ways: the inner development-the embryology or “epigenesis”-is conservative and demands that every new thing shall conform or be compatible with the regularities of the status quo ante. If we think of a natural selection of new features of anatomy or physiology-then it is clear that one side of this selection process will favor those new items which do not upset the old apple cart. This is minimal necessary conservatism.
In contrast, the outside world is perpetually changing and becoming ready to receive creatures which have undergone change, almost insisting upon change. No animal or plant can ever be “readymade.” The internal recipe insists upon compatibility but is never sufficient for the development and life of the organism. Always the creature itself must achieve change of its own body. It must acquire certain somatic characteristics by use, by disuse, by habit, by hardship, and by nurture. These “acquired characteristics” must, however, never be passed on to the offspring. They must not be directly incorporated into the DNA. In organisational terms, the injunction – e.g. to make babies with strong shoulders who will work better in coal mines- must be transmitted through channels, and the channel in this case is via natural external selection of those offspring who happen (thanks to the random shuffling of genes and random creation of mutations) to have a greater propensity for developing stronger shoulders under the stress of working in coal mine.
The upshot of the above is that the genetic code of any species is inherently obsolete because it is, in at least a few ways, maladapted to its environment. This is a good thing. Sustainable and lasting change to the genome of a population should occur only through the trial-and-error process of natural selection over many generations. It is only through such a gradual process that one can be sure that that a) the adaptation is necessary and b) that it occurs with minimal disruption to the existing order.
…and so to enterprise architecture
In essence, the aim of enterprise architecture is to come up with a strategy and plan to move from an old system landscape to a new one. Typically, architectures are proposed based on current technology trends and extrapolations thereof. Frameworks such as The Open Group Architecture Framework (TOGAF) present a range of options for migrating from legacy architecture.
Here’s an excerpt from Chapter 13 of the TOGAF Guide:
[The objective is to] create an overall Implementation and Migration Strategy that will guide the implementation of the Target Architecture, and structure any Transition Architectures. The first activity is to determine an overall strategic approach to implementing the solutions and/or exploiting opportunities. There are three basic approaches as follows:
- Greenfield: A completely new implementation.
- Revolutionary: A radical change (i.e., switches on, switch off).
- Evolutionary: A strategy of convergence, such as parallel running or a phased approach to introduce new capabilities.
What can we say about these options in light of the discussion of the previous sections?
Firstly, from the discussion of the introduction, it is clear that Greenfield situations can be discounted on grounds rarity alone. So let’s look at the second option – revolutionary change – and ask if it is viable in light of the discussion of the previous section.
In the case of a particular organization, the gap between an old architecture and technology trends/extrapolations is analogous to the lag between inherited characteristics and external forces. The former resist change; the latter insist on it. The discussion of the previous section tells us that the former cannot be wished away, they are a natural consequence of “technology genes” embedded in the organization. Because this is so, changes are best introduced in a gradual way that permits adaptation through the slow and painful process of trial and error. This is why the revolutionary approach usually fails.
It follows from the above that the only viable approach to enterprise architecture is an evolutionary one. This process is necessarily gradual. Architects may wish for green fields and revolutions, but the reality is that lasting and sustainable change in an organisation’s technology landscape can only be achieved incrementally, akin to the way in which an aspiring marathon runner’s physiology adapts to the extreme demands of the sport.
The other, perhaps more subtle point made by this analogy is that a particular organization is but one member of a “species” which, in the present context, is a population of organisations that have a certain technology landscape. Clearly, a new style of architecture will be deemed a success only if it is adopted successfully by a significant number of organisations within this population. Equally clear is that this eventuality is improbable because new architectural paradigms are akin to random mutations. Most of these are rightly rejected by organizations, but only after exacting a high price. This explains why most technology fads tend to fade away.
The analogy between the evolution of biological systems and organizational technology landscapes has some interesting implications for enterprise architects. Here are a few that are worth highlighting:
- Enterprise architects are caught between a rock and a hard place: to demonstrate value they have to change things rapidly, but rapid changes are more likely to fail than succeed.
- The best chance of success lies in an evolutionary approach that accepts trial and error as a natural part of the process. The trick lies in selling that to management…and there are ways to do that.
- A corollary of (2) is that old and new elements of the landscape will necessarily have to coexist, often for periods much longer than one might expect. One must therefore design for coexistence. Above all, the focus here should be on the interfaces for these are the critical elements that enable the old and the new to “talk” to each other.
- Enterprise architects should be skeptical of cutting edge technologies. It almost always better to bet on proven technologies because they have the benefit of the experience of others.
- One of the consequences of an evolutionary process of trial and error is that benefits (or downsides) are often not evident upfront. One must therefore always keep an eye out for these unexpected features.
Finally, it is worth pointing out that an interesting feature of all the above points is that they are consistent with the principles of emergent design.
In this article I’ve attempted to highlight a connection between the evolution of organizational technology landscapes and the process of biological evolution. At the heart of both lie a fundamental tension between inherent conservatism (the tendency to preserve the status quo change) and the imperative to evolve in order to adapt to changes imposed by the environment. There is no question that maintaining the status quo is never an option. The question is how to evolve in order to ensure the best chance of success. Evolution tells us that the best approach is a gradual one, via a process of trial, error and learning.
Graph theory is the an area of mathematics that analyses relationships between pairs of objects. Typically graphs consist of nodes (points representing objects) and edges (lines depicting relationships between objects). As one might imagine, graphs are extremely useful in visualizing relationships between objects. In this post, I provide a detailed introduction to network graphs using R, the premier open source tool statistics package for calculations and the excellent Gephi software for visualization.
The article is organised as follows: I begin by defining the problem and then spend some time developing the concepts used in constructing the graph Following this, I do the data preparation in R and then finally build the network graph using Gephi.
In an introductory article on cluster analysis, I provided an in-depth introduction to a couple of algorithms that can be used to categorise documents automatically. Although these techniques are useful, they do not provide a feel for the relationships between different documents in the collection of interest. In the present piece I show network graphs can be used to to visualise similarity-based relationships within a corpus.
There are many ways to quantify similarity between documents. A popular method is to use the notion of distance between documents. The basic idea is simple: documents that have many words in common are “closer” to each other than those that share fewer words. The problem with distance, however, is that it can be skewed by word count: documents that have an unusually high word count will show up as outliers even though they may be similar (in terms of words used) to other documents in the corpus. For this reason, we will use another related measure of similarity that does not suffer from this problem – more about this in a minute.
Representing documents mathematically
As I explained in my article on cluster analysis, a document can be represented as a point in a conceptual space that has dimensionality equal to the number of distinct words in the collection of documents. I revisit and build on that explanation below.
Say one has a simple document consisting of the words “five plus six”, one can represent it mathematically in a 3 dimensional space in which the individual words are represented by the three axis (See Figure 1). Here each word is a coordinate axis (or dimension). Now, if one connects the point representing the document (point A in the figure) to the origin of the word-space, one has a vector, which in this case is a directed line connecting the point in question to the origin. Specifically, the point A can be represented by the coordinates in this space. This is a nice quantitative representation of the fact that the words five, plus and one appear in the document exactly once. Note, however, that we’ve assumed the order of words does not matter. This is a reasonable assumption in some cases, but not always so.
As another example consider document, B, which consists of only two words: “five plus” (see Fig 2). Clearly this document shares some similarity with document but it is not identical. Indeed, this becomes evident when we note that document (or point) B is simply the point $latex(1, 1, 0)$ in this space, which tells us that it has two coordinates (words/frequencies) in common with document (or point) A.
To be sure, in a realistic collection of documents we would have a large number of distinct words, so we’d have to work in a very high dimensional space. Nevertheless, the same principle holds: every document in the corpus can be represented as a vector consisting of a directed line from the origin to the point to which the document corresponds.
Now it is easy to see that two documents are identical if they correspond to the same point. In other words, if their vectors coincide. On the other hand, if they are completely dissimilar (no words in common), their vectors will be at right angles to each other. What we need, therefore, is a quantity that varies from 0 to 1 depending on whether two documents (vectors) are dissimilar(at right angles to each other) or similar (coincide, or are parallel to each other).
Now here’s the ultra-cool thing, from your high school maths class, you know there is a trigonometric ratio which has exactly this property – the cosine!
What’s even cooler is that the cosine of the angle between two vectors is simply the dot product of the two vectors, which is sum of the products of the individual elements of the vector, divided by the product of the lengths of the two vectors. In three dimensions this can be expressed mathematically as:
where the two vectors are and , and is the angle between the two vectors (see Fig 2).
The upshot of the above is that the cosine of the angle between the vector representation of two documents is a reasonable measure of similarity between them. This quantity, sometimes referred to as cosine similarity, is what we’ll take as our similarity measure in the rest of this article.
The adjacency matrix
If we have a collection of documents, we can calculate the similarity between every pair of documents as we did for A and B in the previous section. This would give us a set of numbers between 0 and 1, which can be conveniently represented as a matrix. This is sometimes called the adjacency matrix. Beware, though, this term has many different meanings in the math literature. I use it in the sense specified above.
Since every document is identical to itself, the diagonal elements of the matrix will all be 1. These similarities are trivial (we know that every document is identical to itself!) so we’ll set the diagonal elements to zero.
Another important practical point is that visualizing every relationship is going to make a very messy graph. There would be edges in such a graph, which would make it impossible to make sense of if we have more than a handful of documents. For this reason, it is normal practice to choose a cutoff value of similarity below which it is set to zero.
Building the adjacency matrix using R
We now have enough background to get down to the main point of this article – visualizing relationships between documents.
The first step is to build the adjacency matrix. In order to do this, we have to build the document term matrix (DTM) for the collection of documents, a process which I have dealt with at length in my introductory pieces on text mining and topic modeling. In fact, the steps are actually identical to those detailed in the second piece. I will therefore avoid lengthy explanations here. However, I’ve listed all the code below with brief comments (for those who are interested in trying this out, the document corpus can be downloaded here and a pdf listing of the R code can be obtained here.)
OK, so here’s the code listing:
docs <- tm_map(docs, toSpace, "-")
docs <- tm_map(docs, toSpace, "’")
docs <- tm_map(docs, toSpace, "‘")
docs <- tm_map(docs, toSpace, "•")
docs <- tm_map(docs, toSpace, "”")
docs <- tm_map(docs, toSpace, "“")
pattern = "organiz", replacement = "organ")
docs <- tm_map(docs, content_transformer(gsub),
pattern = "organis", replacement = "organ")
docs <- tm_map(docs, content_transformer(gsub),
pattern = "andgovern", replacement = "govern")
docs <- tm_map(docs, content_transformer(gsub),
pattern = "inenterpris", replacement = "enterpris")
docs <- tm_map(docs, content_transformer(gsub),
pattern = "team-", replacement = "team")
The rows of a DTM are document vectors akin to the vector representations of documents A and B discussed earlier. The DTM therefore contains all the information we need to calculate the cosine similarity between every pair of documents in the corpus (via equation 1). The R code below implements this, after taking care of a few preliminaries.
A few lines need a brief explanation:
First up, although the DTM is a matrix, it is internally stored in a special form suitable for sparse matrices. We therefore have to explicitly convert it into a proper matrix before using it to calculate similarity.
Second, the names I have given the documents are way too long to use as labels in the network diagram. I have therefore mapped the document names to the row numbers which we’ll use in our network graph later. The mapping back to the original document names is stored in filekey.csv. For future reference, the mapping is shown in Table 1 below.
Table 1: File mappings
Finally, the distance function (as.dist) in the cosine similarity function sets the diagonal elements to zero because the distance between a document and itself is zero…which is just a complicated way of saying that a document is identical to itself 🙂
The last three lines of code above simply implement the cutoff that I mentioned in the previous section. The comments explain the details so I need say no more about it.
…which finally brings us to Gephi.
Visualizing document similarity using Gephi
Gephi is an open source, Java based network analysis and visualisation tool. Before going any further, you may want to download and install it. While you’re at it you may also want to download this excellent quick start tutorial.
Go on, I’ll wait for you…
To begin with, there’s a little formatting quirk that we need to deal with. Gephi expects separators in csv files to be semicolons (;) . So, your first step is to open up the adjacency matrix that you created in the previous section (AdjacencyMatrix.csv) in a text editor and replace commas with semicolons.
Once you’ve done that, fire up Gephi, go to File > Open, navigate to where your Adjacency matrix is stored and load the file. If it loads successfully, you should see a feedback panel as shown in Figure 3. By default Gephi creates a directed graph (i.e one in which the edges have arrows pointing from one node to another). Change this to undirected and click OK.
Once that is done, click on overview (top left of the screen). You should end up with something like Figure 4.
Gephi has sketched out an initial network diagram which depicts the relationships between documents…but it needs a bit of work to make it look nicer and more informative. The quickstart tutorial mentioned earlier describes various features that can be used to manipulate and prettify the graph. In the remainder of this section, I list some that I found useful. Gephi offers many more. Do explore, there’s much more than I can cover in an introductory post.
First some basics. You can:
- Zoom and pan using mouse wheel and right button.
- Adjust edge thicknesses using the slider next to text formatting options on bottom left of main panel.
- Re-center graph via the magnifying glass icon on left of display panel (just above size adjuster).
- Toggle node labels on/off by clicking on grey T symbol on bottom left panel.
Figure 5 shows the state of the diagram after labels have been added and edge thickness adjusted (note that your graph may vary in appearance).
The default layout of the graph is ugly and hard to interpret. Let’s work on fixing it up. To do this, go over to the layout panel on the left. Experiment with different layouts to see what they do. After some messing around, I found the Fruchtermann-Reingold and Force Atlas options to be good for this graph. In the end I used Force Atlas with a Repulsion Strength of 2000 (up from the default of 200) and an Attraction Strength of 1 (down from the default of 10). I also adjusted the figure size and node label font size from the graph panel in the center. The result is shown in Figure 6.
This is much better. For example, it is now evident that document 9 is the most connected one (which table 9 tells us is a transcript of a conversation with Neil Preston on organisational change).
It would be nice if we could colour code edges/nodes and size nodes by their degree of connectivity. This can be done via the ranking panel above the layout area where you’ve just been working.
In the Nodes tab select Degree as the rank parameter (this is the degree of connectivity of the node) and hit apply. Select your preferred colours via the small icon just above the colour slider. Use the colour slider to adjust the degree of connectivity at which colour transitions occur.
Do the same for edges, selecting weight as the rank parameter(this is the degree of similarity between the two douments connected by the edge). With a bit of playing around, I got the graph shown in the screenshot below (Figure 7).
If you want to see numerical values for the rankings, hit the results list icon on the bottom left of the ranking panel. You can see numerical ranking values for both nodes and edges as shown in Figures 8 and 9.
It is easy to see from the figure that documents 21 and 29 are the most similar in terms of cosine ranking. This makes sense, they are pieces in which I have ranted about the current state of enterprise architecture – the first article is about EA in general and the other about the TOGAF framework. If you have a quick skim through, you’ll see that they have a fair bit in common.
Finally, it would be nice if we could adjust node size to reflect the connectedness of the associated document. You can do this via the “gem” symbol on the top right of the ranking panel. Select appropriate min and max sizes (I chose defaults) and hit apply. The node size is now reflective of the connectivity of the node – i.e. the number of other documents to which it is cosine similar to varying degrees. The thickness of the edges reflect the degree of similarity. See Figure 10.
Now that looks good enough to export. To do this, hit the preview tab on main panel and make following adjustments to the default settings:
Under Node Labels:
1. Check Show Labels
2. Uncheck proportional size
3. Adjust font to required size
1. Change thickness to 10
2. Check rescale weight
Hit refresh after making the above adjustments. You should get something like Fig 11.
All that remains now is to do the deed: hit export SVG/PDF/PNG to export the diagram. My output is displayed in Figure 12. It clearly shows the relationships between the different documents (nodes) in the corpus. The nodes with the highest connectivity are indicated via node size and colour (purple for high, green for low) and strength of similarity is indicated by edge thickness.
…which brings us to the end of this journey.
The techniques of text analysis enable us to quantify relationships between documents. Document similarity is one such relationship. Numerical measures are good, but the comprehensibility of these can be further enhanced through meaningful visualisations. Indeed, although my stated objective in this article was to provide an introduction to creating network graphs using Gephi and R (which I hope I’ve succeeded in doing), a secondary aim was to show how document similarity can be quantified and visualised. I sincerely hope you’ve found the discussion interesting and useful.
Many thanks for reading! As always, your feedback would be greatly appreciated.