We discuss bootstrapping in Natural Language Processing. We read from the paper by Ehara, Sato, Oiwa, and Nakagawa and from nlp blogger. Bootstrapping is a technique by which we use a binary classifer in an iterative manner.  In Bootstrapping unlabeled instances can be labeled using the initial labeled "seed" set with iterations The  steps involved are
build a classifier with rules to select the positive answer with high precision and
build a classifier with rules to select the negative answer with high precision
Run the classifiers  on a large data set to collect a labeled set.
Train the classifier on the labeled set.
Run the classifier on the original data.
 The choice of the seed set is important and hence its chosen based on two requirements - the choice of seed set affects the accuracy and there's labeling cost associated with it. The authors present a model called the expected model rotation that works well on realistic data. With this model, they propose an "iterative seeding framework" . At the end of each iteration, the seeds are assessed for quality and improved in response to the current human labels and characteristics. This involves a criteria that improves the seeds as well as a score to keep track of the similarity of the seeds that is updated with each iteration.
In bootstrapping given a dataset we can consider the first l data to be labeled and the rest u data to be unlabeled. The dataset consists of m dimensional feature vectors and the first l have labels that belong to a set C of semantic classes.Suppose we were to pick out the animals names from the given instances then the set C consists of animal or not animal labels and is binary. The ranking is given by the score vector y-animal - y-not-animal seed vectors. The simple bootstrapping proceeds by setting the score vector with the first classifier rule for the first label and continues until all of the rules for each label is identified.
If X is the feature matrix pertaining to a given text, the score vector after c iterations is obtained by (1/m.1/n. X X-Transpose) ^c. y
To make f seed dependent, Komachi et al 2008 mentioned using an equation to include the score vector as (-Laplacian)^c.y   since a Laplacian is defined as 1-D^(-1/2)X.X-TransposedD^(-1/2) . This method is called the Laplacian propagation and the score vector is given by (I+ Beta L)^(-1) y

We will shortly see how this Laplacian propagation works. The thing to note here is that bootstrapping works with supervised and unsupervised  modes only and even though it is said to work well, it doesn't have the same rigor as Vector space model or graph based efforts. The reason we are looking into bootstrapping is merely to see the usage of Laplacian operators.

Let us look further into the paper for the Laplacian operator. The authors propose a criteria for iterative seeding. For an unlabeled instance, they denote the goodness of seed as gi and select the instance with the highest goodness of seed as the next seed added in the next iteration. Each seed selection criterion defines each goodness of seed gi and the unlabeled instance influences the model. They show that the Komachi label propagation score can be considered as the margin between each unlabeled data point and the hyperplane obtained by ridge regression. They denote this with a transformed equation. 

Before we discuss word similarity measures and the OOV term normalization that we wanted to continue from the previous post, I want to take a minute to mention Centrality of the graph which is another useful concept that can help with the word similarity. Centrality is best discussed in Sociology and I refer from the notes of the course in  UCLA by Prof. McFarland and Motoki Watabe.
There are three different centrality measures:
1) degree of centrality
2) closeness centrality
3) betweenness centrality

Given a graph with n nodes, the centrality of  a node, refers to the number of edges attached to the node. To normalize the score for each node, we divide the number of edges attached to each node by n-1.

First, the degree of centrality:
If we have a graph A with four vertices that contains only one central node to which all other nodes attach, then that central node has a centrality of 3 and the other have a centrality of 1.
The degree of centrality is calculated as [ (3-3) + (3 -1) + (3 -1) + (3 -1) ] / max-possible-which-is-(n-1)(n-2) in this case = 6/6 = 1
For a graph B with all the four vertices where each node is connected to every other as in a square with diagonals, each of the vertices now have a centrality of score of 3 and the degree of centrality for the overall graph is [ (3-3) + (3 -3) + (3 -3) + (3 -3) ] / (n-1)(n-2) = 0
The numerator is calculated as the ratio of the individual sum of the differences between the max centrality score and that of individual scores

It may appear that the higher the normalized score the higher a node's likely relevance in the graph. However this is not always true. Cook et al 1983 demonstrated that this is not the case. We will look into the applications of each measure as we define it.

To calculate the closeness centrality, we find the farness of each node and take its inverse. The farness of a node s is defined as the sum of its distance to all other nodes. The more central a node is the lower its total distance to all other nodes. Closeness can be taken as  a measure of how fast the information can spread from a node to all other nodes sequentially.
For network A, the centrality score for node 1 is 3 / 3 and for the other nodes is 3 / 5
Since the maximum score in the above is 1,
the closeness centrality for network A is [( 1 - 1 ) + ( 1 - 3/5 ) + (1 - 3 / 5) + (1 - 3 / 5 )] / [n(n-1)/2 / 5]  = 1
and for network B, the centrality score for each node is uniformly 3 / 3 = 1
and closeness centrality for the overall network B is (0 + 0 + 0 + 0) / (6/5) = 0
 

To calculate the betweenness centrality, we find the number of times a vertex acts as a bridge in the shortest path between two other nodes. It was introduced as a measure for the controllability of a node in the dissemination of a network.

For network A, the centrality score for the most connected node is 3 / 3 = 1 and for all the other nodes is 0
The maximum score in the above is 3 / 3 = 1
The betweenness score for network A is [(1-1) + (1-0) + (1-0) + (1-0)]/ [(n - 1)(n-2)/2] = 3 /3 = 1
and
for network B the centrality score is for each node is the same which is 0 since the node can be  bypassed.
The maximum score is 0
and the overall score for network B is 0 / 3 = 0


Thus we see that in all the three cases, network A is more centralized than network B.
For information flow, network A has high controllability and high efficiency in that there is no redundant edges. At the same time, network A is riskier.
For network B, there is high flexibility and better tolerance to failures. However the cost from redundant edges is higher.

We saw different scores for vertices. To determine the admittance matrix for the vertices, we have to calculate a different kind of score.

In today's post we look at some of the details on graph based word similarity measures. While we looked at word similarity measure in the Saluja, Navratil 2012 paper, I'm going to focus on normalization of words. We mentioned the holing system in Bieman and Riedl. This holing system is only part of their system but they describe a way to capture distributional and contextual similarity.  The idea here is to represent observations as <t,c> pair where t is the term (at a certain offset) and c is the context feature. The position of t in c is denoted by the @ hole symbol. The authors give an example where dependency (nsub;gave2;I1) could be transferred to <gave2, (nsub; @; I1) > Notice how the holing operator is used to give the position of the term. and this in turn could be represented by <I1, (nsub; gave2;@)>. Note the change in the context with the terms and the use of the holing operator. In the second dependency representation, the @ symbol has been introduced to give the position of gave2 and in the third representation the @ symbol gives the position of I1. The last two dependency representations are in the <t,c> pairs.
This paper also uses a term-context feature bipartite graph just like the last paper we saw. In addition it calculates a significance score sig for each pair <t,c> using the counts of the terms, the counts of the context features and the counts of their co-occurrence. If the significance score is negative, the corresponding edge is not added. Also features that have more than a thousand words is removed because they are overly general. This way the distributional similarity is calculated but the contextual similarity is calculated instead from the second order graph.
This way the authors showed that with the sentence "I caught a nasty cold" the holing system produced <cold5, (amod,@, nasty4)>, and <cold5, (dobj;caught2; @)> and the scores were <heat, (dobj; caught; @)> with an LMI score of 42.0 and <weather, (amod; @; nasty)> with a score of 139.4. The word disease came highest in rank for the above sentence.

we will continue on this discussion.

I've been looking at some objective functions for graph based similarity between words and I came across "Graph based Unsupervised Learning of Word Similarities using Heterogeneous Feature Types" by Saluja and Navratil. This seems a simple way to express the similarity. The graph they use is bipartite between words and feature sets. Edges connect two words or two feature sets or a word and a feature set.
To learn the graph, the following objective function in minimized:
Omega(Wv, Wf, Wz) = a0 Sum ( Wfp fq - (Wfp fq)-initial )^2
                                   + a1 Sum over vi Sum over fp ( Zvi fp - Zvi-initial fp) ^2
                                   + a2 Sum over vi, vj Sum over fp fq  Zvi fp Zvj fq ( Wvi, vj - Wfp,fq) ^ 2
                                   + a3 Sum over vi, vj  Sum over fp, fq Wvivj WfpWfq (Zvi,fp - Zvj, fq) ^ 2
where
Wfp,fq is the current similarity between feature fp and fq
Wvi vj is the current similarity between word vi and vj
Zvi, fp is the current importance weight of feature fp for word vi
a0 to a3 are constants that add up to 1 for the relative importance of each term
The first two terms are described as minimizing the l2-norm between the initial and the current values of Wfp,fq and Zvi, fp
The third term minimizes the similarity between the words vi and j and the features fp and fq
The fourth term minimizes the similarity between the importance weights in proportion to the similarities
As you can see the terms are progressive and enable smoothing over the two graphs.
But can we express this with a different equation that enables Laplacian smoothing and matrices
The Laplacian matrix sometimes called the admittance matrix or Kirchoff matrix of a graph G which is undirected and unweighted, is an n * n symmetric matrix with one row and column for each node defined by L = D - A where  D is the degree matrix, which is the diagonal matrix formed from the vertex degrees and A is the adjacency matrix.
A normalized vector of the Laplacian matrix of a graph is implemented by
L(G) = 1 if i == j and di != 0
         = -1 / sq rt (di.dj) if i and j are adjacent
         = 0 otherwise.
The Laplacian matrix measures to what extent a graph differs at one vertex from its values at nearby vertices. 

I'm going to take a break to discuss a topic that I've been asked to look into. A python library is not able to make an SSL Connection with an application that uses libssl. The error message received is that the 'The handshake operation timed out'. This is because the server is not completing the handshake in some cases.
We first look at what all steps are involved in the TLS handshake. TLS and SSL are different in that they don't interpolate and TLS 1.0 is often referred to as SSL 3.1 but at the same time the differences are not that much in our discussion and TLS 1.0 has a way to fall back to SSL 3.0. The handshake we describe is responsible for the authentication and the key exchange necessary to establish or resume secure sessions. In establishing a secure session, the following steps are involved :
cipher suite negotiation
authentication of the server and optionally the client
session key information exchange
The first step refers to the exchange of the cipher suite that both the client and the server will be using for the duration of the session.
The second step refers to the step where the server proves its identity to the client. The client might also need to prove its identity to the server.
The third step refers to the exchange of random numbers and the selection of a special number called the Pre-Master Secret which helps in creating a Master Secret and that in turn helps create the MAC secret which is the session key used for hashing and the write key, which is the session key used for encryption.
After the initial client hello, server hello and the server hello done message, the pre-master secret is generated by the client and the master secret is generated by both the client and the server. The client sends the change cipher spec notification to the server
Cryptographic algorithms can vary. Some fall in the bucket of Federal Information Processing Standards also called FIPS standard. These can be enabled or disabled  with FIPS mode and often is used to troubleshoot SSL issues. There are dedicated libraries  designed to support cross-platform development of security enabled client and server applications with optional support for hardware SSL acceleration on the server side and smart cards on the client side. These are called Network Security Services.

The previous post discussed a paper that formalized the usage of Graphs for describing reasoning chain relationships. It introduced the TRN graph and described two different types of nodes and three different edges.The nodes were either text nodes and section nodes and the edges were structural, similarity and causal. This graph is constructed from the text with the help of a syntactic parser which adds the text nodes Section nodes are attached to the sentence nodes and all the text nodes are added under these. Similarity measures help add edges for similarity to the node pairs. Only those measures that are above a threshold are added. Graphs that are extracted from different sections are combined Next Causal relations are added with the help of a discourse parser. With the structural, similarity and causal edges added we now have a complete TRN graph. Then with this graph, we can choose source destination pairs and find paths. Paths are combined, post-processed and visualized.
The dataset used for this study was the aviation investigation reports from Transportation Safety Board of Canada. Each report in this collection is an incident report and has sections titled summary, factual information, analysis and findings. The documents are available for download from the TSB of Canada and then they were pre-processed by the authors using GATE NLP platform. The preprocessing steps included tokenization, sentence splitting and part of speech tagging.  The sections on the summary is a brief description, the section on the factual information is the details of the aircraft or circumstance, the section on the analysis is a discussion on what might have happened and the section on the findings describes the causes. Therefore the reasoning chain was chosen as the shortest path from Summary to Causes. The constraints for the reasoning chain path was defined in the Backus-Naur Form as one comprising of a summary-path with an edge to a factual-path with an edge to an analysis path with an edge to the causes-path add the intermediaries in this representation are optional. Each of the paths can be recursively defined as one or more nodes with edges.  While these edges can be one of the  three aforementioned edges such as partof-edge, contains-edge, similar-edge and cause-edge,  only the causes path explicitly has part-of edges. A post-processing steps shrinks the path by eliminating transitives. Then the compressed graphs are laid out for visualization.

We read the paper :  automatic extraction of reasoning chains from textual reports by Sizov and Ozturk. They extract reasoning chains from documents such as medical patient reports, accident reports. Reasoning chains contain information useful to analyze the problem at hand. They use a graph based approach that makes the relations between textual units explicit. Reasoning chains are a sequence of transitions from piece of information to another that connect the problem with the resolution and thus are very valuable in future problem triages.  Moreover they determine the validity or the fallaciousness of the arguments presented.

This paper decomposes a document into text units and discovers the connections between the text units and makes them explicit. TRN is automatically acquired from text using a syntactic parser and a semantic similarity measure. We now discuss this TRN in detail.  A reasoning chain is extracted as a path from the graph-based text representation. TRN is a graph with two types of nodes. text nodes and section nodes and three types of edges - structural, similarity and causal. This graph is contructed from the text in the following manner: 1) syntax trees obtained from a syntactic parser are added to the graph, 2) section nodes are attached to the sentence nodes, 3) similarity edges are added between similar text nodes and 4) cause relations identified by a discourse paper are added. When representing text units, graph based approaches have used terms or short phrases as text units that are too small for this approach. Another popular choice is to use a whole sentence or a few. However, such text units may contain several pieces of information where only one is relevant for the reasoning chain. In this paper, the authors use a Stanford parser to extract the syntax tree and pick out the S(sentence, clause), NP (noun phrase) and VP (verb phrase) which are referred to as text nodes. Text nodes are identified by a set of stemmed words. Along with these structural relations such as Contains and PartOf are also added as edges. Graphs extracted from different sentences in a document are combined into one. To obtain similarity relations, a similarity value is computed for each pair of text nodes of the same category(S,VP, NP) and Similar edges are added to the graph for node pairs where the similarity is above a threshold. Their similarity measure finds a one to one alignment of words from two text units The LCH for these words are computed using the shortest path between the corresponding senses in WordNet. Then a complete bipartite graph is constructed. Nodes in the bipartite graph represent words from the text units while the edges have weights that correspond to similarities between words. A maximum weighted bipartite matching finds a one-to-one alignment that maximizes the sum of similarities between aligned words.  This sum is then normalized and thresholded to add corresponding Similar edges to the graph. Next Causal relations are added to the graph. Causal relations are found by a discourse parser. In this case, they used a PDTB-styled End to End discourse parser. Cause relations found by the parser are added to the TRN graph as Cause edges. This is how the TRN graph is built.
Once the TRN graph is constructed, the reasoning chain is generated based on a three stage process:
1) a report is converted from text into a TRN graph
2) given a start and an end node, several paths are extracted from the graphs and
3) paths are combined, post processed and visualized.