# Web Science/Part2: Emerging Web Properties
## Lessons

* The question will remain unanswered during the lesson and the entire course.
* question of size is underspecified because a measure is needed.
* measure depends heavily on the choice of how we model the web.
* We have not yet defined what we mean when we say World Wide Web.
* The web as a software system.
* The web as a collection of text documents.
* The web as a graph of interlinked documents.
* Even when choosing 1 point of view we have fundamentally different ways of modelling.
* understand that only the model is described.
* description of the model can be used for interpretation.
* within the descriptive model one chooses measures to describe the object of study.
* understand the notion of a modelling choice
* be able to criticise a descriptive model and the modelling choices
* Can be used to try to give a reason why something works.
* need to be run more than once!
* understand the notion of a modeling parameter
* will be compared to the descriptive model of our object of study.
* Understand why we selected simple English Wikipedia as a toy example for modeling the web
* Understand that a task already as simple as counting words includes modeling choices
* Be familiar with the term “unique word token”
* Know some basic tools to count words and documents
* Be familiar with some basic statistical objects like Median, Mean, and Histograms
* Should be able to relate a histogram to its cumulative distribution function
* Understand the ongoing, cyclic process of research
* Know what falsifiable means and why every research hypothesis needs to be falsifiable
* Be able to formulate your own research hypothesis
* Understand what a log-log plot is
* Improve your skills in reading and interpreting diagrams
* Know about the word rank / frequency plot
* Should be able to transfer a histogram or curve into a cumulative distribution function
* Get a feeling for interdisciplinary research
* Know the Automated Readability Index
* Have a strong sense of support for our research hypothesis
* Be able to critically discuss the limits of our models
* Be able to name some fundamental properties about how frequencies of words in texts are distributed
* Be a little bit more cautious about visual impressions when looking at log-log plots
* Know both formulations of Zipf’s law
* Be able to do a coordinate transformation to change the scales of your plots
* Understand in which scenario power functions appear as straight lines
* Know in which scenarios exponential functions appear as straight lines
* Be even more cautious about your visual impressions
* Know the axioms for a distance measure and how they relate to norms.
* Know at least two distance measures on functions spaces.
* Understand why changing to the CDF makes sense when looking at distance between functions.
* Understand the principle of the Kolomogorov-Smirnov test for fitting curves
* Know how to transform a rank frequency diagram to a powerlaw plot.
* Understand how powerlaw and pareto plots relate to each other.
* Be able to explain why a pareto plot is just and inverted rank frequency diagram
* Be able to transform the zipf coefficient to the powerlaw and pareto coefficient and vice versa.
* Understand that building the CDF is basically like building the integral.
* Know the properties of a similarity measure
* Be able to relate similarity and distance measures
* Know of two applications for modelling similarity
* Understand how text documents can be modeled as sets
* Know the Jaccard coefficient as a similarity measure on sets
* Know a trick how to remember the formula
* Be aware of the possible outcomes of the Jaccard index
* As always be able to criticize your model
* Be familiar with the vector space model for text documents
* Be aware of term frequency and (inverse) document frequency
* Have reviewed the definitions of base and dimension
* Realize that the angle between two vectors can be seen as a similarity measure
* Be aware of a unigram Language Model
* Know Laplacian (aka +1) smoothing
* Know the query likelihood model
* The Kullback Leibler Divergence
* See how a similarity measure can be derived from Kullback Leibler Divergence
* Understand that different modeling choices can produce very different results.
* Have a feeling how you could statistically compare the differences of the models.
* Know how you could extract keywords from documents with the tf-idf approach.
* Try to argue which model you like best in a certain scenario.
* Understand the principle methodology for building generative models
* Remember why people are interested in generative models
* Know why descriptive models are needed when evaluating a generative model
* Be aware of one way to create a model for text generation
* Understand how to sample values from an arbitrary probability distribution
* Have seen yet another application of the cumulative distribution function
* Understand that sampling from a distribution is just a coordinate transformation of the uniform distribution
* See that it makes sense to compare statistics
* Understand that comparing statistics is not a well defined task
* Be aware of the fact that very different models could lead to the same statistics
* See that one can always increase the model parameters
* Know that increasing model parameters often yields a more accurate model
* Be aware of the bigram and mixed models as examples for our generative processes
* Be familiar with a set theoretic way of denoting a graph
* Know at least 4 different types of graphs
* Have practiced your abilities in reading and writing mathematical formulas
* Be able to model web pages as a graph
* Know that the authorship graph is bipartite
* Know what kind of graph the graph of web pages is
* (as always) be aware of the fact that modeling is done by making choices
* Know terms like Size and (unique) volume
* Be able to count the in and out degree of web pages
* Have an idea what kind of law (in & out) degree distributions follow
* Know that degree is not distributed in a fair way
* Know that the Gini coefficient can be used to measure fairness
* Understand the notion of a path in a (directed) graph
* Know that shortest paths between nodes need not be unique
* Understand the notion of a strongly connected component
* Know about the diameter of a graph
* Be aware of the bow tie structure of the Web
* Be able to read and build an adjacency matrix of a graph
* Know some basic matrix vector multiplications to generate some statistics out of the adjacency matrix
* Understand what is encoded in the components of the k-th power of the Adjacency matrix of a graph

## Discussion

* How big is the World Wide Web
** Problems with the question about the size of the Web
** 3 ways to study the Web
** A simplistic descriptive model
** An unrealistic, simplistic generative model
** Summary, further reading, homework
* Simple statistical descriptive Models for the Web
** Counting Words And Documents
** Typical length of a document
** How to formulate a research hypothesis
** Number of words needed to understand most of Wikipedia
** Linguists way of checking simplicity of text
* Advanced statistical descriptive models for the Web
** The Zipf law for text
** Visually straight lines on log log plots
** Fitting a curve on a log log plot
** Zipf law powerlaw or pareto law.webm
* Modelling Similarity of Text
** Similarity Measures and their Applications
** Jaccard Similarity for Sets
** Cosine Similarity For Vectorspaces
** Probabilistic Similarity Measures Kullback Leibler Divergence
** Comparing Results of Similarity Merasures
* Generative Models for the Web
** Introduction to generative modelling.webm
** Sampling from a probability distribution
** Evaluating a generative model
** Pittfalls when increasing the number of model parameters
* Modeling the Web as a graph
** Reviewing terms from graph theory
** The standard web graph model
** Descriptive statistics of the web graph
** Topology of the web graph
** Modelling-graphs-with-linear-algebra