Web Science/Part2: Emerging Web Properties/Advanced statistical descriptive models for the Web/Visually straight lines on log log plots

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Web Science/Part2: Emerging Web Properties

Web Science/Part2: Emerging Web Properties/MoocIndex

Web Science/Part2: Emerging Web Properties/Advanced statistical descriptive models for the Web/Visually straight lines on log log plots

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Visually straight lines on log log plots

Learning goals

Video

Script

Quiz

Further reading

Discussion

Learning goals

1. Be able to do a coordinate transformation to change the scales of your plots
2. Understand in which scenario power functions appear as straight lines
3. Know in which scenarios exponential functions appear as straight lines
4. Be even more cautious about your visual impressions

Video

Script

find the slide deck at File:Visually_straight_lines_on_log_log_plots.pdf

Quiz

1 Which functions appear as straight lines on log log plots?

	linear functions
	sine, cosine, tan
	power functions
	exponential functions
	logarithms
	square root functions

2 Which functions appear as straight lines on linear plots plots?

	linear functions
	sine, cosine, tan
	power functions
	exponential functions
	logarithms
	square root functions

3 Which functions appear as straight lines on plots that are only logarithmic on the y scale?

	linear functions
	sine, cosine, tan
	power functions
	exponential functions
	logarithms
	square root functions

Further reading

1. tba

Discussion

Navigation

1. How big is the World Wide Web
   1. Problems with the question about the size of the Web
   2. 3 ways to study the Web
   3. A simplistic descriptive model
   4. An unrealistic, simplistic generative model
   5. Summary, further reading, homework
2. Simple statistical descriptive Models for the Web
   1. Counting Words And Documents
   2. Typical length of a document
   3. How to formulate a research hypothesis
   4. Number of words needed to understand most of Wikipedia
   5. Linguists way of checking simplicity of text
3. Advanced statistical descriptive models for the Web
   1. The Zipf law for text
   2. Visually straight lines on log log plots
   3. Fitting a curve on a log log plot
   4. Zipf law powerlaw or pareto law.webm
4. Modelling Similarity of Text
   1. Similarity Measures and their Applications
   2. Jaccard Similarity for Sets
   3. Cosine Similarity For Vectorspaces
   4. Probabilistic Similarity Measures Kullback Leibler Divergence
   5. Comparing Results of Similarity Merasures
5. Generative Models for the Web
   1. Introduction to generative modelling.webm
   2. Sampling from a probability distribution
   3. Evaluating a generative model
   4. Pittfalls when increasing the number of model parameters
6. Modeling the Web as a graph
   1. Reviewing terms from graph theory
   2. The standard web graph model
   3. Descriptive statistics of the web graph
   4. Topology of the web graph
   5. Modelling-graphs-with-linear-algebra

The Zipf law for text

Fitting a curve on a log log plot