Web Science/Part2: Emerging Web Properties/Modelling Similarity of Text/Cosine Similarity For Vectorspaces

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Web Science/Part2: Emerging Web Properties

Web Science/Part2: Emerging Web Properties/MoocIndex

Web Science/Part2: Emerging Web Properties/Modelling Similarity of Text/Cosine Similarity For Vectorspaces

• edit MOOC index

Cosine Similarity For Vectorspaces

Learning goals

Video

Script

Quiz

Further reading

Discussion

Learning goals

1. Be familiar with the vector space model for text documents
2. Be aware of term frequency and (inverse) document frequency
3. Have reviewed the definitions of base and dimension
4. Realize that the angle between two vectors can be seen as a similarity measure

Video

Script

The slides can be found at File:Cosine-Similarity-For-Vectorspaces.pdf

Quiz

1 Calculate the scalar product between ${\begin{pmatrix}2\\2\\5\end{pmatrix}}$ and ${\begin{pmatrix}2\\3\\0\end{pmatrix}}$.

	9
	10
	14
	54

2 What is true about the distance measures on vector spaces?

	they can have arbitrary large distances
	the cosine distance can be arbitrary large
	the euclidean distance is bound to a value of $2\pi$
	they can be transformed to a similarity measure

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

Jaccard Similarity for Sets

Probabilistic Similarity Measures Kullback Leibler Divergence