To do
CociteSeer
Tsung Teng Chen, David C Yen: CociteSeer: A system to visualize large cocitation networks. The Electronic Library · August 2010, DOI: 10.1108/02640471011033602
Shrink groups of nodes of degree 2 (small degree) to get an overall structure.
Extreme Multilabel Classification
Network multiplication with threshold
December 14, 2017
Skip small values. Introduce a threshold value. At the end correct values of existing links.
Leaders approach to clustering with RC
December 14, 2017
Dissimilarities are computed between leaders.
Corrected fractional bibliographic coupling
January 2018
Jaccard(A,B;k) = |A ∩ B| / max(k,|A ∪ B|)
Intensity of node activity in temporal networks
January 2018
u → v : v(i) = u(i)/(t(i)-t(i-1))
Wasserstein and TQ
March 20, 2018
Can the Wasserstein distance be combined with TQ?
Interval → Quantiles
Clauset ordering of journals
March 21, 2018
Compute JCi = JW * Ci * WJ . What is the condensation structure (of the main weak component)? Apply Clauset ordering to it.
JA = JW * WA. What is “the right” normalization of JAJ = JA * AJ ?
Symbolic data
March 31, 2018, Piran
Let S1 = ∑ xi and S2 = ∑ xi2. We define μ = S1/n and σ2 = ∑ (xi - μ)2 / n = S2 / n - μ2 .
Instead of μ or ( μ, σ ) it is better to use ( n, μ ) or ( n, μ, σ ) because we can compute also the representative of
a union of disjoint sets X and Y, X ∩ Y = ∅ :
nX∪Y = nX + nY
μX∪Y = (nX⋅μX + nY⋅μY) / nX∪Y
σX∪Y2 = S2;X∪Y / nX∪Y - μX∪Y2
where: S2;X∪Y = S2;X + S2;Y and S2;X = nX⋅(σX2 + μX2)
https://en.wikipedia.org/wiki/Standard_deviation
Ward's clustering method has a criterion function P(C) = ∑C∈C σC2 .
Brain networks
Is there a fast criterion to decide that a node is isolated (of degree 0)?
Citation analysis
April 25, 2018
Extend bibliography from “Exploring the Limits of Complexity: A Survey of Empirical Studies on Graph Visualisation” (review for Information Visualization).
August 20, 2018
- Use node weights in citation networks for analysis
- Does Kirchoff law hold for node weights?
- Standardization of any network: link s to all IN-nodes, link all OUT-nodes to t, add (t,s) arc. The standardized network is strongly connected. It can be periodic. A loop on (t,s) arc?
Bibliographic analysis
See 1findr.pdf. Analysis of works using important “keywords” from text.
Small world
Moskva, May 27, 2018
Milgram paper. Inbreeding can lead also some levels back. Clustering coefficient considers only one level inbreeding.
Configuration model
Moskva, May 29, 2018
Chung-Lu method for large networks. Each row u (or column) has the same partial distribution indeg[v]/m. Select randomly in each row u outdeg[u] nodes following this distribution using an improved tabelaric method - merging a sequence of basic random numbers? If you get duplicates or loops skip them.
Can be extended to https://mathinsight.org/generating_networks_second_order_motif_frequency ?
See regularity measures in Module 2 at http://www.pitt.edu/~kpele/tele2125_spring15.html#lectures
Markov chains
Moskva, June 2, 2018
Markov chains can be used to summarize sequences of events. For example sequence of letters in text → transition matrix
- generate random sequence determined by a MC
- can we use MC to measure the conformance of a sequence to MC ? Would this work: assign to each sequence as its value the geometrical mean of MC transition probabilities? Small values - atypical sequence; 0 value - forbiden sequence.
- normalization of the value? multiply it by number of states n ?
Network measures
Moskva, June 4, 2018
Zhukov's slides: Lecture 5/slide 8: Harmonic centrality; Lecture 7/slide 12: Regularity measure !?
Topogical approach to networks
LJ, November 8, 2018
Try to extend the approach from
prof. dr. Robin Henderson, Newcastle University: Statistical Topology and the Random Interstellar Medium (8. november 2018 - 11:00, IBMI)
to networks. See photos.
The results are the same for all monotonically increasing transformed values?!
Genealogy of the field
LJ, November 11, 2018
How to produce the genealogy (Figure 1) from Spatial Decision Support Systems: Three decades on
Dictionary networks
Moscow, December 6, 2018
Use n(Dic)*t(n(Dic)) or d(X,Y) = |X ∩ Y| / min(|X|, |Y|) to define a (dis)similarity and determine the islands.
Network spreadsheet
Moscow, December 6, 2018
Igraph node/link attributes can be also structured object. Develop computation engine for values and functions on nodes/linka.
Function form
LJ, Januray 5, 2019
Express the function from the blog / picture.
Lognormal + natural growth (max,min,lim,shrink)
Interesting
Brian Nguyen: Multivariate Statistical Analysis with R: PCA & Friends making a Hotdog https://bookdown.org/brian_nguyen0305/Multivariate_Statistical_Analysis_with_R/
Temporal groups
14. Jul 2022
A temporal group is formed around a “leader” (generator, attractor).
Specificity
28. Mar 2024
# citatitons (w) inside the topic bibliography / total # of citations (w) inside OpenAlex
TF-IDF
29. Mar 2024
topic bibliography vs. OpenAlex
