# Stop Thinking, Just Do!

Sung-Soo Kim's Blog

# Large Graph-Mining: Power Tools and a Practitioner’s Guide

## Abstract

How to find patterns in large graphs, spanning Giga and Tera bytes? What are the best tools from matrix algebra, and how can they help us solve graph mining problems? These are exactly the goals of this tutorial. Matrix algebra and graph theory can offer powerful tools and theorems, like SVD, spectral analysis, community detection, and more; we single out the most useful tools, we show the intuition behind them, and we give one or more practical settings that each tool performed well. We also cover the emerging map/reduce architecture, and its impact on large graph mining.

Large Graph-Mining: Power Tools and a Practitioner’s Guide

Christos Faloutsos, Gary L Miller, Charalampos E. Tsourakakis
2 videos

## Outline and Foils

All pdfs (1-per-page, 4-per-page, and  6-per-page).
Video of the lecture.

(pdf ) Introduction

(pdf) Task 1: Node importance

• SVD
• HITS
• PageRank

(pfd) Task 2: Community detection

• METIS, Spectral partitioning
• co-clustering, cross-associations

(pdf) Task 3: Recommendations

• Proximity

(pdf) Task 4: Connection sub-graphs

(pdf) Task 5: Mining graphs over time & tensors

• PARAFAC, Tucker

(pdf) Task 6: Virus/influence propagation

(pdf) Task 7: Spectral Graph Theory:

• Properties of Adjacency Matrix, Laplacian,
• Sparsest cut and Cheeger Inequality, Normalized Laplacian

(pdf) Task 8: Tera/peta graph mining: Hadoop

(pdf) Conclusions

## Target Audience

The target audience are data mining and machine learning professionals who wish to know the most important matrix algebra tools and their applications in large graph mining.

## Prerequisites

Computer science background (B.Sc or equivalent); familiarity with undergraduate linear algebra.

## References

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3. Deepayan Chakrabarti, Spiros Papadimitriou, Dharmendra S. Modha, and Christos Faloutsos. Fully Automatic Cross-Associations, KDD 2004, Washington, DC.
4. Fan R. K. Chung: Spectral Graph Theory (AMS)
5. Inderjit S. Dhillon, Subramanyam Mallela, and Dharmendra S. Modha. Information-theoretic co-clustering. KDD 2003, Washington, DC.
6. Jeffrey Dean and Sanjay Ghemawat. MapReduce: Simplified Data Processing on Large Clusters. OSDI’04 ,San Francisco, CA
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10. Tamara Kolda, Brett Bader, and Joseph Kenny. Higher-order Web link analysis using multilinear algebra, ICDM 2005, Houston, Texas.
11. Jure Leskovec, Jon Kleinberg and Christos Faloutsos. Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations, KDD 2005, Chicago, IL. (“Best Research Paper” award).
12. Jure Leskovec, Deepayan Chakrabarti, Jon Kleinberg, and Christos Faloutsos. Realistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication, ECML/PKDD 2005, Porto, Portugal.
13. Jure Leskovec and Christos Faloutsos. Scalable Modeling of Real Graphs using Kronecker Multiplication, ICML 2007, Corvallis, OR, USA
14. Jure Leskovec, Mary McGlohon, Christos Faloutsos, Natalie S. Glance, and Matthew Hurst. Patterns of Cascading Behavior in Large Blog Graphs, SDM 2007, Minneapolis, Minnesota.
15. Bojan Mohar and Svatopluk Poljak: Eigenvalues in Combinatorial Optimization, IMA Preprint Series #939
16. Shashank Pandit, Duen Horng (Polo) Chau, Samuel Wang and Christos Faloutsos. NetProbe: A Fast and Scalable System for Fraud Detection in Online Auction Networks WWW 2007, Banff, Alberta, Canada, May 8-12, 2007.
17. Gilbert Strang: Introduction to Applied Mathematics (Wellesley-Cambridge Press)
18. Jimeng Sun, Dacheng Tao, and Christos Faloutsos. Beyond Streams and Graphs: Dynamic Tensor Analysis, KDD 2006, Philadelphia, PA.
19. Jimeng Sun, Yinglian Xie, Hui Zhang, Christos Faloutsos. Less is More: Compact Matrix Decomposition for Large Sparse Graphs, SDM 2007, Minneapolis, Minnesota. (“Best Research Paper” award)
20. Jimeng Sun, Spiros Papadimitriou, Philip S. Yu, and Christos Faloutsos. GraphScope: parameter-free mining of large time-evolving graphs, KDD 2007, San Jose, CA.
21. Hanghang Tong, Christos Faloutsos, and Jia-Yu Pan. Fast Random Walk with Restart and Its Applications, ICDM 2006, Hong Kong. (“Best Research Paper” award)
22. Hanghang Tong and Christos Faloutsos. Center-Piece Subgraphs: Problem Definition and Fast Solutions, KDD 2006, Philadelphia, PA.
23. Hanghang Tong, Brian Gallagher, Tina Eliassi-Rad, and Christos Faloutsos. Fast best-effort pattern matching in large attributed graphs, KDD 2007, San Jose, CA.
24. Hanghang Tong, Yehuda Koren, and Christos Faloutsos. Fast direction-aware proximity for graph mining, KDD 2007, San Jose, CA.
25. Hanghang Tong, Spiros Papadimitriou, Philip S. Yu and Christos Faloutsos. Proximity Tracking on Time-Evolving Bipartite Graphs. SDM 2008, Atlanta, GA.
26. Hanghang Tong, Spiros Papadimitriou, Jimeng Sun, Philip S. Yu, and Christos Faloutsos. Colibri: Fast Mining of Large Static and Dynamic Graphs, KDD 2008, Las Vegas, NV.
27. Charalampos Tsourakakis: Fast Counting of Triangles in Large Real Networks, without counting: Algorithms and Laws, ICDM ‘08
28. Yang Wang, Deepayan Chakrabarti, Chenxi Wang and Christos Faloutsos. Epidemic Spreading in Real Networks: an Eigenvalue Viewpoint, SRDS 2003, Florence, Italy.