# An Optimization Approach to Locally-Biased Graph Algorithms

@article{Fountoulakis2017AnOA, title={An Optimization Approach to Locally-Biased Graph Algorithms}, author={Kimon Fountoulakis and David F. Gleich and Michael W. Mahoney}, journal={Proc. IEEE}, year={2017}, volume={105}, pages={256-272} }

Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph algorithm; but more interesting are locally-biased graph algorithms that compute answers by running a procedure that does not even look at most of the input graph. This corresponds more closely to what practitioners from various data science domains do, but it…

## Figures and Tables from this paper

## 15 Citations

### A Short Introduction to Local Graph Clustering Methods and Software

- Computer ScienceArXiv
- 2018

A brief introduction to local graph clustering is provided, some representative examples of the perspective are provided, and the software named Local Graph Clustering (LGC) is introduced.

### p-Norm Flow Diffusion for Local Graph Clustering

- Computer ScienceICML
- 2020

This work proposes a family of convex optimization formulations based on the idea of diffusion with p-norm network flow for local clustering and demonstrates the optimal solutions for these optimization problems and their usefulness in finding low conductance cuts around input seed set.

### Statistical guarantees for local graph clustering

- Computer Science, MathematicsAISTATS
- 2020

It is shown that l1-regularized PageRank and approximate personalized PageRank (APPR), another very popular method for local graph clustering, are equivalent in the sense that one can lower and upper bound the output of one with theoutput of the other.

### Learning Resolution Parameters for Graph Clustering

- Computer ScienceWWW
- 2019

This work views its framework as a type of single-shot hyperparameter tuning, as it is able to learn a good resolution parameter with just a single example, and can be applied to learn resolution parameters for both local and global graph clustering objectives.

### Local Hypergraph Clustering using Capacity Releasing Diffusion

- Computer SciencePloS one
- 2020

A local hypergraph clustering technique called hypergraph CRD is proposed by extending the CRD process to cluster based on higher order patterns, encoded as hyperedges of a hypergraph, and theoretically shows that HG-CRD gives results about a quantity called motif conductance, rather than a biased version used in previous experiments.

### Sublinear Algorithms for Local Graph Centrality Estimation

- Computer Science, Mathematics2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
- 2018

These are the first algorithms yielding worst-case sublinear bounds for general directed graphs and any choice of the target node.

### Learning by Unsupervised Nonlinear Diffusion

- Computer ScienceJ. Mach. Learn. Res.
- 2019

A novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation is proposed and analyzed, demonstrating the theoretical and empirical advantages over both spectral clustering and density-based clustering techniques.

### Compressive Sensing for Cut Improvement and Local Clustering

- Computer ScienceSIAM J. Math. Data Sci.
- 2020

This work shows how one can phrase the cut improvement problem for graphs as a sparse recovery problem, whence one can use algorithms originally developed for use in compressive sensing (such as SubspacePursuit or CoSaMP) to solve it and proposes new methods for local clustering and semi-supervised clustering.

### GraphRAD : A Graph-based Risky Account Detection System

- Computer Science
- 2018

GraphRAD, a risky account detection system based on local graph clustering algorithms, is proposed, hypothesize that fraud accounts share dense connections within a "fraud community", but have less so with accounts outside of the community.

### Targeted pandemic containment through identifying local contact network bottlenecks

- Computer SciencePLoS Comput. Biol.
- 2021

This paper proposes a new flow-based edge-betweenness centrality method for detecting bottleneck edges that connect communities in contact networks and demonstrates empirically that the proposed method is orders of magnitude faster than existing methods.

## References

SHOWING 1-10 OF 81 REFERENCES

### Exploiting Optimization for Local Graph Clustering

- Computer Science
- 2016

This work clarifies the relationship between the local spectral algorithm of (Andersen, Chung and Lang, FOCS '06) and a variant of a well-studied optimization objective and develops a local spectral graph clustering algorithm that has improved theoretical convergence properties.

### A Local Algorithm for Finding Well-Connected Clusters

- Computer ScienceICML
- 2013

This work develops a method with better theoretical guarantee compared to all previous work, both in terms of the clustering accuracy and the conductance of the output set, and outperforms prior work when the cluster is well-connected.

### Flow-Based Algorithms for Local Graph Clustering

- Computer Science, MathematicsSODA
- 2014

This work shows how to use LocalImprove to obtain a constant approximation O(OPT) as long as CONN/OPT = Omega(1), the first flow-based algorithm and shows that spectral methods are not the only viable approach to the construction of local graph partitioning algorithm and open door to the study of algorithms with even better approximation and locality guarantees.

### A local spectral method for graphs: with applications to improving graph partitions and exploring data graphs locally

- Computer ScienceJ. Mach. Learn. Res.
- 2012

This paper introduces a locally-biased analogue of the second eigenvector of the Laplacian matrix, and demonstrates its usefulness at highlighting local properties of data graphs in a semi-supervised manner and shows how it can applied to finding locally- biased sparse cuts around an input vertex seed set in social and information networks.

### A Local Clustering Algorithm for Massive Graphs and Its Application to Nearly Linear Time Graph Partitioning

- Computer ScienceSIAM J. Comput.
- 2013

This work presents a local clustering algorithm, a useful primitive for handling massive graphs, such as social networks and web-graphs, that finds a good cluster---a subset of vertices whose internal connections are significantly richer than its external connections---near a given vertex.

### Using Local Spectral Methods to Robustify Graph-Based Learning Algorithms

- Computer ScienceKDD
- 2015

This work studies robustness with respect to the details of graph constructions, errors in node labeling, degree variability, and a variety of other real-world heterogeneities, studying these methods through a precise relationship with mincut problems.

### Empirical comparison of algorithms for network community detection

- Computer ScienceWWW '10
- 2010

Considering community quality as a function of its size provides a much finer lens with which to examine community detection algorithms, since objective functions and approximation algorithms often have non-obvious size-dependent behavior.

### Finding sparse cuts locally using evolving sets

- Computer ScienceSTOC '09
- 2009

A randomized local partitioning algorithm is introduced that finds a sparse cut by simulating the volume-biased evolving set process, which is a Markov chain on sets of vertices and the expected value of the work/volume ratio is polylognoparen(φ-1/2).

### Anti-differentiating approximation algorithms: A case study with min-cuts, spectral, and flow

- Computer ScienceICML
- 2014

A case study of approximation algorithms for finding locally-biased partitions in data graphs, demonstrating connections between min-cut objectives, a personalized version of the popular PageRank vector, and the highly effective "push" procedure for computing an approximation to personalized PageRank.

### The Web as a Graph: Measurements, Models, and Methods

- Computer ScienceCOCOON
- 1999

This paper describes two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery, and proposes a new family of random graph models that point to a rich new sub-field of the study of random graphs, and raises questions about the analysis of graph algorithms on the Internet.