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Charu C. Aggarwal (I2 Contributions)

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Charu C. Aggarwal (I2 Contributions)

Scalable Graph Querying and Indexing

Task I2.2

Charu C. Aggarwal

IBM

Collaborators (across all tasks): Jiawei Han (UIUC), Guojun Qi (UIUC), Thomas Huang (UIUC), Tarek Abdelzaher (UIUC), Xifeng Yan (UCSB), Arjit Khan (UCSB), Nan Li (UCSB), Amotz Bar-Noy (CUNY), Simon Shamoun (CUNY)

Other Tasks: I1.2 (funded), I3 (collaborator)

Overview of Contributions

- Project I1 Contributions:
- Methods for Sensor Selection in Dynamic Information Networks (Collaboration with A. Bar-Noy (CUNY) and S. Shamoun (CUNY))=>Submitted to DCOSS 2011
- Data fusion of heterogeneous data with the use of network links: specific application to text and visual data
- QoI robust inference with the use of heterogeneous data fusion
- Joint work with G. Qi (UIUC) and T. Huang (UIUC)
- Papers accepted in CVPR, WWW 2011; one submitted to KDD 2011

- Collaboration with Tarek Abdelzaher (UIUC) on data selection for regression and fact-finders for fusion=> Submitted to DCOSS 2011, Fusion 2011

- Project I2 Contributions: Large Scale Indexing (Focus of this talk):
- Methods for Indexing Massive Disk-Resident Graphs (Aggarwal (IBM), Zhao (UIUC), and Han (UIUC))=> Submit to PVLDB 2012
- Methods for Indexing Dynamic Network Streams (Aggarwal (IBM), Khan (UCSB), Yan (UCSB))=> Submit to PVLDB 2012
- Methods for label-based query index (Joint work with Li (UCSB))=>SDM 2011

Overview of Contributions

- Project I3 Contributions:
- Unfunded Collaborator for project I3=> Actively collaborated with Jiawei Han on mining of networks with heterogeneous links and incomplete attributes (Task I3.1)
- Designed methods for clustering heterogeneous information networks with heterogeneous links and incomplete attributes (joint work with Yizhou Sun (UIUC) and Jiawei Han (UIUC)) => Submitted to KDD 2011
- Designed methods for link inference in the noise and heterogeneous information network scenario (joint work with Barbier (UIUC), Gupta (UIUC), Sun (UIUC) and Han (UIUC))=> Submitted to ASONAM 2011

Scalable Indexing and Querying Massive Graphs (I2.2)

- Indexing Methods for Large Scale Static and Dynamic Networks
- Methods for Indexing Massive Disk-Resident Graphs (Aggarwal (IBM), Zhao (UIUC), and Han (UIUC))
- Application to Shortest Path Queries
- Can be extended to connectivity and other structural queries

- Methods for Indexing Dynamic Network Streams (Aggarwal (IBM), Khan (UCSB), Yan (UCSB))
- Applications such as social and information networks show continuous edge-base activity
- Results in edge streams
- Methods for frequency-based and structural indexing of graph streams

- Methods for Indexing Massive Disk-Resident Graphs (Aggarwal (IBM), Zhao (UIUC), and Han (UIUC))

Label-based Querying of Massive Dynamic Graphs

- Many networks have labels associated with some of the nodes which may need to be learned or queried
- Eg. Which node belongs to a specific topic?

- Challenges:
- Network may be dynamic with edges and nodes which continuously evolve over time
- The nodes in the network may contain content, which needs to be used in the classification process
- The classification-queries need to be resolved in real-time.

- Designed methods for constructing dynamic structural index, which can be continuously updated and used for label-based queries (Aggarwal (IBM) and Li (UCSB)): Accepted to SIAM Conference on Data Mining, 2011.

Indexing Graphs: The compression approach

- Core idea is to coarsen the graph into a smaller number of nodes
- Method for coarsening depends upon application:
- In static (disk-resident) methods, we use dense pattern mining methods in order to coarsen graph into a smaller number of nodes
- In dynamic (stream-based) methods, we use a hash-based probabilistic sketch in order to coarsen graph into a smaller number of nodes.

- Use probabilistic query-processing on the coarsened graph in order to provide approximate responses to queries

Static Indexing of Disk-Resident Graphs

- Design methods for indexing massive disk-resident networks
- Typical social and information networks may be massive and may need to be stored on disk
- For example, for a network containing 10^7 nodes, we may have of the order of 10^(13) edges
- Network cannot be held in main memory, and in some cases not even on disk
- First present methods where network cannot be held in main memory, but is stored on disk
- Design methods for shortest path indexing methods: For a given pair of nodes s and t, determine shortest distance between them
- Very fast for memory resident graphs=> Very slow for disk-resident case

Static Indexing of Disk-Resident Graphs

- Core Approach for static indexing: Determine dense sets of nodes in the network using a pattern mining approach
- Compress sets of nodes into supernodes
- Node compression will result in self-loops: Eliminate self-loops

- Perform query-processing on compressed graph
- Note that passing through super-node is equivalent to passing through a set of edges: associate node-penalty with super-node
- Observation: Vast majority of edges lie in dense regions which are compressed into self-loops
- Massive reduction in size of network: allows main-memory storage for query-processing

Setting Node Penalties (Observations)

- When we run the query-processing technique on the coarsened graph as a surrogate, passing through a super-node is modeled as entering through a random node in the compressed subgraph and exiting another random node
- Use probabilistic node penalty associated with such nodes corresponding to pairwise shortest-path distances in the compressed portion
- Modified Query Processing: Determine shortest-path distance between s’ and t’ in compressed graph with node-penalties
- Note that node-penalties are random variables and the shortest-path distance could be average or worst-case.
- Important: Dense region compression leads to histogram with small number of buckets (most distances are 1 or 2 within region).

Setting Node Penalties

Query Processing

- Start at node s’ and progressively maintain the random variables corresponding to the shortest average (or worst-case) distances to the nodes.
- Maintain probabilistic label with each node containing the probabilistic histogram with shortest-path distance
- Grow set S of nodes with probabilistic shortest path distances
- In each iteration, we grow set S by one node after updating the node labels of its nearest neighbors (requires probabilistic addition of distances of shortest path to edge weight and node penalty).
- Terminate on reaching sink node t’
- Provides either approximation using compressed graph or access compressed fragments from disk to get exact distances

Adding shortest path distances to node penalty

Other details of approach

- Other algorithmic components of approach
- A dense pattern mining algorithm which is designed in order to determine the dense regions of the network for compression purposes
- Design a sampling-based approach which uses a limited number of passes over the disk-resident data set

- A method for reconstructing the shortest path from the compressed shortest path distance
- Retrieve fragments from disk-resident data set
- Use shortest path distance within each fragment to reconstruct the distance

- A dense pattern mining algorithm which is designed in order to determine the dense regions of the network for compression purposes

Experimental Results (DBLP Data Set)

Dynamic Indexing of Massive Graph Streams (Joint work with A. Khan (UCSB) and X. Yan (UCSB))

- The previous methods were designed for static indexing of massive graphs
- In many applications, we need indexes for the case in which the graphs may continuously be updated over time (edge activity)
- Edge-based activity in networks result in a stream of edges
- Activity in a social network can be modeled as an edge-stream

- Assumption is much more rigorous in previous case
- Not enough space to hold even the edges on disk and their arrival times
- Not enough space to hold even the total number of possible distinct edges on disk
- Hard to perform structural analysis when the network is so dynamic and cannot even be stored at a given point in time

Dynamic Indexing of Massive Graph Streams

- Use a 3-dimensional hash-based sketch structure in order to create the dynamic index
- Borrows the concept of a sketch structure from data stream analysis and generalizes it to the case of structural data
- Queries which can be handled:
- Determine the frequency of a given edge in the graph
- Determine the aggregate frequency of edges in a subgraph
- Determine the minimum frequency of edges in a subgraph
- Determine all edges with frequency above a given threshold
- Determine the connected components with frequency above a given threshold

The sketch based approach: Core Idea

- Model: Assume that edges are received continuously over time
- Use a 3-dimensional matrix of size h X h X w
- The parameter h indicates the range of the hashing
- The parameter w indicates the number of hash functions
- For an edge (i, j) the node i is hashed into the first dimension using k-th hash function g^k() with range [0, h-1]
- The node j is hashed into the second dimension using k-th hash function g^k() in the range [0, h-1]
- There are w slices of size h X h corresponding to different hash functions g^k() where k lies in the range [1, w]
- Multiple hash functions provide robustness

- The entire frequency behavior of edges is mapped into the structure of size h X h X w

The sketch based approach: Core Idea

- Model: Assume that edges are received continuously over time
- Use a 3-dimensional matrix of size h X h X w
- The parameter h indicates the range of the hashing
- The parameter w indicates the number of hash functions
- For an edge (i, j) the node i is hashed into the first dimension using k-th hash function g^k() with range [0, h-1]
- The node j is hashed into the second dimension using k-th hash function g^k() in the range [0, h-1]
- There are w slices of size h X h corresponding to different hash functions g^k() where k lies in the range [1, w]
- Multiple hash functions provide robustness

- The entire frequency behavior of edges is mapped into the structure of size h X h X w

The sketch based approach: Stream Incremental Update

- The update process is straightforward and requires an incremental step involving the application of w different hash functions for each incoming edge (i, j)
- Start off by setting each cell in the h X h x w synopsis matrix V to 0
- Assume incoming edge (i, j) and frequency r(i, j)
- For each incoming edge (i, j) and k-th hash function g^k(), update the cell V(g^k(i), g^k(j), k) by r(i, j)
- The update process is applied for each of the w different hash functions

Subgraph Frequency-based Queries

- Query: Determine frequency of edges in subgraph with node set S
- For each edge (i, j) in subgraph S, determine the value of V(g^k(i), g^k(j), k) for different hash functions k
- Determine the minimum value of V(g^k(i), g^k(j), k) over the different hash functions k
- Sum up value over different edges
- Key Result: Derived mathematical error bound => With probability at least 1 – (|S|*|S|/(h*h*f))^w the error is at most L.f, where L is the total frequency of edges received=> Details of proof available in paper.

Inverse Frequency-based Queries

- Query: Determine all edges with frequency above a given threshold
- Key Augmentation to Data Structure: Each hash cell contains an inverted list of all the nodes which map to it
- For a given frequency threshold determine all hash cells (for each hash function) above the threshold
- Determine the intersection of all the inverted lists pointed to by determined hash cells=> using multiple hash functions to reduce collision error.
- Report only edges which are present in the intersection of the hash functions => error reduces logarithmically with number of hash functions

Connected-subgraph Queries

- Query: Determine all connected subgraphs containing only edges with frequency above a given threshold
- Determine edges using the approach discussed in previous query
- Determine connected components with the use of the found edges
- Numerous other structural queries can be handled with the use of the compressed graph.
- Error bounds hold for a subset of queries

Experimental Results (last.fm Data Set)

Label-based querying of Massive Graphs (Joint work With N. Li (UCSB))

- We assume that we have a massive graph with nodes interconnected by edges, and nodes which contain content.
- The nodes and edges of the graph are continuously received over time.
- Need to respond to label-based queries dynamically using both the structure and content
- Need to use the content in the classification process
- Core Idea:
- Construct semi-bipartite augmentation of the network which uses the content in the form of synthetic word nodes
- Create a fast inverted index which can respond to label-based queries.

Augmented Bipartite Network

Key Results

- Method is designed for dynamic classification queries (no static pre-processing) A dynamic classification index
- Maintain the semi-bipartite augmentation dynamically
- Maintain inverted representation with the word nodes=>Incorporation of content with structure
- Perform random walk starting at query node and report majority label as the appropriate class
- Theoretical Result: Sampling a certain number of walks reduces the error estimation exponentially=> Proof available in paper => Use of Hoeffding bound
- Paper accepted in SDM, 2011.

Experimental Results

Military Relevance

- Military information networks are extremely large and require dynamic and time-varying methods for querying and indexing
- Require real-time responses to structural queries for data which is large and may be added to rapidly => network stream scenario
- Methods are also applicable to resource-constrained environments even for very large data sets
- Classification query provides methods to identify nodes of relevance in a given information network query => which is the node most relevant to a given topic? => Where is the information I want?

The Path Ahead: Future Work

- Extend the kinds of queries which can be handled by different kinds of methods:
- Structural connectivity queries
- Shortest paths in dynamic graph streams
- Extend first method to dynamic case

- Extend methods to uncertain graphs
- Challenge of uncertainty: Expected path length methods do not work!
- Even a small probability of disconnection of source and sink leads to expected path length of infinity
- Design probabilistic model which uses the shortest path with threshold probability

- Challenge of uncertainty: Expected path length methods do not work!

Publications (Accepted)

- C. C. Aggarwal (IBM), N. Li (UCSB). On Dynamic Node-Classification in Content-based Networks, Accepted to the SDM Conference, 2011.
- G. Qi (UIUC), C. C. Aggarwal (IBM), T. Huang. (UIUC) Towards Semantic Knowledge Propagation between Text and Web Images, Accepted to the WWW Conference, 2011.
- G. Qi (UIUC), C. C. Aggarwal (IBM), T. Huang (UIUC). Towards Cross-Category Learning of Visual Concepts. Accepted to the CVPR Conference, 2011.
- C. C. Aggarwal (IBM), A. Khan (UCSB), X. Yan (UCSB). On Flow Authority Discovery in Social Networks, Accepted to the SDM Conference, 2011.
- C. C. Aggarwal, Y. Xie, P. Yu. On Community Discovery in Locally Heterogeneous Networks, Accepted to the SDM Conference, 2011.
- C. C Aggarwal, Y. Zhao, P. Yu. On Wavelet Decomposition of Uncertain Streams, CIKM Conference, 2010.
- M. Masud, L. Khan, B. Thuraisingham, C. Aggarwal (IBM), J Gao (UIUC), J. Han (UIUC), On Novel Class Detection in Concept Drifting Data Streams, ICDM Conference, 2010

Publications (Submitted)

- G. Qi (UIUC), C. C. Aggarwal (IBM), T. Huang (UIUC). Community Detection with Edge Content, Submitted to the SIGIR Conference, 2011.
- Y. Sun (UIUC), C. C. Aggarwal (IBM), J. Han (UIUC), On Community Discovery in Heterogeneous Networks with Incomplete Attributes, Submitted to the KDD Conference, 2011.
- G. Qi (UIUC), C, C, Aggarwal (IBM), T. Huang (UIUC), Transfer Learning with Distance Functions between Text and Images, Submitted to the KDD Conference, 2011.
- C. C. Aggarwal (IBM), A. Bar-Noy (CUNY), S. Shamoun (CUNY). On Sensor Selection in Linked Information Networks, Submitted to the DCOSS Conference, 2011.

Publications (Submitted)

- Y. Sun (UIUC), C. C. Aggarwal (IBM), J. Han (UIUC), On Link Inference in Bibliographic Networks, Submitted to the ASONAM Conference, 2011.
- M. Gupta (UIUC), C, C, Aggarwal (IBM), J. Han (UIUC), On Evolutionary Clustering and Analysis of Heterogeneous Information Networks, Submitted to the ASONAM Conference, 2011.
- C. C. Aggarwal (IBM), A. Bar-Noy (CUNY), S. Shamoun (CUNY). On Sensor Selection in Linked Information Networks, Submitted to the DCOSS Conference, 2011.
- C. C. Aggarwal (IBM), P. Zhao (UIUC), J. Han (UIUC). On Shortest Path Indexing with Disk-Resident Graphs, Submitted to the PVLDB Conference, 2012.
- C. C. Aggarwal (IBM), A. Khan (UCSB), X. Yan (UCSB). On Query Processing of Massive Graph Streams, Submitted to the PVLDB Conference, 2012.

Publications (Submitted)

- T. Abdelzaher (UIUC), D. Wang (UIUC), H. Ahmadi (UIUC), J. Pasternack (UIUC), M. Gupta (UIUC), J. Han (UIUC), O. Fetemieh (UIUC), H. Le (UIUC) C. C. Aggarwal (IBM), On Bayesian Information of Fact-Finding in Information networks, Submitted to the Fusion Conference, 2011.
- D. Wang (UIUC), H. Ahmadi (UIUC), T. Abdelzaher (UIUC), H. Chenji. R. Stoleru, C, C, Aggarwal (IBM). Data Models for Optimizing Quality-of-Information in Cost-Sensitive Data Fusion, Submitted to the DCOSS Conference, 2011.