1. A Framework for Clustering Evolving Data Streams Charu C. Aggarwal, Jiawei Han, Jianyong Wang, Philip S. Yu Presented by: Di Yang Charudatta Wad

2. Outline Background of Clustering Motivation for Clustering over Streaming Data. Overall Solution Micro Clusters Pyramid Time Frame Macro Cluster Cluster Maintenance

3. Background of Clustering Definition of Clustering  For a given set of data points, partitioning them into one or more groups of similar objects.  “Similarity” is often defined with the use of some distance measure. Difference between “group by” queries and clustering.

4. Background of Clustering Some of the most popular clustering algorithms:  K- Means, BIRCH, CURE, Density Based Clustering. Clustering has many applications in data bases, information visualization, data mining. What are Oultiers?

5. Motivation Challenge in Streaming Environment:  Clustering is an expensive process.  Resource constraints.  Infinite streams. Can simply extending one pass algorithms for static databases to stream processing suffice?

6. Motivation Requirements of clustering for stream processing:  Statistical summary information storage.  Efficient update process.  Ability to cluster for a specific time horizon,

7. Overall Solution of the Paper Divide the clustering process to two phases Online Component: periodically stores detailed summary statistics Offline Component uses only the summary statistics to do clustering

8. Micro-Clusters What is a Micro-Cluster A Micro-Cluster is a set of individual data points that are close to each other and will be treated as a single unit in further offline Macro-clustering. View of Micro-ClusterView of Macro-Cluster

9. Micro-Clusters What to Store in a Micro-Cluster = Key idea: Additivity Property

10. Pyramidal Time Frame The snapshots follow a pyramidal pattern … … When should we make the snapshot? The micro-clusters are stored at snapshots. Snapshot

11. Pyramidal Time Frame Snapshots are classified into different orders which can vary from 1 to log α(T). For example, T is 55, α=2, then we have orders 0 with interval 2^0=1, order 1 with interval 2^1=2, order 2 with interval 2^2=4, order 3 with interval 2^3=8, order 4 with interval 2^4=16, order 5 with interval 2^5=32. For a data stream the maximum number of snap- shots maintained at T time units since the beginning of the stream mining process is (α + 1) log α(T). (α + 1 for each order)

12. Why Pyramidal Pattern? For any user-specified time window of h, at least one stored snapshot can be found within 2 h units of the current time. Please Note: Only Approximate Answers!!!

13. Micro Cluster Creation It is assumed that a total of q micro- clusters are maintained at any moment by the algorithm. This is done using an offline process (k- means) at the very beginning of the data stream computation process.

14. Online Micro Cluster Maintenance How to deal with a new coming point? 1. Join one of the old cluster 2. Create a new cluster by its own How to deal with the old clusters 1. Delete them (based on relevance stamp) 2. Merge them (merge the closest two) A merged cluster will have all the IDs its components have

15. Macro-Cluster Creation Based on the Additivity Property of cluster feature vector

16. Macro-Cluster Creation Current Time T, the window size is h. That means the user want to find the clusters formed in (T-h, T). Approach: 1. 1st step: Find the snapshot for T, get the micro-cluster set S(T). 2. 2nd step: Find the snapshot for T-h, get the micro-cluster set S(T-h). 3. Use S(T)-S(T-h) Specifically, we have a merged cluster with Id list (C1, C2, C3) in S(T) and a cluster with Id C1 in S(T-h). Then the we use CFT(C1,C2,C3)-CFT(C1)=CFT(C2,C3), because C1 are formed before T-h, thus should not contribute to the micro-cluster formed in (T-h,T)

17. Example C_ID: [C1] Time: T-h C_ID: [C1, C2, C3] Time: T C_ID: [C2, C3] Result: T-h

18. Macro-Cluster Creation Run K-means on Micro-Clusters

19. How do you feel about this paper? My feeling: Quite Fuzzy Results: Approximation is every where. Nothing New: Micro-Clusters, K-means, Cluster Feature Vectors, Pyramidal Time Frame are all old stuffs.

20. Counter Example C_ID: [C2] C_ID: [C1, C2, C3] Time: T C_ID: [C1, C3] Time: T-h Result

21. Advertisement Di and Charu’s project deals with: 1. Deterministic Clusters 2. Clusters with Arbitrary Shapes 3. Real Expirations 4. Disk Version 5. Outlier Detection by Free