A Framework for Clustering Evolving Data Streams

Charu C. Aggarwal, Jiawei Han, Jianyong Wang, Philip S. Yu

Presented by: Di Yang

Charudatta Wad

Outline

Background of ClusteringMotivation for Clustering over Streaming

Data.Overall SolutionMicro ClustersPyramid Time FrameMacro ClusterCluster Maintenance

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.

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?

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?

Motivation

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

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

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-Cluster View of Macro-Cluster

Micro-Clusters

What to Store in a Micro-Cluster

=

Key idea: Additivity Property

Pyramidal Time Frame

The snapshots follow a pyramidal pattern

… …

When should we make the snapshot?

The micro-clusters are stored at snapshots.

Snapshot

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)

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!!!

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.

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

Macro-Cluster Creation

Based on the Additivity Property of cluster feature vector

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)

Example

C_ID: [C1]

Time: T-h

C_ID: [C1, C2, C3]

Time: T

C_ID: [C2, C3]

Result: T-h

Macro-Cluster Creation

Run K-means on Micro-Clusters

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.

Counter Example

C_ID: [C2] C_ID: [C1, C2, C3]

Time: T

C_ID: [C1, C3]

Time: T-hResult

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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