Software Clustering Based on Information Loss Minimization

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Software Clustering Based on Information Loss
Minimization

• Periklis Andritsos
• University of Toronto
• Vassilios Tzerpos
• York University

The 10th Working Conference on Reverse
Engineering 
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The Software Clustering Problem

• Input
• A set of software artifacts (files, classes)
• Structural information, i.e. interdependencies
  between the artifacts (invocations, inheritance)
• Non-structural information (timestamps,
  ownership)
• Goal Partition the artifacts into meaningful
  groups in order to help understand the software
  system at hand

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Example
Program files
Utility files
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Open questions

• Validity of clusters discovered based on
  high-cohesion and low-coupling
• No guarantee that legacy software was developed
  in such a way
• Discovering utility subsystems
• Utility subsystems are low-cohesion /
  high-coupling
• They commonly occur in manual decompositions
• Utilizing non-structural information
• What types of information has value?
• LOC, timestamps, ownership, directory structure

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Our goals

• Create decompositions that convey as much
  information as possible about the artifacts they
  contain
• Discover utility subsystems as well as subsystems
  based on high-cohesion and low-coupling
• Evaluate the usefulness of any combination of
  structural and non-structural information

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Information Theory Basics

• Entropy H(A)
• Measures the Uncertainty in a random variable A
• Conditional Entropy H(BA)
• Measures the Uncertainty of a variable B,given a
  value for variable A.
• Mutual Information I(AB)
• Measures the Dependence of two random variables A
  and B.

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Information Bottleneck (IB) Method

• A random variable that ranges over the
  artifacts to be clustered
• B a random variable that ranges over the
  artifacts features
• I(AB) mutual information of A and B
• Information Bottleneck Method TPB99
• Compress A into a clustering Ck so that the
  information preserved about B is maximum
  (knumber of clusters).
• Optimization criterion
• minimize I(AB) - I(CkB) ? minimize H(BCk)
  H(BA)

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Information Bottleneck Method
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Agglomerative IB

• Conceptualize graph as an nxm matrix (artifacts
  by features)

• Compute an nxn matrix indicating the
  information loss we would incur if we joined any
  two artifacts into a cluster

• Merge tuples with the minimum information loss

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Adding Non-Structural Data

• If we have information about the Developer and
  Location of files we express the artifacts to be
  clustered using a new matrix
• Instead of B we use B to include non-structural
  data
• We can compute I(AB) and proceed as before

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ScaLable InforMation BOttleneck

• AIB has quadratic complexity since we need to
  compute an (nxn) distance matrix.
• LIMBO algorithm
• Produce summaries of the artifacts
• Apply agglomerative clustering on the summaries

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Experimental Evaluation

• Data Sets
• TOBEY 939 files / 250,000 LOC
• LINUX 955 files / 750,000 LOC
• Clustering Algorithms
• ACDC Pattern-based
• BUNCH Adheres to High-Cohesion and Low-Coupling
• NAHC, SAHC
• Cluster Analysis Algorithms
• Single linkage (SL)
• Complete linkage (CL)
• Weighted average linkage (WA)
• Unweighted average linkage (UA)

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Experimental Evaluation

• Compared output of different algorithms using
  MoJo
• MoJo measures the number of Move/Join operations
  needed to transform one clustering to another.
• The smaller the MoJo value of a particular
  clustering, the more effective the algorithm that
  produced it.
• We compute MoJo with respect to an authoritative
  decomposition

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Structural Feature Results
Limbo found Utility Clusters
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Non-Structural Feature Results

• We considered all possible combinations of
  structural and non-structural features.
• Non-Structural Features available only for Linux
• Developers (dev)
• Directory (dir)
• Lines of Code (loc)
• Time of Last Update (time)
• For each combination we report the number of
  clusters k when the MoJo value between k and k1
  differs by one.

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Non-Structural Feature Results

• 8 combinations outperform structural results.
• Dir information produced better decompositions.
• Dev information has a positive effect.
• Time leads to worse clusterings.