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Fractal Analysis of Datasets Using Distributed Computing

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Fractal Analysis of Datasets Using Distributed Computing
論文目錄
 
Acknowledgements第1-5頁
abstract第5-9頁
Chapter 1. Introduction第9-15頁
  1.1 Introduction to the topic and its relevance第9-10頁
  1.2 Goals, objectives and structure of the thesis第10-11頁
  1.3 Basic concepts of clustering第11-15頁
Chapter 2. Reduction of dimension using the fractal dimension第15-60頁
  2.1 Application of fractal theory to data sets第15-31頁
    2.1.1 General information about fractals第15-20頁
    2.1.2 Hausdorff distance第20-21頁
    2.1.3 Mathematical foundations of fractal compression第21-23頁
    2.1.4 Methods of Fractal Data Mining第23-25頁
    2.1.5 Understanding a table as a fractal第25-29頁
    2.1.6 The reduction of the dimensionality第29-31頁
  2.2 The design of the algorithm第31-60頁
    2.2.1 General view of the searching domains algorithm第31-34頁
    2.2.2 Creating a list of possible domain structures第34-35頁
    2.2.3 Calculating the number of different domain values for each set第35-36頁
    2.2.4 Creating a list of all possible domain structures第36-40頁
      2.2.4.1 Searching optimal set of domains and analysis of results第36-38頁
      2.2.4.2 The algorithm of brute force of searching domains第38-40頁
    2.2.5 The algorithm searching the optimal number of domains, number of distinct values of a domain and the analysis of the results第40-45頁
    2.2.6 Improved algorithm using Map Reduce第45-60頁
      2.2.6.1 Why we use Hadoop MapReduce第45-48頁
      2.2.6.2 The problem of counting unique values in big datasets第48-51頁
      2.2.6.3 Designing the algorithm of calculation using MapReduce第51-60頁
Chapter 3. Clustering of the obtained domains第60-91頁
  3.1 Clustering of the obtained domains第60-61頁
  3.2 Review of clustering algorithms第61-67頁
  3.3 Grid-based clustering Halite第67-74頁
  3.4 Improvement of the algorithm Halite第74-91頁
    3.4.1 Improved MDL model in determining the relevance of the axes of the clusters第74-81頁
    3.4.2 The application of Laplacian filter and the behavior at the boundaries and corners of the space第81-91頁
Chapter 4. Experiments and conclusion第91-104頁
  4.1 Review of test cases第91-96頁
  4.2 The results of the experiments第96-102頁
  4.3 Conclusion第102-104頁
References第104-105頁

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