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Core Concepts in Data Analysis: Summarization, Correlation and Visualizationprovides in-depth descriptions of those data analysis approaches that either summarize data (principal component analysis and clustering, including hierarchical and network clustering) or correlate different aspects of data (decision trees, linear rules, neuron networks, and Bayes rule).
Boris Mirkin takes an unconventional approach and introduces the concept of multivariate data summarization as a counterpart to conventional machine learning prediction schemes, utilizing techniques from statistics, data analysis, data mining, machine learning, computational intelligence, and information retrieval.
Innovations following from his in-depth analysis of the models underlying summarization techniques are introduced, and applied to challenging issues such as the number of clusters, mixed scale data standardization, interpretation of the solutions, as well as relations between seemingly unrelated concepts: goodness-of-fit functions for classification trees and data standardization, spectral clustering and additive clustering, correlation and visualization of contingency data.
The mathematical detail is encapsulated in the so-called “formulation” parts, whereas most material is delivered through “presentation” parts that explain the methods by applying them to small real-world data sets; concise “computation” parts inform of the algorithmic and coding issues.
Four layers of active learning and self-study exercises are provided: worked examples, case studies, projects and questions.
Content Level »Upper undergraduate
Keywords »Clustering - Data Analysis - K-means - Principal component analysis - Visualization
Introduction.-Summarization and Correlation-Two Main Goals of Data Analysis.-Case Study Problems.-An Account of Data Visualization.-Summary.-1D Analysis: Summarization and Visualisation of a Single Feature.-Quantitative Feature: Distribution and Histogram.-Further Summarization:Centers and Spreads.-Binary and Categorical Features.-Modeling Uncertainty: Intervals and Fuzzy Sets.-Summary.-2D Analysis: Correlation and Visualition of Two Features.-General.-Two Quantitative Features Case.-Linear Regression: Formulation.-Linear Regression: Computation.-Mixed Scale Case: Nominal Feature Versus a Quantitative One.-Two Nominal Features Case.-Summary.-Learning Multivariate Correlations in Data.-General: Decision Rules, Fitting Criteria and Learning Protocols.-Naive Bayes Approach.-Linear Regression.-Linear Discrimination and SVM.-Decision Trees.-Learning Correlation with Neuron Networks.-Summary.-Principal Component Analysis and SVD.-Decoder Based Data Summarization.-Principal Component Analysis: Model, Method, Usage.-Application: Latent Semantic Analysis.-Application: Correspondence Analysis.-Summary.-K-Means and Related Clustering Methods.-General.-K-Means Clustering.-Cluster Interpretation Aids.-Extensions of K-Means to Different Cluster Structures.-Summary.-Hierarchial Clustering.-General.-Agglomerative Clustering and Ward's Criterion.-Divisive and Conceptual Clustering.-Single Linkage Clustering, Connected Components and Maximum Spanning Tree.-Summary.-Approximate and Spectral Clustering for Network and Affinity Data.-One Cluster Summary Similarity with Background Subtracted.-Two Cluster Case: Cut, Normalized Cut and Spectral Clustering.-Additive Clusters.-Summary.-Appendix