DATA MINING from data to information Ronald Westra Dep. Mathematics Knowledge Engineering Maastricht University

PART 1 Introduction

All information on math-part of course on: DAM/DataMiningPage.htm

Data mining - a definition "Data mining is the process of exploration and analysis, by automatic or semi-automatic means, of large quantities of data in order to discover meaningful patterns and results." (Berry & Linoff, 1997, 2000)

DATA MINING Course Description: In this course the student will be made familiar with the main topics in Data Mining, and its important role in current Computer Science. In this course we’ll mainly focus on algorithms, methods, and techniques for the representation and analysis of data and information.

DATA MINING Course Objectives: To get a broad understanding of data mining and knowledge discovery in databases. To understand major research issues and techniques in this new area and conduct research. To be able to apply data mining tools to practical problems.

LECTURE 1: Introduction 1.Fayyad, U., Piatetsky-Shapiro, G., and Smyth, P. (1996), Data Mining to Knowledge Discovery in Databases: Fayyad.pdf Fayyad.pdf 2.Hand, D., Manilla, H., Smyth, P. (2001), Principles of Data Mining, MIT press, Boston, USA MORE INFORMATION ON: ELEUM and: MiningPage.htm

Hand, D., Manilla, H., Smyth, P. (2001), Principles of Data Mining, MIT press, Boston, USA + MORE INFORMATION ON: ELEUM or DAM-website

LECTURE 1: Introduction What is Data Mining? data information knowledge patterns structures models The use of Data Mining increasingly larger databases TB (TeraBytes) N datapoints and K components (fields) per datapoint not accessible for fast inspection incomplete, noise, wrong design different numerical formats, alfanumerical, semantic fields necessity to automate the analysis

LECTURE 1: Introduction Applications astronomical databases marketing/investment telecommunication industrial biomedical/genetica

LECTURE 1: Introduction Historical Context in mathematical statistics negative connotation: danger for overfitting and erroneous generalisation

LECTURE 1: Introduction Data Mining Subdisciplines Databases Statistics Knowledge Based Systems High-performance computing Data visualization Pattern recognition Machine learning

LECTURE 1: Introduction Data Mining -methodes Clustering classification (off- & on-line) (auto)-regression visualisation techniques: optimal projections and PCA (principal component analysis) discrimnant analysis decomposition parameteriical modelling non-parameteric modeling

LECTURE 1: Introduction Data Mining essentials model representation model evaluation search/optimisation Data Mining algorithms Decision trees/Rules Nonlinear Regression and Klassificatie Example-based methods AI-tools: NN, GA,...

LECTURE 1: Introduction Data Mining and Mathematical Statistics when Statistics and when DM? is DM a sort of Mathematical Statistics? Data Mining and AI AI is instrumental in finding knowledge in large chunks of data

Mathematical Principles in Data Mining Part I: Exploring Data Space * Understanding and Visualizing Data Space Provide tools to understand the basic structure in databases. This is done by probing and analysing metric structure in data-space, comprehensively visualizing data, and analysing global data structure by e.g. Principal Components Analysis and Multidimensional Scaling. * Data Analysis and Uncertainty Show the fundamental role of uncertainty in Data Mining. Understand the difference between uncertainty originating from statistical variation in the sensing process, and from imprecision in the semantical modelling. Provide frameworks and tools for modelling uncertainty: especially the frequentist and subjective/conditional frameworks.

Mathematical Principles in Data Mining PART II: Finding Structure in Data Space * Data Mining Algorithms & Scoring Functions Provide a measure for fitting models and patterns to data. This enables the selection between competing models. Data Mining Algorithms are discussed in the parallel course. * Searching for Models and Patterns in Data Space Describe the computational methods used for model and pattern-fitting in data mining algorithms. Most emphasis is on search and optimisation methods. This is required to find the best fit between the model or pattern with the data. Special attention is devoted to parameter estimation under missing data using the maximum likelihood EM-algorithm.

Mathematical Principles in Data Mining PART III: Mathematiscal Modelling of Data Space * Descriptive Models for Data Space Present descriptive models in the context of Data Mining. Describe specific techniques and algorithms for fitting descriptive models to data. Main emphasis here is on probabilistic models. * Clustering in Data Space Discuss the role of data clustering within Data Mining. Showing the relation of clustering in relation to classification and search. Present a variety of paradigms for clustering data.

EXAMPLES * Astronomical Databases * Phylogenetic trees from DNA-analysis

Example 1: Phylogenetic Trees The last decade has witnessed a major and historical leap in biology and all related disciplines. The date of this event can be set almost exactly to November 1999 as the Humane Genome Project (HGP) was declared completed. The HGP resulted in (almost) the entire humane genome, consisting of about base pairs (bp) code, constituting all approximately 35K humane genes. Since then the genomes of many more animal and plant species have come available. For our sake, we can consider the humane genome as a huge database, existing of a single string with characters from the set {C,G,A,T}.

Example 1: Phylogenetic Trees This data constitutes the human ‘source code’. From this data – in principle – all ‘hardware’ characteristics, such as physiological and psychological features, can be deduced. In this block we will concentrate on another aspect that is hidden in this information: phylogenetic relations between species. The famous evolutionary biologist Dobzhansky once remarked that: ‘Everything makes sense in the light of evolution, nothing makes sense without the light of evolution’. This most certainly applies to the genome. Hidden in the data is the evolutionary history of the species. By comparing several species with various amount of relatedness, we can from systematic comparison reconstruct this evolutionary history. For instance, consider a species that lived at a certain time in earth history. It will be marked by a set of genes, each with a specific code (or rather, a statistical variation around the average).

Example 1: Phylogenetic Trees If this species is by some reason distributed over a variety of non- connected areas (e.g. islands, oases, mountainous regions), animals of the species will not be able to mate at a random. In the course of time, due to the accumulation of random mutations, the genomes of the separated groups will increasingly differ. This will result in the origin of sub-species, and eventually new species. Comparing the genomes of the new species will shed light on the evolutionary history, in that: we can draw a phylogenetic tree of the sub-species leading to the ‘founder’-species; given the rate of mutation we can estimate how long ago the founder- species lived; reconstruct the most probable genome of the founder- species.

Example 2: data mining in astronomy

DATA AS SETS OF MEASUREMENTS AND OBSERVATIONS Data Mining Lecture II [Chapter 2 from Principles of Data Mining by Hand,, Manilla, Smyth ]

LECTURE 2: DATA AS SETS OF MEASUREMENTS AND OBSERVATIONS Readings: Chapter 2 from Principles of Data Mining by Hand, Mannila, Smyth.

2.1 Types of Data 2.2 Sampling 1.(re)sampling 2.oversampling/undersampling, sampling artefacts 3.Bootstrap and Jack-Knife methodes 2.3 Measures for Similarity and Difference 1.Phenomenological 2.Dissimilarity coefficient 3.Metric in Data Space based on distance measure

Types of data Sampling : – the process of collecting new (empirical) data Resampling : – selecting data from a larger already existing collection

Sampling –Oversampling –Undersampling –Sampling artefacts (aliasing, Nyquist frequency)

Sampling artefacts (aliasing, Nyquist frequency) Moire fringes

Resampling Resampling is any of a variety of methods for doing one of the following: – Estimating the precision of sample statistics (medians, variances, percentiles) by using subsets of available data (= jackknife) or drawing randomly with replacement from a set of data points (= bootstrapping) – Exchanging labels on data points when performing significance tests (permutation test, also called exact test, randomization test, or re-randomization test) – Validating models by using random subsets (bootstrap, cross validation)

Bootstrap & Jack-Knife methodes using inferential statistics to account for randomness and uncertainty in the observations. These inferences may take the form of answers to essentially yes/no questions (hypothesis testing), estimates of numerical characteristics (estimation), prediction of future observations, descriptions of association (correlation), or modeling of relationships (regression).

Bootstrap method bootstrapping is a method for estimating the sampling distribution of an estimator by resampling with replacement from the original sample. "Bootstrap" means that resampling one available sample gives rise to many others, reminiscent of pulling yourself up by your bootstraps. cross-validation: verify replicability of results Jackknife: detect outliers Bootstrap: inferential statistics

2.3 Measures for Similarity and Dissimilarity 1.Phenomenological 2.Dissimilarity coefficient 3.Metric in Data Space based on distance measure

2.4 Distance Measure and Metric 1.Euclidean distance 2.Metric 3.Commensurability 4.Normalisatie 5.Weighted Distances 6.Sample covariance 7.Sample covariance correlation coefficient 8.Mahalanobis distance 9.Normalised distance and Cluster Separation (zie aanvullende tekst) 10. Generalised Minkowski

2.4 Distance Measure and Metric 1.Euclidean distance

2.4 Distance Measure and Metric 2.Generalized p-norm

Generalized Norm / Metric

Minkowski Metric

Generalized Minkowski Metric In the data space is already a structure present. The structure is represented by the correlation and given by the covariance matrix G The Minkowski-norm of a vector x is:

2.4 Distance Measure and Metric 1.Euclidean distance 2.2.Metric 3.Commensurability 4.Normalisatie 5.Weighted Distances 6.Sample covariance 7.Sample covariance correlation coefficient 8.Mahalanobis distance 9.Normalised distance and Cluster Separation (zie aanvullende tekst) 10. Generalised Minkowski

2.4 Distance Measure and Metric Mahalanobis distance

2.4 Distance Measure and Metric 8.Mahalanobis distance The Mahalanobis distance is a distance measure introduced by P. C. Mahalanobis in It is based on correlations between variables by which different patterns can be identified and analysed. It is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set.

2.4 Distance Measure and Metric 8.Mahalanobis distance The Mahalanobis distance from a group of values with mean and covariance matrix Σ for a multivariate vector is defined as:

2.4 Distance Measure and Metric 8.Mahalanobis distance Mahalanobis distance can also be defined as dissimilarity measure between two random vectors x and y of the same distribution with the covariance matrix Σ :

2.4 Distance Measure and Metric 8.Mahalanobis distance If the covariance matrix is the identity matrix then it is the same as Euclidean distance. If covariance matrix is diagonal, then it is called normalized Euclidean distance : where σ i is the standard deviation of the x i over the sample set.

2.4 Distance measures and Metric 8.Mahalanobis distance

2.4 Distance measures and Metric 8.Mahalanobis distance

2.4 Distance measures and Metric 8.Mahalanobis distance

2.5 Distortions in Data Sets 1.outlyers 2.Variance 3.sampling effects 2.6 Pre-processong data with mathematical transformationes 2.7 Data Quality Data quality of individual measurements [GIGO] Data quality of Data collections