Unsupervised learning: Clustering
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Intuition and mathematics behind K-Means, Hierarchical Clustering & DBSCAN using Python
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Unsupervised learning: Clustering
- 1. Deepak George Staff Data Scientist Unsupervised Learning: Clustering K-Means, Hierarchical Clustering & DBSCAN
- 2. ➢ Data Science Career ▪ General Electric ▪ Accenture Management Consulting ▪ Mu Sigma ➢ Highlights ▪ 1st Prize Best Data Science Project (BAI 5) – IIM Bangalore ▪ Co-author of Markdown Optimization case published at Harvard Business School ▪ Kaggle Bronze medal – Toxic Comment Classification ▪ Kaggle Bronze medal - Coupon Purchase Prediction (Recommender System) ▪ SAS Certified Statistical Business Analyst: Regression and Modeling Credentials ➢ Education ▪ Indian Institute Of Management Bangalore - Business Analytics & Intelligence ▪ College Of Engineering Trivandrum - Computer Science Engineering ➢ Passion ▪ Deep Learning, Photography, Football ▪ Profile ▪ linkedin.com/in/deepakgeorge7/ ▪ https://github.com/deepakiim Deepak George, IIM Bangalore 2 About Me
- 3. 1. Introduction to clustering and unsupervised learning 2. K means 3. Divisive and agglomerative clustering (Hierarchical) 4. Density-based clustering (DBSCAN) 5. Recommendations Agenda Deepak George, IIM Bangalore
- 4. What is Unsupervised Learning? • Training data is labelled • Used for predict the label • Classification and Regression • Training data is unlabelled • Used for finding patterns in the data • Clustering, Dimensionality reduction, Association Rules . Deepak George, IIM Bangalore
- 5. What is Clustering? Deepak George, IIM Bangalore
- 6. What is Norm? Let p ≥ 1 be a real number. The p-norm (also called of Lp norm) of vector x =(x1, x2 ….,xn) • Norm measures the magnitude (or size, length) of vector • On an intuitive level, the norm of a vector x measures the distance from the origin to the point x. Geometric Interpretation of L2 Norm Consider a unit ball containing the origin. The Euclidean norm of a vector is simply the factor by which the ball must be expanded or shrunk in order to fit the given vector exactly Deepak George, IIM Bangalore
- 7. Dissimilarity/Proximity Matrix Euclidean distance Dissimilarity Matrix Weighted Dissimilarity Matrix Data Matrix (n*p) Dissimilarity Matrix (n*n) Distance is inversely proportional to Similarity Deepak George, IIM Bangalore
- 8. Types of Clustering Algorithms 1.Combinatorial algorithms 2.Mixture modelling 3.Mode Seekers Deepak George, IIM Bangalore
- 9. Minimizing W(C) is equivalent to maximizing B(C) given that T is constant for any given data. C(i) is the encoder that we seek which assigns the ith observation to the kth cluster Within Cluster Point Scatter Total point scatter Between Cluster Point Scatter Combinatorial algorithm directly specify a mathematical loss function and attempt to minimize it through some combinatorial optimization algorithm. Since the goal is to assign close points to the same cluster, a natural loss function would be Combinatorial Algorithm Deepak George, IIM Bangalore
- 10. K-Means Visual Explanation Random seeds Assign Update It is intended for situations in which all variables are of the quantitative type, and squared Euclidean distance Deepak George, IIM Bangalore
- 11. K-Means Mathematical Explanation (for special case of K means) * The Elements of Statistical Learning Deepak George, IIM Bangalore
- 12. K-Means algorithm animation X1 X2 Deepak George, IIM Bangalore Kmeans_animation.gif
- 13. X1 X2 K-Means starting seed position issue animation Deepak George, IIM Bangalore Kmeans_starting_issue_animation.gif
- 14. K-Means Clustering Advantages • Scales well on large dataset • Does NOT require ANY assumptions about data distribution Disadvantages • Assumes clusters are spherical • Assumes clusters are approximately equal in size • Can only use Euclidean dissimilarity • Choosing the wrong K • Doesn’t guarantee global optima • Could depend on choice of initial seeds • Works only with continuous data Deepak George, IIM Bangalore
- 15. Hierarchical Clustering Agglomerative Clustering: • Bottom Up • Each object is initially considered as a single-element cluster • At each step, the two clusters that are the most similar are combined into a new bigger cluster • Repeated until all points are member of just one single big cluster Divisive Clustering: • Top Down • Initially all objects are assigned to a single cluster • At each step, the most heterogeneous cluster is divided into two. • Repeated until all objects are in their own cluster Deepak George, IIM Bangalore
- 16. Measuring Dissimilarity between two clusters Deepak George, IIM Bangalore
- 17. Hierarchical Clustering Visual Explanation Deepak George, IIM Bangalore
- 18. Hierarchical Clustering Algorithm * The Elements of Statistical Learning Deepak George, IIM Bangalore
- 19. Hierarchical Clustering algorithm animation X1 X2 Deepak George, IIM Bangalore Hierarchical_animation.gif
- 20. Hierarchical Clustering Advantages • No need to choose K before running the algorithm • Dendrogram will give visual guidance in choosing K • Can use any dissimilarity measure • Works on any kind of data including categorical and mixed • Does NOT require ANY assumptions about data distribution Disadvantages • Doesn’t scales well on large dataset • Doesn’t guarantee global optima Deepak George, IIM Bangalore
- 21. Density-based spatial clustering of applications with noise DBSCAN Parameters: 1. Minpts - Minimum number of points required to form a cluster 2. Epsilon – Radius of the circle drown around a point within which all points falling inside the circle belong to the same cluster. DBSCAN Fundamentals • Clusters are considered zones that are sufficiently dense. • Points that lack neighbours i.e. not dense do not belong to any cluster are classified as noise • DBSCAN can return clusters of any shape Deepak George, IIM Bangalore
- 22. DBSCAN Algorithm Density Reachable Not Density Reachable Deepak George, IIM Bangalore
- 23. DBSCAN algorithm animation Deepak George, IIM Bangalore DBSCAN_animation.gif
- 24. Advantages • It can discover any number of clusters • Clusters of varying shapes and sizes can be obtained using the DBSCAN algorithm • It can detect and ignore outliers Disadvantages • Assumes that’s clusters are of uniform density • The epsilon value could be sensitive • Too small a value can result in elimination of spare clusters as outliers • Too large a value would merge dense clusters together giving incorrect clusters DBSCAN Pros & Cons Deepak George, IIM Bangalore
- 25. General recommendations Profiling • Identify the unique properties of each cluster and give appropriate labels • Identify which feature is dominating in which cluster • Ensure that clusters are well separated and can be explained from business point of view Appropriate Dissimilarity measure • For mix data try Gower distance Feature scaling • Always scale/normalize the features before training the clustering algorithm Stability check • Before clustering split data into training and test. • Run the same final clustering model on both • If clustering is stable, you will get the same metrics in both the datasets Deepak George, IIM Bangalore