Lecture

Characterisation of Clusters: Homogeneity, Separability

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In course

EE-311: Fundamentals of machine learning

Ce cours présente une vue générale des techniques d'apprentissage automatique, passant en revue les algorithmes, le formalisme théorique et les protocoles expérimentaux. ...

Description

This lecture covers the concepts of centroid and medoid, homogeneity, and separability in clustering. It explains how to calculate homogeneity and separability, illustrating with examples of high and low homogeneity and separability. The lecture also introduces the Davies-Bouldin index and silhouette coefficient for evaluating clustering quality, as well as cluster stability and the Rand index. Additionally, it discusses expert knowledge in clustering, including ontology and enrichment analysis. Different clustering algorithms such as clustering by density, centroids, and hierarchical clustering are presented, emphasizing the importance of homogeneity and separability.

Instructors (2)

Michael Stefan Daniel Liebling

Teaching & PhD Past EPFL PhD Students as codirector Christian Jaques, Olivia Mariani, Adrian Shajkofci, François Thierry M Marelli Courses Fundamentals of machine learning EE-311 This course provides a general overview of machine learning, covering the main algorithms, theoretical formalisms, and experimental protocols.

François Fleuret

Official source

Ontological neighbourhood

Information engineering

Machine learning: Unsupervised learning

Related concepts (27)

Hierarchical clustering

In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.

K-means clustering

k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. k-means clustering minimizes within-cluster variances (squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors, whereas only the geometric median minimizes Euclidean distances.

Single-linkage clustering

In statistics, single-linkage clustering is one of several methods of hierarchical clustering. It is based on grouping clusters in bottom-up fashion (agglomerative clustering), at each step combining two clusters that contain the closest pair of elements not yet belonging to the same cluster as each other. This method tends to produce long thin clusters in which nearby elements of the same cluster have small distances, but elements at opposite ends of a cluster may be much farther from each other than two elements of other clusters.

Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, , information retrieval, bioinformatics, data compression, computer graphics and machine learning.

Ontology

In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into and which of these entities exist on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses the classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs, and events.

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