Lecture

Clustering: Dimensionality Reduction

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In course

FIN-525: Financial big data

The course introduces modern methods to acquire, clean, and analyze large quantities of financial data efficiently. The second part expands on how to apply these techniques and robust statistics to financial analysis, in particular to intraday data and inv ...

Description

This lecture covers techniques for clustering and dimensionality reduction in finance, including supervised and unsupervised classification, community detection in networks, and maximum likelihood clustering. It explores methods to clean and simplify data, reduce noise, and stabilize portfolios through structure and constraints.

Instructor

Damien Challet

Teaching & PhD Courses Financial big data FIN-525 The course introduces modern methods to acquire, clean, and analyze large quantities of financial data efficiently. The second part expands on how to apply these techniques and robust statistics to financial analysis, in particular to intraday data and investment strategies.

Official source

Ontological neighbourhood

Information engineering

Machine learning: Unsupervised learning

Related concepts (32)

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.

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.

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

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.

Maximum spacing estimation

In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points.

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Likelihood function

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Maximum spacing estimation