Lecture

Structure Discovery: Tracing Student Knowledge

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In course

CS-421: Machine learning for behavioral data

Computer environments such as educational games, interactive simulations, and web services provide large amounts of data, which can be analyzed and serve as a basis for adaptation. This course will cover the core methods of user modeling and personalizatio ...

Description

This lecture covers the assumptions behind Bayesian Knowledge Tracing (BKT) and introduces the Additive Factors Model (AFM) and Performance Factors Analysis (PFA) for tracing student knowledge. It also delves into Generalized Linear Mixed Effects Models, Item Response Theory, and the evaluation of student models using RMSE and AUC. The lecture further explores clustering algorithms such as K-Means, Spectral Clustering, and Hierarchical Agglomerative Clustering, discussing their assumptions, initialization, and selection of the optimal number of clusters.

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.

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.

Nonlinear mixed-effects model

Nonlinear mixed-effects models constitute a class of statistical models generalizing linear mixed-effects models. Like linear mixed-effects models, they are particularly useful in settings where there are multiple measurements within the same statistical units or when there are dependencies between measurements on related statistical units. Nonlinear mixed-effects models are applied in many fields including medicine, public health, pharmacology, and ecology.

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