Clustering 77B Recommender Systems

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Presentation transcript:

Clustering 77B Recommender Systems

What if not all rating are observed?

Correction to Book

K Means Clustering Idea: Cluster the items OR users For new item-user pair Assign it to one of the clusters Predict by using the average rating cluster

Clustering: K-means We iterate two operations: 1. Update the assignment of data-cases to clusters 2. Update the location of the cluster. Denote the assignment of data-case “i” to cluster “c”. Denote the position of cluster “c” in a d-dimensional space. Denote the location of data-case i Then iterate until convergence: 1. For each data-case, compute distances to each cluster and the closest one: 2. For each cluster location, compute the mean location of all data-cases assigned to it: Nr. of data-cases in cluster c Set of data-cases assigned to cluster c

K-means Cost function: Each step in k-means decreases this cost function. Often initialization is very important since there are very many local minima in C. Relatively good initialization: place cluster locations on K randomly chosen data-cases. How to choose K? Add complexity term: and minimize also over K

K-medians Cost function: Algorithm: iterate until convergence: For each data-case, compute distances to each cluster and the closest one: 2. For each cluster location, compute the mean location of all data-cases assigned to it: ( the median is middle point (n=odd) or halfway between the middle 2 points (n=even) )

Vector Quantization K-means divides the space up in a Voronoi tesselation. Every point on a tile is summarized by the code-book vector “+”. This clearly allows for data compression !