Lecture6a.slides.pdf - CS4487 Machine Learning Lecture 6a...

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CS4487 - Machine Learning Lecture 6a - Unsupervised Learning - Clustering Dr. Antoni B. Chan Dept. of Computer Science, City University of Hong Kong Outline 1. Unsupervised Learning 2. Parametric clustering A. K-means B. Gaussian mixture models (GMMs) C. Dirichlet Process GMMs 3. Non-parametric clustering and Mean-shift 4. Spectral clustering Supervised Learning Supervised learning considers input-output pairs learn a mapping from input to output. classification : output regression : output "Supervised" here means that the algorithm is learning the mapping that we want. Unsupervised Learning Unsupervised learning only considers the input data . There are no output values. Goal: Try to discover inherent properties in the data. Clustering Dimensionality Reduction Manifold Embedding Clustering Find clusters of similar items in the data. Find a representative item that can represent all items in the cluster. For example: grouping iris flowers by their measurements. Features are sepal width and petal length. ( x , y ) y ±1 y ∈ ℝ x
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Dimensionality Reduction Transform high-dimensional vectors into low-dimensional vectors. Dimensions in the low-dim data may have semantic meaning. For example: document analysis high-dim: bag-of-word vectors of documents low-dim: each dimension represents similarity to a topic.
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Manifold Embedding Project high-dimensional vectors into 2- or 3-dimensional space for visualiation. Points in the low-dim space have similar pair-wise distances as in the high-dim space. For example: visualize a collection of hand-written digits (images). Clustering Each data point is a vector . Data is set of vectors Goal: group similar data together. groups are also called clusters. each data point is assigned with a cluster index ( ) is the number of clusters. x ∈ ℝ d { , , } x 1 x n y {1, , K } K
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In [3]: clusterfig K-Means Clustering Idea: there are clusters.
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