Unsupervised learning and clustering algorithms
Last updated on：8 days ago
Unlabelled data is also a key type of input data of machine learning. Usually, we will cluster these data to discover their structures.
In unsupervised learning, you are given an unlabelled dataset and are asked to find “structure” in the data.
Clustering techniques
Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters).
Hierarchical clustering algorithms, Mixtureresolving and modeseeking algorithms, nearest neighbour clustering, Fuzzy clustering, etc.
Partitional algorithms
Squared error clustering method
$$e^2(x, l) = \sum^{K_{j=1}\sum}{n_j}{i=1}x_i^{{(j)}c_j}2$$
Kmeans algorithm
Cluster centroid
In mathematics and physics, the centroid or geometric centre of a plane figure is the arithmetic mean position of all the points in the figure.
Steps
 Cluster assignment step  minimize J， wrt $c^{(1)}, c^{(2)}, c^{(k)}$
 Move cluster centroid step  minimize J , with reference to $\mu_1, \mu_2, \mu_k$
Input
 K (number of clusters)
 Unlabelled Training set
Randomly initialize K cluster centroid

Should have $K<m$

Randomly pick K training examples
Set $\mu_1, … , \mu_K$ equal to these K examples
Try multiple random initializations. Pick clustering theta gave lowest cost J
Optimization objective
$$J(c^{(1)}, …, c^{(m)}, \mu_1, …, \mu_K) = $$
$$\frac{1}{m}\sum^{m_{i=1}x}{(i)}  \mu_{c^{{(i)}}}2$$
Minimize $J(c^{(1)}, …, c^{(m)}, \mu_1, …, \mu_K) $.
Choosing the number of clusters
Elbow method
Others
Graphtheoretic clustering
Applications
Image segmentation, object and character recognition, information retrieval, data mining.
Reference
[1] Andrew NG, Machine learning
[2] Centroid
[3] Jain, A.K., Murty, M.N. and Flynn, P.J., 1999. Data clustering: a review. ACM computing surveys (CSUR), 31(3), pp.264323.
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