Intelligent Image and Graphics Processing
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1 Intelligent Image and Graphics Processing 智能图像图形处理图形处理 布树辉
2 Clustering
3 Clustering Attach label to each observation or data points in a set You can say this unsupervised classification Clustering is alternatively called as grouping Intuitively, if you would want to assign same label to a data points that are close to each other Thus, clustering algorithms rely on a distance metric between data points Sometimes, it is said that the for clustering, the distance metric is more important than the clustering algorithm
4 Clustering
5 Distances: Quantitative Variables Some examples x =[ x 1 Kx ] i Data point: i ip T
6 Partitioning Clustering Approach Partitioning Clustering Approach a typical clustering analysis approach via iteratively partitioning training data set to learn a partition of the given data space learning a partition on a data set to produce several non-empty clusters (usually, the number of clusters given in advance) in principle, optimal partition achieved via minimizing the sum of squared distance to its representative object in each cluster K E = Σ d ( x, m k k = 1Σ x C k ) e.g., Euclidean distance d = N ( x, mk) ( xn mkn n= 1 )
7 Partitioning Clustering Approach Given a K, find a partition of K clusters to optimize the chosen partitioning criterion (cost function) o global optimum: exhaustively search all partitions The K-means algorithm: a heuristic method o K-means algorithm (MacQueen 67): each cluster is represented by the center of the cluster and the algorithm converges to stable centriodsof clusters. o K-means algorithm is the simplest partitioning method for clustering analysis and widely used in data mining applications.
8 Partitioning Clustering Approach Given the cluster number K, the K-means algorithm is carried out in three steps after initialization: Initialisation: set seed points (randomly) 1) Assign each object to the cluster of the nearest seed point measured with a specific distance metric ) Compute new seed points as the centroids of the clusters of the current partition (the centroid is the centre, i.e., mean point, of the cluster) 3) Go back to Step 1), stop when no more new assignment (i.e., membership in each cluster no longer changes)
9 Example Suppose we have 4 types of medicines and each has two attributes (ph and weight index). Our goal is to group these objects into K= group of medicine. Medicine Weight ph- Index A 1 1 C D B 1 C 4 3 D 5 4 A B
10 Example Step 1: Use initial seed points for partitioning D c = A, c 1 = B C Euclidean distance A B d( D, c 1 ) = (5 1) + (4 1) = 5 d( D, c ) = (5 ) + (4 1) = 4.4 Assign each object to the cluster with the nearest seed point
11 Example Step : Compute new centroids of the current partition Knowing the members of each cluster, now we compute the new centroid of each group based on these new memberships. c 1 = (1, 1) c =, = (, ) 3 3 4
12 Example Step : Renew membership based on new centroids Compute the distance of all objects to the new centroids Assign the membership to objects
13 Example Step 3: Repeat the first two steps until its convergence Knowing the members of each cluster, now we compute the new centroid of each group based on these new memberships. ) 1 3, 1 (4 4 3, 5 4 1), 1 (1 1 1, 1 1 = + + = = + + = c c
14 Example Step 3: Repeat the first two steps until its convergence Compute the distance of all objects to the new centroids Stop due to no new assignment Membership in each cluster no longer change
15 Exercise For the medicine data set, use K-means with the Manhattandistance metric for clustering analysis by setting K=and initializing seeds as C1= A and C= C. Answer three questions as follows: 1. How many steps are required for convergence?. What are memberships of two clusters after convergence? 3. What are centroids of two clusters after convergence? Medicine Weight ph- Index A 1 1 C D B 1 C 4 3 A B D 5 4
16 How K-means partitions? When K centroids are set/fixed, they partition the whole data space into K mutually exclusive subspaces to form a partition. A partition amounts to a Voronoi Diagram Changing positions of centroids leads to a new partitioning.
17 Application - Colour-Based Image Segmentation Using K-means Step 1: Loading a colour image of tissue stained with hemotoxylin and eosin (H&E)
18 Application - Colour-Based Image Segmentation Using K-means Step : Convert the image from RGB colour space to L*a*b* colour space Unlike the RGB colour model, L*a*b* colour is designed to approximate human vision. There is a complicated transformation between RGB and L*a*b*. (L*, a*, b*) = T(R, G, B). (R, G, B) = T (L*, a*, b*).
19 Application - Colour-Based Image Segmentation Using K-means Step 3: Undertake clustering analysis in the (a*, b*) colour space with the K-means algorithm In the L*a*b* colour space, each pixel has a properties or feature vector: (L*, a*, b*). Like feature selection, L* feature is discarded. As a result, each pixel has a feature vector (a*, b*). Applying the K-means algorithm to the image in the a*b* feature space where K = 3 (by applying the domain knowledge.
20 Application - Colour-Based Image Segmentation Using K-means Step 4: Label every pixel in the image using the results from K-means Clustering (indicated by three different grey levels)
21 Application - Colour-Based Image Segmentation Using K-means Step 4: Label every pixel in the image using the results from K-means Clustering (indicated by three different grey levels)
22 Application: Learning Feature Representations Adam Coates and Andrew Y. Ng, Learning Feature Representations with K-Means
23 Application: GIF
24 Application: Bag of Words
25 Application Bag of Words (BoW) Image segmentation Superpixel
26 Summary K-means algorithm is a simple yet popular method for clustering analysis Its performance is determined by initialisation and appropriate distance measure There are several variantsof K-means to overcome its weaknesses K-Medoids: resistance to noise and/or outliers K-Modes: extension to categorical data clustering analysis CLARA: extension to deal with large data sets Mixture models (EM algorithm): handling uncertainty of clusters
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