K-means △△ △ △ △ △ >>> <<<< o+ 2。 a)Iteration 1 (b)Iteration 2 (c)Iteration 3 (d) Iteration 4 8/20/2016 PATTERN RECOGNITION
K-means 8/20/2016 PATTERN RECOGNITION 16
K-means Each sub-figure shows The centroids at the start of the iteration and The assignment of the points to those centroids The centroids are indicated by the + symbol All points belonging to the same cluster have the same marker shape 8/20/2016 PATTERN RECOGNITION
K-means Each sub-figure shows ◦ The centroids at the start of the iteration and ◦ The assignment of the points to those centroids. The centroids are indicated by the “+” symbol. All points belonging to the same cluster have the same marker shape. 8/20/2016 PATTERN RECOGNITION 17
K-means In the first step points are assigned to the initial centroids which are all in the largest group of points After points are assigned to a centroid the centroid is then updated In the second step Points are assigned to the updated centroids and The centroids are updated again 8/20/2016 PATTERN RECOGNITION
K-means In the first step, points are assigned to the initial centroids, which are all in the largest group of points. After points are assigned to a centroid, the centroid is then updated. In the second step ◦ Points are assigned to the updated centroids and ◦ The centroids are updated again. 8/20/2016 PATTERN RECOGNITION 18
K-means We can observe that two of the centroids move to the two small groups of points at the bottom of the figures When the K-means agorithm terminates, the centroids have identified the natural groupings of points 8/20/2016 PATTERN RECOGNITION
K-means We can observe that two of the centroids move to the two small groups of points at the bottom of the figures. When the K-means algorithm terminates, the centroids have identified the natural groupings of points. 8/20/2016 PATTERN RECOGNITION 19
Proximity measure To assign a point to the closest centroid we need a proximity measure that quantifies the notion of "closest Euclidean (L2) distance is often used for data point in Euclidean space. 8/20/2016 PATTERN RECOGNITION
Proximity measure To assign a point to the closest centroid, we need a proximity measure that quantifies the notion of “closest”. Euclidean (L2 ) distance is often used for data point in Euclidean space. 8/20/2016 PATTERN RECOGNITION 20