Timeline for scaling before hierarchical clustering by single and complete linkage
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2023 at 9:21 | history | edited | Broele | CC BY-SA 4.0 | Corrected: Mahalanobis distance does kind of a normalization |
| Sep 14, 2023 at 18:10 | comment | added | Broele | Pro Tip: You can run hierarchical clustering with the same data, but alter different numbers of clusters K=2,3,4.... Each reduction of the number of clusters by one should correspond to one merging step. This would show you for selected examples which clusters are merged. | |
| Sep 14, 2023 at 17:59 | comment | added | Broele | Keep in mind that the hierarchical clustering always merges the two clusters with the best metric. That means, complete linkage creates (in a greedy way) clusters that are as compact as possible. Still, depending on the data, that does not need to mean much. If all points are aligned in a straight line then there is not much, complete linkage can do. | |
| Sep 13, 2023 at 20:47 | comment | added | user154385 | I should say "complete linkage will lead to a compact cluster" instead of "complete linkage will lead to a compact linkage" | |
| Sep 13, 2023 at 20:37 | comment | added | user154385 | Then, I just need to understand these 2. Regarding the complete linkage, we say the two clusters that are going to be merged tend to make a new compact cluster if the distance between the 2 farthest observation in the 2 clusters that are going to get merged is small. But, if the distance between the 2 farthest observations in the 2 clusters is rally big, then we cannot say the complete linkage will lead to a compact linkage. Long story short, we have to give a condition that the distance of the 2 farthest observations is relatively close. Is that correct? | |
| Sep 13, 2023 at 9:27 | comment | added | Broele | I would not expect single linkage just to grow clusters, but also to merge clusters of equal size. Suggestion: create an own question for it and I will be happy to answer it and produce images to demonstrate what is going on | |
| Sep 13, 2023 at 3:22 | comment | added | user154385 | Complete linkage does not have a snow ball effect. So, the complete linkage does not have a few big clusters that eat up all the other small clusters or observations. Therefore, we will likely to see more compact clusters than single linkage. thank you for your help! | |
| Sep 13, 2023 at 3:21 | comment | added | user154385 | can you please verify this? Complete linkage tends to produce more compact clusters. I guess it has something to do with not having a snowball effect. Unlike the single linkage where one big cluster eats up a little clusters that have either only one observation or a few observations. Then, the single linkage produces a loose cluster or one giant cluster that has a snowball effect. | |
| Sep 12, 2023 at 22:06 | comment | added | user154385 | I think I understand it now. | |
| Sep 12, 2023 at 19:08 | comment | added | Broele | Basically, Single Linkage only considers the nearest two points between two clusters and Complete Linkage the two points that are furthest away. This means, that Single Linkage can build long lines, stars, filaments, ... as long as all points are close to their neighbors. For Complete Linkage the furthest distances in clusters are relevant and the clustering tries to keep these small. If the furthest distance is small, all distances between the points in one cluster are small. This make the cluster somehow compact. | |
| Sep 12, 2023 at 18:46 | comment | added | user154385 | thank you, Broele. I don't still get why the complete clustering prefers compact cluster. The main reason is the two observation in the two clusters are far apart and they are the chosen ones that are going to get merged. Then, shouldn't we say the"loose cluster" which is the opposite of compact clusters? | |
| Sep 12, 2023 at 17:45 | comment | added | Broele | Complete Linkage merges the two clusters that lead to the smallest diameter (diameter is the maximal distance between two points of the cluster), i.e. the resulting cluster should fit into a circle as small as possible. That probably leads to the weird outcome in the top-righ image. The right blue part will create a slightly bigger diameter if merged with the green part instead of merging it with the left blue part. | |
| Sep 12, 2023 at 17:41 | comment | added | Broele | Single Linkage merges in each step the two clusters that have the closest pair of points (e.g. the smallest gap). It does not matter how long-stretched the clusters are, it just looks at the gaps between the clusters. That leads to the long-stretched long blue and orange clusters on the bottom-right. | |
| Sep 12, 2023 at 14:37 | comment | added | user154385 | Hi Broele. Just have a question. You said at the end that complete linkage prefers compact clusters (top row, both columns), while the single linkage avoids bigger gaps (bottom row, right image). Can you please explain why? | |
| Sep 11, 2023 at 15:58 | comment | added | Broele | Kudos to this answer and the linked website. | |
| Sep 11, 2023 at 15:55 | history | answered | Broele | CC BY-SA 4.0 |