# Python dendrogram from distance matrix

This is a tutorial on how to use scipy's hierarchical clustering. One of the benefits of hierarchical clustering is that you don't need to already know the number of clusters k in your data in advance. Sadly, there doesn't seem to be much documentation on how to actually use scipy's hierarchical clustering to make an informed decision and then retrieve the clusters.

The only thing you need to make sure is that you convert your data into a matrix X with n samples and m features, so that X. Well, sure it was, this is python ;but what does the weird 'ward' mean there and how does this actually work?

## Hierarchical Clustering in Python using Dendrogram and Cophenetic Correlation

As the scipy linkage docs tell us, 'ward' is one of the methods that can be used to calculate the distance between newly formed clusters. I think it's a good default choice, but it never hurts to play around with some other common linkage methods like 'single''complete''average'For example, you should have such a weird feeling with long binary feature vectors e. As you can see there's a lot of choice here and while python and scipy make it very easy to do the clustering, it's you who has to understand and make these choices.

If i find the time, i might give some more practical advice about this, but for now i'd urge you to at least read up on the mentioned linked methods and metrics to make a somewhat informed choice. Another thing you can and should definitely do is check the Cophenetic Correlation Coefficient of your clustering with help of the cophenet function.

This very very briefly compares correlates the actual pairwise distances of all your samples to those implied by the hierarchical clustering. The closer the value is to 1, the better the clustering preserves the original distances, which in our case is pretty close:.

No matter what method and metric you pick, the linkage function will use that method and metric to calculate the distances of the clusters starting with your n individual samples aka data points as singleton clusters and in each iteration will merge the two clusters which have the smallest distance according the selected method and metric. It will return an array of length n - 1 giving you information about the n - 1 cluster merges which it needs to pairwise merge n clusters.

Z[i] will tell us which clusters were merged in the i -th iteration, let's take a look at the first two points that were merged:. In its first iteration the linkage algorithm decided to merge the two clusters original samples here with indices 52 and 53, as they only had a distance of 0.

This created a cluster with a total of 2 samples. In the second iteration the algorithm decided to merge the clusters original samples here as well with indices 14 and 79, which had a distance of 0. This again formed another cluster with a total of 2 samples. The indices of the clusters until now correspond to our samples.Clustering starts by computing a distance between every pair of units that you want to cluster.

A distance matrix will be symmetric because the distance between x and y is the same as the distance between y and x and will have zeroes on the diagonal because every item is distance zero from itself. The table below is an example of a distance matrix. Only the lower triangle is shown, because the upper triangle can be filled in by reflection. Now lets start clustering. The smallest distance is between three and five and they get linked up or merged first into a the cluster '35'. To obtain the new distance matrix, we need to remove the 3 and 5 entries, and replace it by an entry "35". Since we are using complete linkage clustering, the distance between "35" and every other item is the maximum of the distance between this item and 3 and this item and 5.

This gives us the new distance matrix. The items with the smallest distance get clustered next. This will be 2 and 4. Continuing in this way, after 6 steps, everything is clustered.

StatQuest: Hierarchical Clustering

This is summarized below. On this plot, the y-axis shows the distance between the objects at the time they were clustered. This is called the cluster height. Different visualizations use different measures of cluster height.

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Complete Linkage. Below is the single linkage dendrogram for the same distance matrix. It starts with cluster "35" but the distance between "35" and each item is now the minimum of d x,3 and d x,5. One of the problems with hierarchical clustering is that there is no objective way to say how many clusters there are. If we cut the single linkage tree at the point shown below, we would say that there are two clusters.

Let's look at some real data. In homework 5 we consider gene expression in 4 regions of 3 human and 3 chimpanzee brains.Python Hierarchical Clustering Distance Matrix. Python program to calculate clusters using Hierarchical Clustering method - hCluster. Method Distance is. In the k-means cluster analysis tutorial I provided a solid introduction to one of the most popular clustering methods.

Among other, in the specific context of the hierarchical clustering, the dendrogram enables to understand the structure of the groups. Here, you'll create a dendrogram with the X matrix from diabetes, then extend an imaginary line at length 1.

It is defined by matrix dimensions and a single double-array arranged in a column-major order. AKA group-average hierarchical clustering, the Average linkage method uses the average pair-wise proximity among all pairs of objects in different clusters.

K-means covered here requires that we specify the number of clusters first to begin the clustering process. In the context of hierarchical clustering, the hierarchy graph is called a dendogram. Statistical Clustering. When using the AltAnalyze pre-compiled distributions, no additional software is needed. The popular clustering algorithms are the K-means clustering, Gaussian mixture model, Hierarchical clustering.

Hello and welcome. Is Akaike information criterion would of. It proceeds by splitting clusters recursively until individual documents are reached.

At the current stage, I think there are two types of data that will be useful from hierarchical clustering. In a project we're doing in pythonwe want to create a distance matrix for a phylogenetic tree with multiple, different length sequences. Later i want to use this model in java.

These algorithms connect "objects" to form "clusters" based on their distance. Hierarchical Clustering The hierarchical clustering process was introduced in this post. Like K-means clustering, hierarchical clustering also groups together the data points with similar characteristics.

I'm looking for a way to perform clustering separately on matrix rows and than on its columns, reorder the data in the matrix to reflect the clustering and putting it all together. Hierarchical clustering can be divided into two main types:. R has an amazing variety of functions for cluster analysis. The output of Jarvis-Patrick and K-Means clustering is not affected if Euclidean distance is replaced with Euclidean squared. This example uses a scipy.

### Python Hierarchical Clustering Distance Matrix

Artificial Intelligence Foundations This course will teach you the foundations of Supervised machine learning. Hierarchical clustering allows visualization of clusters using dendrograms that can help in better interpretation of results through meaningful taxonomies. In particular, when a new cluster is formed and the distance matrix is updated, all the information about the individual members of the cluster is discarded in order to make the computations faster.

Here, we can see that no links exist above a distance of - so we will set maximum distance at and use the fclusters function from scipy. Hierarchical clustering gives more than one partitioning depending on the resolution or as K-means gives only one partitioning of the data. The advantage of not having to pre-define the number of clusters gives it quite an edge over k-Means. Each of them is 5x6. Clustering starts by computing a distance between every pair of units that you want to cluster.

The scipy clustering package could be usefull scipy. Another thing you can do is to try use fuzzy-methods which tend to work better at least in my experience in this kind of cases, try first Cmeans, Fuzzy K.Hierarchical clustering is the second most popular technique for clustering after K-means.

Remember, in K-means; we need to define the number of clusters beforehand. It proceeds top-down, starting with all points in a single cluster and sequentially splits them until all points are in their own cluster. Hierarchical clustering generates clusters that are organized into a hierarchical structure.

This hierarchical structure can be visualized using a tree-like diagram called dendrogram. Dendrogram records the sequence of merges in case of agglomerative and sequence of splits in case of divisive clustering. Every time we merge or split a cluster it will record the distance between the two cluters. As we have seen earlier it builds the cluster in a bottom-up manner. It starts with each element being a single cluster.

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The distance between each cluster and all other cluster is computed and the closest pairs of clusters are merged sequentially until there is only one cluster.

Agglomerative clustering performs merges based on the distance between the clusters. So, we need to choose a distance or similarity metric and construct a distance matrix.

Euclidean distance is a good choice. However, you can also use other metrics like manhattan or cosine distance. You can read my article Distance Measures in Machine Learning if you want to learn more about some of the commonly used distance metrics. Now, once we have our distance matrix, we need a strategy or linkage criterion to merge the clusters.

The linkage method figures out which clusters should be merged into one. Several types of linkage methods are used. Some of them are discussed below. In single linkage, the distance between two clusters is defined as the minimum distance between a point in one cluster and a point in the other cluster.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I have three matrices to compare. Each of them is 5x6. I originally wanted to use hierarchical clustering to cluster the matrices, such that the most similar matrices are grouped, given a threshold of similarity.

Now I have a 3x3 distance matrix which I believe is also a similarity matrix in this case. I am now trying to produce a dendrogram.

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This is my code, and this is what is wrong. I want to produce a graph a dendrogram if possible that shows clusters of the matrices that are most similar. Of matrices 0,1,2, 0 and 2 are the same and should be clustered together first, and 1 is different. This is the output:. I would have assumed the output graph to look something like this, where the distance is 2. Are there better ways to represent these data? Is there a function that could take in several matrices instead of points, to compare and form a distance matrix, and then cluster? I am open to other suggestions on how to visualize the differences between these matrices.

The first argument of linkage should not be the square distance matrix. It must be the condensed distance matrix. In your case, that would be np. You can convert from the square distance matrix to the condensed form using scipy.

If you pass a two dimensional array to linkage with shape m, nit treats it as an array of m points in n -dimensional space and it computes the distances of those points itself. That's why you didn't get an error when you passed in the square distance matrix--but you got an incorrect plot.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. So as expected, it takes the following form:. Now I wish to cluster these n objects with hierarchical clustering.

Python has an implementation of this called scipy. Its documentation says:. A condensed or redundant distance matrix. A condensed distance matrix is a flat array containing the upper triangular of the distance matrix. This is the form that pdist returns. Alternatively, a collection of m observation vectors in n dimensions may be passed as an m by n array. I am confused by this description of y.

Can I directly feed my M in as the input y? This is exactly what I am concerning about. However, as a newbie to GitHub, I don't know how it works and therefore have no idea how this issue is dealt with. It seems that indeed we cannot directly pass the redundant square matrix in, although the documentation claims we can do so. To benefit anyone who faces the same problem in the future, I write my solution as an additional answer here.

So the copy-and-paste guys can just proceed with the clustering. For now you should pass in the 'condensed distance matrix', i. From the discussion of hongbo-zhu-cn's pull request it looks as though the solution will be to add an extra keyword argument to the linkage function that will allow the user to explicitly specify that they are passing in an n x n distance matrix rather than an m x n observation matrix.

Learn more. Use Distance Matrix in scipy. Ask Question. Asked 7 years ago. Active 7 years ago. Viewed 21k times. Update hongbo-zhu-cn has raised this issue up in GitHub. Sibbs Gambling. Sibbs Gambling Sibbs Gambling 15k 32 32 gold badges 84 84 silver badges bronze badges.

HongboZhu Oh, yes, I nearly forgot that I could do this! Active Oldest Votes. Use the following snippet to condense the matrix and happily proceed. I think it is the way to go for the moment. You can compare your results obtained by using condensed distance matrix as input and results obtained by using observations as input. Sign up or log in Sign up using Google.

Sign up using Facebook.In this article, we will take a look at an alternative approach to K Means clustering, popularly known as the Hierarchical Clustering. The hierarchical Clustering technique differs from K Means or K Mode, where the underlying algorithm of how the clustering mechanism works is different. K Means relies on a combination of centroid and euclidean distance to form clusters, hierarchical clustering on the other hand uses agglomerative or divisive techniques to perform clustering.

Hierarchical clustering allows visualization of clusters using dendrograms that can help in better interpretation of results through meaningful taxonomies. Programming languages like R, Python, and SAS allow hierarchical clustering to work with categorical data making it easier for problem statements with categorical variables to deal with.

Now clusters usually have multiple points in them that require a different approach for the distance matrix calculation. Linkage decides how the distance between clusters, or point to cluster distance is computed. Commonly used linkage mechanisms are outlined below:. These formulas for distance calculation is illustrated in Figure 1 below.

Distance between two or more clusters can be calculated using multiple approaches, the most popular being Euclidean Distance. Figure 2 below outlines how hierarchical clustering is influenced by different distance metrics. A dendrogram is used to represent the relationship between objects in a feature space. It is used to display the distance between each pair of sequentially merged objects in a feature space. Dendrograms are commonly used in studying the hierarchical clusters before deciding the number of clusters appropriate to the dataset.

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The distance at which two clusters combine is referred to as the dendrogram distance. The dendrogram distance is a measure of if two or more clusters are disjoint or can be combined to form one cluster together. Figures 3, 4, and 5 above signify how the choice of linkage impacts the cluster formation.

Visually looking into every dendrogram to determine which clustering linkage works best is challenging and requires a lot of manual effort. To overcome this we introduce the concept of Cophenetic Coefficient. Cophenet index is a measure of the correlation between the distance of points in feature space and distance on the dendrogram.

It usually takes all possible pairs of points in the data and calculates the euclidean distance between the points.