scipy.cluster.hierarchy.

# median#

scipy.cluster.hierarchy.median(y)[source]#

See `linkage` for more information on the return structure and algorithm.

The following are common calling conventions:

1. `Z = median(y)`

Performs median/WPGMC linkage on the condensed distance matrix `y`. See `linkage` for more information on the return structure and algorithm.

2. `Z = median(X)`

Performs median/WPGMC linkage on the observation matrix `X` using Euclidean distance as the distance metric. See `linkage` for more information on the return structure and algorithm.

Parameters:
yndarray

A condensed 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.

Returns:
Zndarray

The hierarchical clustering encoded as a linkage matrix.

`linkage`

for advanced creation of hierarchical clusterings.

`scipy.spatial.distance.pdist`

pairwise distance metrics

Examples

```>>> from scipy.cluster.hierarchy import median, fcluster
>>> from scipy.spatial.distance import pdist
```

First, we need a toy dataset to play with:

```x x    x x
x        x

x        x
x x    x x
```
```>>> X = [[0, 0], [0, 1], [1, 0],
...      [0, 4], [0, 3], [1, 4],
...      [4, 0], [3, 0], [4, 1],
...      [4, 4], [3, 4], [4, 3]]
```

Then, we get a condensed distance matrix from this dataset:

```>>> y = pdist(X)
```

Finally, we can perform the clustering:

```>>> Z = median(y)
>>> Z
array([[ 0.        ,  1.        ,  1.        ,  2.        ],
[ 3.        ,  4.        ,  1.        ,  2.        ],
[ 9.        , 10.        ,  1.        ,  2.        ],
[ 6.        ,  7.        ,  1.        ,  2.        ],
[ 2.        , 12.        ,  1.11803399,  3.        ],
[ 5.        , 13.        ,  1.11803399,  3.        ],
[ 8.        , 15.        ,  1.11803399,  3.        ],
[11.        , 14.        ,  1.11803399,  3.        ],
[18.        , 19.        ,  3.        ,  6.        ],
[16.        , 17.        ,  3.5       ,  6.        ],
[20.        , 21.        ,  3.25      , 12.        ]])
```

The linkage matrix `Z` represents a dendrogram - see `scipy.cluster.hierarchy.linkage` for a detailed explanation of its contents.

We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster each initial point would belong given a distance threshold:

```>>> fcluster(Z, 0.9, criterion='distance')
array([ 7,  8,  9, 10, 11, 12,  1,  2,  3,  4,  5,  6], dtype=int32)
>>> fcluster(Z, 1.1, criterion='distance')
array([5, 5, 6, 7, 7, 8, 1, 1, 2, 3, 3, 4], dtype=int32)
>>> fcluster(Z, 2, criterion='distance')
array([3, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2], dtype=int32)
>>> fcluster(Z, 4, criterion='distance')
array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
```

Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a plot of the dendrogram.