The key idea is that for each point of a cluster, the neighborhood of a given radius has to contain at least a minimum number of points.

- "DBSCAN" =
**D**ensity-**b**ased-**s**patial**c**lustering of**a**pplication with**n**oise.

- Separate clusters of high density from ones of low density.

- Can sort data into clusters of varying shapes.

**Input**: set of points & neighborhood N & minpts (density)

**Output**: clusters with density (+ noises)

- Each point is either:
*Core point*: has at least minpts points in its neighborhood.*Border point*: not a core but has at least 1 core point in its neighborhoods.*Noise point*: not a core or border point.

**Phase**:- Choose a point → it's a core point?
- If yes → expand → check core / check border
- If no → form a cluster
- Repeat to form other clusters
- Eliminate noise points.

**Pros**:- Discover any number of clusters (different from K-Means & K-Medoids Clustering which need an input of number of clusters).
- Cluster of varying sizes and shapes.
- Detect and ignore outliers.

**Cons**:- Sensitive → choice of neighborhood parameters (eg. If minpts is too small → wrong noises)
- Produce noise: unclear → how to calculate metric indexes when there is noise.

**H**igh DBSCAN.

- Difference between DBSCAN and HDBSCAN:
- HDBSCAN: focus much on high density.
- DBSCAN: create right clusters but also create clusters with very low density of examples (Figure 1).
- Check more in this note.

- Reduce the speed of clustering in comparision with other methods (Figure 2).

- HDBScan has the parameter minimum cluster size (
`min_cluster_size`

), which is how big a cluster needs to be in order to form.

- We are not sure the number of clusters (like in KMeans)

- There are outliers or noises in data.

- Arbitrary cluster's shape.

```
1from sklearn.cluster import DBSCAN
2clr = DBSCAN(eps=3, min_samples=2)
```

```
1clr.fit(X)
2clr.predict(X)
```

```
1# or
2clr.fit_predict(X)
```

**Parameters**(others):

`min_samples`

: min number of samples to be called "dense"

`eps`

: max distance between 2 samples to be in the same cluster. Its unit/value based on the unit of data.

- Higher
`min_samples`

+ lower`eps`

indicates higher density necessary to form a cluster.

**Attributes**:

`clr.labels_`

: clusters' labels.

For a ref of paramaters, check the API.

```
1from hdbscan import HDBSCAN
2clr = HDBSCAN(eps=3, min_cluster_size=3, metric='euclidean')
```

**Parameters**:

`min_cluster_size`

: (ref) the smallest size grouping that you wish to consider a cluster.

`min_samples`

: (ref) The number of samples in a neighbourhood for a point to be considered a core point. The larger value → the more points will be declared as noise & clusters will be restricted to progressively more dense areas.

- Working with (more):
`metric='precomputed'`

(ref)

```
1from dtaidistance import dtw
2matrix = dtw.distance_matrix_fast(series) # something likes that
3model = HDBSCAN(metric='precomputed')
4clusters = model.fit_predict(matrix)
```

**Attributes**:

- Label
`1`

means that this sample is not assigned to any cluster, or noise!

`clt.labels_`

: labels of clusters (including`1`

)

`clt.probabilities_`

: scores (between 0 and 1).`0`

means sample is not in cluster at all (noise),`1`

means the heart of cluster.

Note that, HDBSCAN is built based on scikit-learn but it doesn't have an

`.predict()`

method as other clustering methods does on scikit-learn. Below code gives you a new version of HDBSCAN (`WrapperHDBSCAN`

) which has an additional `.predict()`

method.```
1from hdbscan import HDBSCAN
2
3class WrapperHDBSCAN(HDBSCAN):
4 def predict(self, X):
5 self.fit(X)
6 return self.labels_
```

**Official doc**-- How HDBSCAN works?