## What? #

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 #

- "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 â†’ it's a core point?
- If yes â†’ expand â†’ check core / check border
- If no â†’ form a cluster

- Repeat to form other clusters
- Eliminate noise points.

- Choose a point â†’ it's a core point?
**Pros**:- Discover any number of clusters (different from K-Means which need an input of number of clusters).
- Cluster of varying sizes and shapes.
- Detect and ignore outliers.

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

### HDBSCAN #

**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.

**Figure 1**. Difference between DBSCAN (left) and HDBSCAN (right). Source of figure.

**Figure 2**.Performance comparison of difference clustering methods. HDBSCAN is much faster than DBSCAN with more data points. Source of figure.

## When? #

- We are not sure the number of clusters (like in KMeans)
- There are outliers or noises in data.
- Arbitrary cluster's shape.

## In Code #

### DBSCAN with Scikit-learn #

`from sklearn.cluster import DBSCAN`

clr = DBSCAN(eps=3, min_samples=2)

`clr.fit(X)`

clr.predict(X)

`# or`

clr.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.

### HDBSCAN #

For a ref of paramaters, check the API.

`from hdbscan import HDBSCAN`

clr = 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 $\to$ the more points will be declared as noise & clusters will be restricted to progressively more dense areas.Working with DTW (Dynamic Time Warping) (more):

`metric='precomputed'`

^{[ref]}`from dtaidistance import dtw`

matrix = dtw.distance_matrix_fast(series) # something likes that

model = HDBSCAN(metric='precomputed')

clusters = model.fit_predict(matrix)

`min_cluster_size`

and `min_samples`

`min_cluster_size=12`

&`min_samples=2`

gives less noises than`min_cluster_size=12`

&`min_samples=3`

: It's because we need at least`min_samples`

points to determine a core points. That's why the bigger`min_samples`

, the harder to form a cluster, or the more chances we have more noises.`min_cluster_size=7`

&`min_sampls=3`

gives less noises than`min_cluster_size=12`

&`min_samples=3`

: It's because we need at least`min_cluster_size`

points to determine a cluster. That's why the bigger`min_cluster_size`

, the harder the form a cluster, or the more chances we have more noise.

**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.

#### HDBSCAN and scikit-learn #

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.

`from hdbscan import HDBSCAN`

class WrapperHDBSCAN(HDBSCAN):

def predict(self, X):

self.fit(X)

return self.labels_

## Reference #

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

^{â€¢}Notes with this notation aren't good enough. They are being updated.