verticapy.machine_learning.model_selection.elbow¶

verticapy.machine_learning.model_selection.elbow(input_relation: Annotated[str | vDataFrame, ''], X: Annotated[str | list[str], 'STRING representing one column or a list of columns'] | None = None, n_cluster: tuple | list = (1, 15), init: Literal['kmeanspp', 'random', None] = None, max_iter: int = 50, tol: float = 0.0001, use_kprototype: bool = False, gamma: float = 1.0, show: bool = True, chart: PlottingBase | TableSample | Axes | mFigure | Highchart | Highstock | Figure | None = None, **style_kwargs) → TableSample¶

Draws an Elbow curve.

Parameters¶

input_relation: SQLRelation

Relation used to train the model.

X: SQLColumns, optional

list of the predictor columns. If empty, all numerical columns are used.

n_cluster: tuple | list, optional

Tuple representing the number of clusters to start and end with. This can also be a customized list with various k values to test.

init: str | list, optional

The method used to find the initial cluster centers.

kmeanspp:
Only available when use_kprototype = False Use the k-means++ method to initialize the centers.
random:
Randomly subsamples the data to find initial centers.

Default value is kmeanspp if use_kprototype = False; otherwise, random.

max_iter: int, optional

The maximum number of iterations for the algorithm.

tol: float, optional

Determines whether the algorithm has converged. The algorithm is considered converged after no center has moved more than a distance of tol from the previous iteration.

use_kprototype: bool, optional

If set to True, the function uses the KPrototypes algorithm instead of KMeans. KPrototypes can handle categorical features.

gamma: float, optional

Only if use_kprototype = True. Weighting factor for categorical columns. It determines the relative importance of numerical and categorical attributes.

show: bool, optional

If set to True, the Plotting object is returned.

chart: PlottingObject, optional

The chart object to plot on.

**style_kwargs

Any optional parameter to pass to the Plotting functions.

Returns¶

TableSample: nb_clusters,total_within_cluster_ss,between_cluster_ss,total_ss, elbow_score

Examples¶

The following examples provide a basic understanding of usage. For more detailed examples, please refer to the: Elbow Curve page.

Load data for machine learning¶

We import verticapy:

import verticapy as vp

Hint

By assigning an alias to verticapy, we mitigate the risk of code collisions with other libraries. This precaution is necessary because verticapy uses commonly known function names like “average” and “median”, which can potentially lead to naming conflicts. The use of an alias ensures that the functions from verticapy are used as intended without interfering with functions from other libraries.

For this example, we will use the iris dataset.

import verticapy.datasets as vpd

data = vpd.load_iris()

	123 SepalLengthCm Numeric(7)	123 SepalWidthCm Numeric(7)	123 PetalLengthCm Numeric(7)	123 PetalWidthCm Numeric(7)	Abc Species Varchar(30)
1	4.6	3.6	1.0	0.2	Iris-setosa
2	4.7	3.2	1.3	0.2	Iris-setosa
3	4.7	3.2	1.6	0.2	Iris-setosa
4	4.8	3.0	1.4	0.1	Iris-setosa
5	4.8	3.1	1.6	0.2	Iris-setosa
6	4.8	3.4	1.9	0.2	Iris-setosa
7	4.9	3.0	1.4	0.2	Iris-setosa
8	4.9	3.1	1.5	0.1	Iris-setosa
9	4.9	3.1	1.5	0.1	Iris-setosa
10	4.9	3.1	1.5	0.1	Iris-setosa
11	5.0	2.3	3.3	1.0	Iris-versicolor
12	5.0	3.4	1.5	0.2	Iris-setosa
13	5.1	3.5	1.4	0.2	Iris-setosa
14	5.4	3.0	4.5	1.5	Iris-versicolor
15	5.4	3.4	1.5	0.4	Iris-setosa
16	5.4	3.9	1.3	0.4	Iris-setosa
17	5.5	2.4	3.7	1.0	Iris-versicolor
18	5.5	2.4	3.8	1.1	Iris-versicolor
19	5.6	2.7	4.2	1.3	Iris-versicolor
20	5.7	3.0	4.2	1.2	Iris-versicolor
21	5.7	4.4	1.5	0.4	Iris-setosa
22	5.8	2.8	5.1	2.4	Iris-virginica
23	5.9	3.2	4.8	1.8	Iris-versicolor
24	6.1	3.0	4.6	1.4	Iris-versicolor
25	6.1	3.0	4.9	1.8	Iris-virginica
26	6.3	2.5	4.9	1.5	Iris-versicolor
27	6.3	3.3	4.7	1.6	Iris-versicolor
28	6.3	3.3	6.0	2.5	Iris-virginica
29	6.4	2.9	4.3	1.3	Iris-versicolor
30	6.5	3.0	5.5	1.8	Iris-virginica
31	6.5	3.0	5.8	2.2	Iris-virginica
32	6.7	3.0	5.0	1.7	Iris-versicolor
33	6.8	2.8	4.8	1.4	Iris-versicolor
34	6.8	3.2	5.9	2.3	Iris-virginica
35	7.0	3.2	4.7	1.4	Iris-versicolor
36	7.1	3.0	5.9	2.1	Iris-virginica
37	7.7	3.8	6.7	2.2	Iris-virginica
38	4.4	2.9	1.4	0.2	Iris-setosa
39	4.5	2.3	1.3	0.3	Iris-setosa
40	4.8	3.4	1.6	0.2	Iris-setosa
41	5.0	2.0	3.5	1.0	Iris-versicolor
42	5.1	3.3	1.7	0.5	Iris-setosa
43	5.1	3.4	1.5	0.2	Iris-setosa
44	5.2	2.7	3.9	1.4	Iris-versicolor
45	5.2	3.5	1.5	0.2	Iris-setosa
46	5.2	4.1	1.5	0.1	Iris-setosa
47	5.4	3.9	1.7	0.4	Iris-setosa
48	5.5	3.5	1.3	0.2	Iris-setosa
49	5.6	3.0	4.1	1.3	Iris-versicolor
50	5.8	2.7	3.9	1.2	Iris-versicolor
51	5.8	2.7	5.1	1.9	Iris-virginica
52	5.8	2.7	5.1	1.9	Iris-virginica
53	5.9	3.0	4.2	1.5	Iris-versicolor
54	5.9	3.0	5.1	1.8	Iris-virginica
55	6.0	2.7	5.1	1.6	Iris-versicolor
56	6.0	2.9	4.5	1.5	Iris-versicolor
57	6.1	2.8	4.7	1.2	Iris-versicolor
58	6.2	2.8	4.8	1.8	Iris-virginica
59	6.2	2.9	4.3	1.3	Iris-versicolor
60	6.3	2.3	4.4	1.3	Iris-versicolor
61	6.3	2.7	4.9	1.8	Iris-virginica
62	6.4	3.2	5.3	2.3	Iris-virginica
63	6.5	2.8	4.6	1.5	Iris-versicolor
64	6.5	3.0	5.2	2.0	Iris-virginica
65	6.5	3.2	5.1	2.0	Iris-virginica
66	6.6	2.9	4.6	1.3	Iris-versicolor
67	6.6	3.0	4.4	1.4	Iris-versicolor
68	6.7	3.1	4.4	1.4	Iris-versicolor
69	6.7	3.1	4.7	1.5	Iris-versicolor
70	6.9	3.1	4.9	1.5	Iris-versicolor
71	6.9	3.1	5.4	2.1	Iris-virginica
72	6.9	3.2	5.7	2.3	Iris-virginica
73	7.2	3.0	5.8	1.6	Iris-virginica
74	7.2	3.2	6.0	1.8	Iris-virginica
75	7.3	2.9	6.3	1.8	Iris-virginica
76	7.7	2.6	6.9	2.3	Iris-virginica
77	3.3	4.5	5.6	7.8	Iris-setosa
78	3.3	4.5	5.6	7.8	Iris-setosa
79	3.3	4.5	5.6	7.8	Iris-setosa
80	3.3	4.5	5.6	7.8	Iris-setosa
81	3.3	4.5	5.6	7.8	Iris-setosa
82	3.3	4.5	5.6	7.8	Iris-setosa
83	3.3	4.5	5.6	7.8	Iris-setosa
84	3.3	4.5	5.6	7.8	Iris-setosa
85	3.3	4.5	5.6	7.8	Iris-setosa
86	3.3	4.5	5.6	7.8	Iris-setosa
87	3.3	4.5	5.6	7.8	Iris-setosa
88	3.3	4.5	5.6	7.8	Iris-setosa
89	3.3	4.5	5.6	7.8	Iris-setosa
90	3.3	4.5	5.6	7.8	Iris-setosa
91	3.3	4.5	5.6	7.8	Iris-setosa
92	3.3	4.5	5.6	7.8	Iris-setosa
93	3.3	4.5	5.6	7.8	Iris-setosa
94	3.3	4.5	5.6	7.8	Iris-setosa
95	3.3	4.5	5.6	7.8	Iris-setosa
96	3.3	4.5	5.6	7.8	Iris-setosa
97	3.3	4.5	5.6	7.8	Iris-setosa
98	3.3	4.5	5.6	7.8	Iris-setosa
99	3.3	4.5	5.6	7.8	Iris-setosa
100	3.3	4.5	5.6	7.8	Iris-setosa

Rows: 1-100 | Columns: 5

Note

VerticaPy offers a wide range of sample datasets that are ideal for training and testing purposes. You can explore the full list of available datasets in the Datasets, which provides detailed information on each dataset and how to use them effectively. These datasets are invaluable resources for honing your data analysis and machine learning skills within the VerticaPy environment.

Data Exploration¶

Through a quick scatter plot, we can observe that the data has three main clusters.

data.scatter(
    columns = ["PetalLengthCm", "SepalLengthCm"],
    by = "Species",
)

Elbow Curve¶

Let’s compute the optimal k for our KMeans algorithm and check if it aligns with the three clusters we observed earlier.

To achieve this, let’s create the Elbow curve.

from verticapy.machine_learning.model_selection import elbow

elbow(
    input_relation = data,
    X = data.get_columns(exclude_columns= "Species"), # All columns except Species
    n_cluster = (1, 100),
    init = "kmeanspp",
)

Note

You can experiment with the Elbow score to determine the optimal number of clusters. The score is based on the ratio of Between -Cluster Sum of Squares to Total Sum of Squares, providing a way to assess the clustering accuracy. A score of 1 indicates a perfect clustering.

Note

It’s evident from the Elbow curve that k=3 is a suitable choice, indicating the optimal number of clusters for the KMeans algorithm.