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vastorbit.machine_learning.model_selection.elbow

vastorbit.machine_learning.model_selection.elbow(input_relation: Annotated[str | VastFrame, ''], X: Annotated[str | list[str], 'STRING representing one column or a list of columns'] | None = None, n_clusters: tuple | list = (1, 15), init: Literal['k-means++', 'random', None] = None, max_iter: int = 50, tol: float = 0.0001, show: bool = True, chart: PlottingBase | TableSample | Axes | mFigure | 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_clusters (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.

    • k-means++:

      Use the k-means++ method to initialize the centers.

    • random:

      Randomly subsamples the data to find initial centers.

    Default value is k-means++.

  • 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.

  • 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:

nb_clusters,total_within_clusters_ss,between_clusters_ss,total_ss, elbow_score

Return type:

TableSample

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 vastorbit:

import vastorbit as vo

Hint

By assigning an alias to vastorbit, we mitigate the risk of code collisions with other libraries. This precaution is necessary because vastorbit 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 vastorbit are used as intended without interfering with functions from other libraries.

For this example, we will use the iris dataset.

import vastorbit.datasets as vod

data = vod.load_iris()
123
sepallengthcm
Decimal(5, 2)
123
sepalwidthcm
Decimal(5, 2)
123
petallengthcm
Decimal(5, 2)
123
petalwidthcm
Decimal(5, 2)
Abc
species
Varchar(30)
15.13.51.40.2Iris-setosa
24.93.01.40.2Iris-setosa
34.73.21.30.2Iris-setosa
44.63.11.50.2Iris-setosa
55.03.61.40.2Iris-setosa
65.43.91.70.4Iris-setosa
74.63.41.40.3Iris-setosa
85.03.41.50.2Iris-setosa
94.42.91.40.2Iris-setosa
104.93.11.50.1Iris-setosa
115.43.71.50.2Iris-setosa
124.83.41.60.2Iris-setosa
134.83.01.40.1Iris-setosa
144.33.01.10.1Iris-setosa
155.84.01.20.2Iris-setosa
165.74.41.50.4Iris-setosa
175.43.91.30.4Iris-setosa
185.13.51.40.3Iris-setosa
195.73.81.70.3Iris-setosa
205.13.81.50.3Iris-setosa
215.43.41.70.2Iris-setosa
225.13.71.50.4Iris-setosa
234.63.61.00.2Iris-setosa
245.13.31.70.5Iris-setosa
254.83.41.90.2Iris-setosa
265.03.01.60.2Iris-setosa
275.03.41.60.4Iris-setosa
285.23.51.50.2Iris-setosa
295.23.41.40.2Iris-setosa
304.73.21.60.2Iris-setosa
314.83.11.60.2Iris-setosa
325.43.41.50.4Iris-setosa
335.24.11.50.1Iris-setosa
345.54.21.40.2Iris-setosa
354.93.11.50.1Iris-setosa
365.03.21.20.2Iris-setosa
375.53.51.30.2Iris-setosa
384.93.11.50.1Iris-setosa
394.43.01.30.2Iris-setosa
405.13.41.50.2Iris-setosa
415.03.51.30.3Iris-setosa
424.52.31.30.3Iris-setosa
434.43.21.30.2Iris-setosa
445.03.51.60.6Iris-setosa
455.13.81.90.4Iris-setosa
464.83.01.40.3Iris-setosa
475.13.81.60.2Iris-setosa
484.63.21.40.2Iris-setosa
495.33.71.50.2Iris-setosa
505.03.31.40.2Iris-setosa
517.03.24.71.4Iris-versicolor
526.43.24.51.5Iris-versicolor
536.93.14.91.5Iris-versicolor
545.52.34.01.3Iris-versicolor
556.52.84.61.5Iris-versicolor
565.72.84.51.3Iris-versicolor
576.33.34.71.6Iris-versicolor
584.92.43.31.0Iris-versicolor
596.62.94.61.3Iris-versicolor
605.22.73.91.4Iris-versicolor
615.02.03.51.0Iris-versicolor
625.93.04.21.5Iris-versicolor
636.02.24.01.0Iris-versicolor
646.12.94.71.4Iris-versicolor
655.62.93.61.3Iris-versicolor
666.73.14.41.4Iris-versicolor
675.63.04.51.5Iris-versicolor
685.82.74.11.0Iris-versicolor
696.22.24.51.5Iris-versicolor
705.62.53.91.1Iris-versicolor
715.93.24.81.8Iris-versicolor
726.12.84.01.3Iris-versicolor
736.32.54.91.5Iris-versicolor
746.12.84.71.2Iris-versicolor
756.42.94.31.3Iris-versicolor
766.63.04.41.4Iris-versicolor
776.82.84.81.4Iris-versicolor
786.73.05.01.7Iris-versicolor
796.02.94.51.5Iris-versicolor
805.72.63.51.0Iris-versicolor
815.52.43.81.1Iris-versicolor
825.52.43.71.0Iris-versicolor
835.82.73.91.2Iris-versicolor
846.02.75.11.6Iris-versicolor
855.43.04.51.5Iris-versicolor
866.03.44.51.6Iris-versicolor
876.73.14.71.5Iris-versicolor
886.32.34.41.3Iris-versicolor
895.63.04.11.3Iris-versicolor
905.52.54.01.3Iris-versicolor
915.52.64.41.2Iris-versicolor
926.13.04.61.4Iris-versicolor
935.82.64.01.2Iris-versicolor
945.02.33.31.0Iris-versicolor
955.62.74.21.3Iris-versicolor
965.73.04.21.2Iris-versicolor
975.72.94.21.3Iris-versicolor
986.22.94.31.3Iris-versicolor
995.12.53.01.1Iris-versicolor
1005.72.84.11.3Iris-versicolor
Rows: 1-100 | Columns: 5

Note

vastorbit 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 vastorbit 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 vastorbit.machine_learning.model_selection import elbow

elbow(
    input_relation = data,
    X = data.get_columns(exclude_columns= "Species"), # All columns except Species
    n_clusters = (1, 100),
    init = "k-means++",
)

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.

See also

best_k() : Finds the KMeans k based on a score.