verticapy.machine_learning.vertica.cluster.KMeans#
- class verticapy.machine_learning.vertica.cluster.KMeans(name: str = None, overwrite_model: bool = False, n_cluster: int = 8, init: Literal['kmeanspp', 'random'] | list = 'kmeanspp', max_iter: int = 300, tol: float = 0.0001)#
Creates a KMeans object using the Vertica k-means algorithm. k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells.
Parameters#
- name: str, optional
Name of the model. The model is stored in the database.
- overwrite_model: bool, optional
If set to
True
, training a model with the same name as an existing model overwrites the existing model.- n_cluster: int, optional
Number of clusters
- init: str | list, optional
The method used to find the initial cluster centers.
- kmeanspp:
Uses the KMeans++ method to initialize the centers.
- random:
The centers are initialized randomly.
You can also provide a list with the initial cluster centers.
- max_iter: int, optional
The maximum number of iterations the algorithm performs.
- 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.
Attributes#
Many attributes are created during the fitting phase.
- clusters_: numpy.array
Cluster centers.
- p_: int
The
p
of thep
-distances.- between_cluster_ss_: float
The between-cluster sum of squares (BSS) measures the dispersion between different clusters and is an important metric in evaluating the effectiveness of a clustering algorithm.
- total_ss_: float
The total sum of squares (TSS) is used to assess the total dispersion of data points from the overall mean, providing a basis for evaluating the clustering algorithm’s performance.
- total_within_cluster_ss_: float
The within-cluster sum of squares (WSS) gauges the dispersion of data points within individual clusters in a clustering analysis. It reflects the compactness of clusters and is instrumental in evaluating the homogeneity of the clusters produced by the algorithm.
- elbow_score_: float
The elbow score. It helps identify the optimal number of clusters by observing the point where the rate of WSS reduction slows down, resembling the bend or ‘elbow’ in the plot, indicative of an optimal clustering solution. The bigger the better.
- converged_: boolean
True if the model converged.
Note
All attributes can be accessed using the
get_attributes()
method.Note
Several other attributes can be accessed by using the
get_vertica_attributes()
method.Examples#
The following examples provide a basic understanding of usage. For more detailed examples, please refer to the Machine Learning or the Examples section on the website.
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 fromverticapy
are used as intended without interfering with functions from other libraries.For this example, we will use the winequality dataset.
import verticapy.datasets as vpd data = vpd.load_winequality()
123fixed_acidityNumeric(8)123volatile_acidityNumeric(9)123citric_acidNumeric(8)123residual_sugarNumeric(9)123chloridesFloat(22)123free_sulfur_dioxideNumeric(9)123total_sulfur_dioxideNumeric(9)123densityFloat(22)123pHNumeric(8)123sulphatesNumeric(8)123alcoholFloat(22)123qualityInteger123goodIntegerAbccolorVarchar(20)1 3.8 0.31 0.02 11.1 0.036 20.0 114.0 0.99248 3.75 0.44 12.4 6 0 white 2 3.9 0.225 0.4 4.2 0.03 29.0 118.0 0.989 3.57 0.36 12.8 8 1 white 3 4.2 0.17 0.36 1.8 0.029 93.0 161.0 0.98999 3.65 0.89 12.0 7 1 white 4 4.2 0.215 0.23 5.1 0.041 64.0 157.0 0.99688 3.42 0.44 8.0 3 0 white 5 4.4 0.32 0.39 4.3 0.03 31.0 127.0 0.98904 3.46 0.36 12.8 8 1 white 6 4.4 0.46 0.1 2.8 0.024 31.0 111.0 0.98816 3.48 0.34 13.1 6 0 white 7 4.4 0.54 0.09 5.1 0.038 52.0 97.0 0.99022 3.41 0.4 12.2 7 1 white 8 4.5 0.19 0.21 0.95 0.033 89.0 159.0 0.99332 3.34 0.42 8.0 5 0 white 9 4.6 0.445 0.0 1.4 0.053 11.0 178.0 0.99426 3.79 0.55 10.2 5 0 white 10 4.6 0.52 0.15 2.1 0.054 8.0 65.0 0.9934 3.9 0.56 13.1 4 0 red 11 4.7 0.145 0.29 1.0 0.042 35.0 90.0 0.9908 3.76 0.49 11.3 6 0 white 12 4.7 0.335 0.14 1.3 0.036 69.0 168.0 0.99212 3.47 0.46 10.5 5 0 white 13 4.7 0.455 0.18 1.9 0.036 33.0 106.0 0.98746 3.21 0.83 14.0 7 1 white 14 4.7 0.6 0.17 2.3 0.058 17.0 106.0 0.9932 3.85 0.6 12.9 6 0 red 15 4.7 0.67 0.09 1.0 0.02 5.0 9.0 0.98722 3.3 0.34 13.6 5 0 white 16 4.7 0.785 0.0 3.4 0.036 23.0 134.0 0.98981 3.53 0.92 13.8 6 0 white 17 4.8 0.13 0.32 1.2 0.042 40.0 98.0 0.9898 3.42 0.64 11.8 7 1 white 18 4.8 0.17 0.28 2.9 0.03 22.0 111.0 0.9902 3.38 0.34 11.3 7 1 white 19 4.8 0.21 0.21 10.2 0.037 17.0 112.0 0.99324 3.66 0.48 12.2 7 1 white 20 4.8 0.225 0.38 1.2 0.074 47.0 130.0 0.99132 3.31 0.4 10.3 6 0 white 21 4.8 0.26 0.23 10.6 0.034 23.0 111.0 0.99274 3.46 0.28 11.5 7 1 white 22 4.8 0.29 0.23 1.1 0.044 38.0 180.0 0.98924 3.28 0.34 11.9 6 0 white 23 4.8 0.33 0.0 6.5 0.028 34.0 163.0 0.9937 3.35 0.61 9.9 5 0 white 24 4.8 0.34 0.0 6.5 0.028 33.0 163.0 0.9939 3.36 0.61 9.9 6 0 white 25 4.8 0.65 0.12 1.1 0.013 4.0 10.0 0.99246 3.32 0.36 13.5 4 0 white 26 4.9 0.235 0.27 11.75 0.03 34.0 118.0 0.9954 3.07 0.5 9.4 6 0 white 27 4.9 0.33 0.31 1.2 0.016 39.0 150.0 0.98713 3.33 0.59 14.0 8 1 white 28 4.9 0.335 0.14 1.3 0.036 69.0 168.0 0.99212 3.47 0.46 10.4666666666667 5 0 white 29 4.9 0.335 0.14 1.3 0.036 69.0 168.0 0.99212 3.47 0.46 10.4666666666667 5 0 white 30 4.9 0.345 0.34 1.0 0.068 32.0 143.0 0.99138 3.24 0.4 10.1 5 0 white 31 4.9 0.345 0.34 1.0 0.068 32.0 143.0 0.99138 3.24 0.4 10.1 5 0 white 32 4.9 0.42 0.0 2.1 0.048 16.0 42.0 0.99154 3.71 0.74 14.0 7 1 red 33 4.9 0.47 0.17 1.9 0.035 60.0 148.0 0.98964 3.27 0.35 11.5 6 0 white 34 5.0 0.17 0.56 1.5 0.026 24.0 115.0 0.9906 3.48 0.39 10.8 7 1 white 35 5.0 0.2 0.4 1.9 0.015 20.0 98.0 0.9897 3.37 0.55 12.05 6 0 white 36 5.0 0.235 0.27 11.75 0.03 34.0 118.0 0.9954 3.07 0.5 9.4 6 0 white 37 5.0 0.24 0.19 5.0 0.043 17.0 101.0 0.99438 3.67 0.57 10.0 5 0 white 38 5.0 0.24 0.21 2.2 0.039 31.0 100.0 0.99098 3.69 0.62 11.7 6 0 white 39 5.0 0.24 0.34 1.1 0.034 49.0 158.0 0.98774 3.32 0.32 13.1 7 1 white 40 5.0 0.255 0.22 2.7 0.043 46.0 153.0 0.99238 3.75 0.76 11.3 6 0 white 41 5.0 0.27 0.32 4.5 0.032 58.0 178.0 0.98956 3.45 0.31 12.6 7 1 white 42 5.0 0.27 0.32 4.5 0.032 58.0 178.0 0.98956 3.45 0.31 12.6 7 1 white 43 5.0 0.27 0.4 1.2 0.076 42.0 124.0 0.99204 3.32 0.47 10.1 6 0 white 44 5.0 0.29 0.54 5.7 0.035 54.0 155.0 0.98976 3.27 0.34 12.9 8 1 white 45 5.0 0.3 0.33 3.7 0.03 54.0 173.0 0.9887 3.36 0.3 13.0 7 1 white 46 5.0 0.31 0.0 6.4 0.046 43.0 166.0 0.994 3.3 0.63 9.9 6 0 white 47 5.0 0.33 0.16 1.5 0.049 10.0 97.0 0.9917 3.48 0.44 10.7 6 0 white 48 5.0 0.33 0.16 1.5 0.049 10.0 97.0 0.9917 3.48 0.44 10.7 6 0 white 49 5.0 0.33 0.16 1.5 0.049 10.0 97.0 0.9917 3.48 0.44 10.7 6 0 white 50 5.0 0.33 0.18 4.6 0.032 40.0 124.0 0.99114 3.18 0.4 11.0 6 0 white 51 5.0 0.33 0.23 11.8 0.03 23.0 158.0 0.99322 3.41 0.64 11.8 6 0 white 52 5.0 0.35 0.25 7.8 0.031 24.0 116.0 0.99241 3.39 0.4 11.3 6 0 white 53 5.0 0.35 0.25 7.8 0.031 24.0 116.0 0.99241 3.39 0.4 11.3 6 0 white 54 5.0 0.38 0.01 1.6 0.048 26.0 60.0 0.99084 3.7 0.75 14.0 6 0 red 55 5.0 0.4 0.5 4.3 0.046 29.0 80.0 0.9902 3.49 0.66 13.6 6 0 red 56 5.0 0.42 0.24 2.0 0.06 19.0 50.0 0.9917 3.72 0.74 14.0 8 1 red 57 5.0 0.44 0.04 18.6 0.039 38.0 128.0 0.9985 3.37 0.57 10.2 6 0 white 58 5.0 0.455 0.18 1.9 0.036 33.0 106.0 0.98746 3.21 0.83 14.0 7 1 white 59 5.0 0.55 0.14 8.3 0.032 35.0 164.0 0.9918 3.53 0.51 12.5 8 1 white 60 5.0 0.61 0.12 1.3 0.009 65.0 100.0 0.9874 3.26 0.37 13.5 5 0 white 61 5.0 0.74 0.0 1.2 0.041 16.0 46.0 0.99258 4.01 0.59 12.5 6 0 red 62 5.0 1.02 0.04 1.4 0.045 41.0 85.0 0.9938 3.75 0.48 10.5 4 0 red 63 5.0 1.04 0.24 1.6 0.05 32.0 96.0 0.9934 3.74 0.62 11.5 5 0 red 64 5.1 0.11 0.32 1.6 0.028 12.0 90.0 0.99008 3.57 0.52 12.2 6 0 white 65 5.1 0.14 0.25 0.7 0.039 15.0 89.0 0.9919 3.22 0.43 9.2 6 0 white 66 5.1 0.165 0.22 5.7 0.047 42.0 146.0 0.9934 3.18 0.55 9.9 6 0 white 67 5.1 0.21 0.28 1.4 0.047 48.0 148.0 0.99168 3.5 0.49 10.4 5 0 white 68 5.1 0.23 0.18 1.0 0.053 13.0 99.0 0.98956 3.22 0.39 11.5 5 0 white 69 5.1 0.25 0.36 1.3 0.035 40.0 78.0 0.9891 3.23 0.64 12.1 7 1 white 70 5.1 0.26 0.33 1.1 0.027 46.0 113.0 0.98946 3.35 0.43 11.4 7 1 white 71 5.1 0.26 0.34 6.4 0.034 26.0 99.0 0.99449 3.23 0.41 9.2 6 0 white 72 5.1 0.29 0.28 8.3 0.026 27.0 107.0 0.99308 3.36 0.37 11.0 6 0 white 73 5.1 0.29 0.28 8.3 0.026 27.0 107.0 0.99308 3.36 0.37 11.0 6 0 white 74 5.1 0.3 0.3 2.3 0.048 40.0 150.0 0.98944 3.29 0.46 12.2 6 0 white 75 5.1 0.305 0.13 1.75 0.036 17.0 73.0 0.99 3.4 0.51 12.3333333333333 5 0 white 76 5.1 0.31 0.3 0.9 0.037 28.0 152.0 0.992 3.54 0.56 10.1 6 0 white 77 5.1 0.33 0.22 1.6 0.027 18.0 89.0 0.9893 3.51 0.38 12.5 7 1 white 78 5.1 0.33 0.22 1.6 0.027 18.0 89.0 0.9893 3.51 0.38 12.5 7 1 white 79 5.1 0.33 0.22 1.6 0.027 18.0 89.0 0.9893 3.51 0.38 12.5 7 1 white 80 5.1 0.33 0.27 6.7 0.022 44.0 129.0 0.99221 3.36 0.39 11.0 7 1 white 81 5.1 0.35 0.26 6.8 0.034 36.0 120.0 0.99188 3.38 0.4 11.5 6 0 white 82 5.1 0.35 0.26 6.8 0.034 36.0 120.0 0.99188 3.38 0.4 11.5 6 0 white 83 5.1 0.35 0.26 6.8 0.034 36.0 120.0 0.99188 3.38 0.4 11.5 6 0 white 84 5.1 0.39 0.21 1.7 0.027 15.0 72.0 0.9894 3.5 0.45 12.5 6 0 white 85 5.1 0.42 0.0 1.8 0.044 18.0 88.0 0.99157 3.68 0.73 13.6 7 1 red 86 5.1 0.42 0.01 1.5 0.017 25.0 102.0 0.9894 3.38 0.36 12.3 7 1 white 87 5.1 0.47 0.02 1.3 0.034 18.0 44.0 0.9921 3.9 0.62 12.8 6 0 red 88 5.1 0.51 0.18 2.1 0.042 16.0 101.0 0.9924 3.46 0.87 12.9 7 1 red 89 5.1 0.52 0.06 2.7 0.052 30.0 79.0 0.9932 3.32 0.43 9.3 5 0 white 90 5.1 0.585 0.0 1.7 0.044 14.0 86.0 0.99264 3.56 0.94 12.9 7 1 red 91 5.2 0.155 0.33 1.6 0.028 13.0 59.0 0.98975 3.3 0.84 11.9 8 1 white 92 5.2 0.155 0.33 1.6 0.028 13.0 59.0 0.98975 3.3 0.84 11.9 8 1 white 93 5.2 0.16 0.34 0.8 0.029 26.0 77.0 0.99155 3.25 0.51 10.1 6 0 white 94 5.2 0.17 0.27 0.7 0.03 11.0 68.0 0.99218 3.3 0.41 9.8 5 0 white 95 5.2 0.185 0.22 1.0 0.03 47.0 123.0 0.99218 3.55 0.44 10.15 6 0 white 96 5.2 0.2 0.27 3.2 0.047 16.0 93.0 0.99235 3.44 0.53 10.1 7 1 white 97 5.2 0.21 0.31 1.7 0.048 17.0 61.0 0.98953 3.24 0.37 12.0 7 1 white 98 5.2 0.22 0.46 6.2 0.066 41.0 187.0 0.99362 3.19 0.42 9.73333333333333 5 0 white 99 5.2 0.24 0.15 7.1 0.043 32.0 134.0 0.99378 3.24 0.48 9.9 6 0 white 100 5.2 0.24 0.45 3.8 0.027 21.0 128.0 0.992 3.55 0.49 11.2 8 1 white Rows: 1-100 | Columns: 14Note
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.
Model Initialization#
First we import the
KMeans
model:from verticapy.machine_learning.vertica import KMeans
Then we can create the model:
model = KMeans( n_cluster = 8, init = "kmeanspp", max_iter = 300, tol = 1e-4, )
Hint
In
verticapy
1.0.x and higher, you do not need to specify the model name, as the name is automatically assigned. If you need to re-use the model, you can fetch the model name from the model’s attributes.Important
The model name is crucial for the model management system and versioning. It’s highly recommended to provide a name if you plan to reuse the model later.
Model Training#
We can now fit the model:
model.fit(data, X = ["density", "sulphates"])
Important
To train a model, you can directly use the
vDataFrame
or the name of the relation stored in the database. The test set is optional and is only used to compute the test metrics. Inverticapy
, we don’t work usingX
matrices andy
vectors. Instead, we work directly with lists of predictors and the response name.Hint
For clustering and anomaly detection, the use of predictors is optional. In such cases, all available predictors are considered, which can include solely numerical variables or a combination of numerical and categorical variables, depending on the model’s capabilities.
Metrics#
You can also find the cluster positions by:
model.clusters_ Out[4]: array([[0.99323361, 0.35585533], [0.9978 , 1.97 ], [0.99615961, 0.98726563], [0.99493945, 0.52172628], [0.99587528, 0.77439929], [0.997116 , 1.37866667], [0.99424531, 0.43739159], [0.99531657, 0.62767176]])
To evaluate the model, various attributes are computed, such as the between sum of squares, the total within clusters sum of squares, and the total sum of squares.
model.between_cluster_ss_ Out[5]: 136.36947 model.total_within_cluster_ss_ Out[6]: 7.5310924 model.total_ss_ Out[7]: 143.90056
Some other useful attributes can be used to evaluate the model, like the Elbow Score (the bigger it is, the better it is).
model.elbow_score_ Out[8]: 0.9476646234038283
Prediction#
Predicting or ranking the dataset is straight-forward:
model.predict(data, ["density", "sulphates"], name = "Cluster IDs")
123fixed_acidityNumeric(8)123volatile_acidityNumeric(9)123citric_acidNumeric(8)123residual_sugarNumeric(9)123chloridesFloat(22)123free_sulfur_dioxideNumeric(9)123total_sulfur_dioxideNumeric(9)123densityFloat(22)123pHNumeric(8)123sulphatesNumeric(8)123alcoholFloat(22)123qualityInteger123goodIntegerAbccolorVarchar(20)123Cluster IDsInteger1 3.8 0.31 0.02 11.1 0.036 20.0 114.0 0.99248 3.75 0.44 12.4 6 0 white 6 2 3.9 0.225 0.4 4.2 0.03 29.0 118.0 0.989 3.57 0.36 12.8 8 1 white 0 3 4.2 0.17 0.36 1.8 0.029 93.0 161.0 0.98999 3.65 0.89 12.0 7 1 white 2 4 4.2 0.215 0.23 5.1 0.041 64.0 157.0 0.99688 3.42 0.44 8.0 3 0 white 6 5 4.4 0.32 0.39 4.3 0.03 31.0 127.0 0.98904 3.46 0.36 12.8 8 1 white 0 6 4.4 0.46 0.1 2.8 0.024 31.0 111.0 0.98816 3.48 0.34 13.1 6 0 white 0 7 4.4 0.54 0.09 5.1 0.038 52.0 97.0 0.99022 3.41 0.4 12.2 7 1 white 6 8 4.5 0.19 0.21 0.95 0.033 89.0 159.0 0.99332 3.34 0.42 8.0 5 0 white 6 9 4.6 0.445 0.0 1.4 0.053 11.0 178.0 0.99426 3.79 0.55 10.2 5 0 white 3 10 4.6 0.52 0.15 2.1 0.054 8.0 65.0 0.9934 3.9 0.56 13.1 4 0 red 3 11 4.7 0.145 0.29 1.0 0.042 35.0 90.0 0.9908 3.76 0.49 11.3 6 0 white 3 12 4.7 0.335 0.14 1.3 0.036 69.0 168.0 0.99212 3.47 0.46 10.5 5 0 white 6 13 4.7 0.455 0.18 1.9 0.036 33.0 106.0 0.98746 3.21 0.83 14.0 7 1 white 4 14 4.7 0.6 0.17 2.3 0.058 17.0 106.0 0.9932 3.85 0.6 12.9 6 0 red 7 15 4.7 0.67 0.09 1.0 0.02 5.0 9.0 0.98722 3.3 0.34 13.6 5 0 white 0 16 4.7 0.785 0.0 3.4 0.036 23.0 134.0 0.98981 3.53 0.92 13.8 6 0 white 2 17 4.8 0.13 0.32 1.2 0.042 40.0 98.0 0.9898 3.42 0.64 11.8 7 1 white 7 18 4.8 0.17 0.28 2.9 0.03 22.0 111.0 0.9902 3.38 0.34 11.3 7 1 white 0 19 4.8 0.21 0.21 10.2 0.037 17.0 112.0 0.99324 3.66 0.48 12.2 7 1 white 3 20 4.8 0.225 0.38 1.2 0.074 47.0 130.0 0.99132 3.31 0.4 10.3 6 0 white 6 21 4.8 0.26 0.23 10.6 0.034 23.0 111.0 0.99274 3.46 0.28 11.5 7 1 white 0 22 4.8 0.29 0.23 1.1 0.044 38.0 180.0 0.98924 3.28 0.34 11.9 6 0 white 0 23 4.8 0.33 0.0 6.5 0.028 34.0 163.0 0.9937 3.35 0.61 9.9 5 0 white 7 24 4.8 0.34 0.0 6.5 0.028 33.0 163.0 0.9939 3.36 0.61 9.9 6 0 white 7 25 4.8 0.65 0.12 1.1 0.013 4.0 10.0 0.99246 3.32 0.36 13.5 4 0 white 0 26 4.9 0.235 0.27 11.75 0.03 34.0 118.0 0.9954 3.07 0.5 9.4 6 0 white 3 27 4.9 0.33 0.31 1.2 0.016 39.0 150.0 0.98713 3.33 0.59 14.0 8 1 white 7 28 4.9 0.335 0.14 1.3 0.036 69.0 168.0 0.99212 3.47 0.46 10.4666666666667 5 0 white 6 29 4.9 0.335 0.14 1.3 0.036 69.0 168.0 0.99212 3.47 0.46 10.4666666666667 5 0 white 6 30 4.9 0.345 0.34 1.0 0.068 32.0 143.0 0.99138 3.24 0.4 10.1 5 0 white 6 31 4.9 0.345 0.34 1.0 0.068 32.0 143.0 0.99138 3.24 0.4 10.1 5 0 white 6 32 4.9 0.42 0.0 2.1 0.048 16.0 42.0 0.99154 3.71 0.74 14.0 7 1 red 4 33 4.9 0.47 0.17 1.9 0.035 60.0 148.0 0.98964 3.27 0.35 11.5 6 0 white 0 34 5.0 0.17 0.56 1.5 0.026 24.0 115.0 0.9906 3.48 0.39 10.8 7 1 white 0 35 5.0 0.2 0.4 1.9 0.015 20.0 98.0 0.9897 3.37 0.55 12.05 6 0 white 3 36 5.0 0.235 0.27 11.75 0.03 34.0 118.0 0.9954 3.07 0.5 9.4 6 0 white 3 37 5.0 0.24 0.19 5.0 0.043 17.0 101.0 0.99438 3.67 0.57 10.0 5 0 white 3 38 5.0 0.24 0.21 2.2 0.039 31.0 100.0 0.99098 3.69 0.62 11.7 6 0 white 7 39 5.0 0.24 0.34 1.1 0.034 49.0 158.0 0.98774 3.32 0.32 13.1 7 1 white 0 40 5.0 0.255 0.22 2.7 0.043 46.0 153.0 0.99238 3.75 0.76 11.3 6 0 white 4 41 5.0 0.27 0.32 4.5 0.032 58.0 178.0 0.98956 3.45 0.31 12.6 7 1 white 0 42 5.0 0.27 0.32 4.5 0.032 58.0 178.0 0.98956 3.45 0.31 12.6 7 1 white 0 43 5.0 0.27 0.4 1.2 0.076 42.0 124.0 0.99204 3.32 0.47 10.1 6 0 white 6 44 5.0 0.29 0.54 5.7 0.035 54.0 155.0 0.98976 3.27 0.34 12.9 8 1 white 0 45 5.0 0.3 0.33 3.7 0.03 54.0 173.0 0.9887 3.36 0.3 13.0 7 1 white 0 46 5.0 0.31 0.0 6.4 0.046 43.0 166.0 0.994 3.3 0.63 9.9 6 0 white 7 47 5.0 0.33 0.16 1.5 0.049 10.0 97.0 0.9917 3.48 0.44 10.7 6 0 white 6 48 5.0 0.33 0.16 1.5 0.049 10.0 97.0 0.9917 3.48 0.44 10.7 6 0 white 6 49 5.0 0.33 0.16 1.5 0.049 10.0 97.0 0.9917 3.48 0.44 10.7 6 0 white 6 50 5.0 0.33 0.18 4.6 0.032 40.0 124.0 0.99114 3.18 0.4 11.0 6 0 white 6 51 5.0 0.33 0.23 11.8 0.03 23.0 158.0 0.99322 3.41 0.64 11.8 6 0 white 7 52 5.0 0.35 0.25 7.8 0.031 24.0 116.0 0.99241 3.39 0.4 11.3 6 0 white 6 53 5.0 0.35 0.25 7.8 0.031 24.0 116.0 0.99241 3.39 0.4 11.3 6 0 white 6 54 5.0 0.38 0.01 1.6 0.048 26.0 60.0 0.99084 3.7 0.75 14.0 6 0 red 4 55 5.0 0.4 0.5 4.3 0.046 29.0 80.0 0.9902 3.49 0.66 13.6 6 0 red 7 56 5.0 0.42 0.24 2.0 0.06 19.0 50.0 0.9917 3.72 0.74 14.0 8 1 red 4 57 5.0 0.44 0.04 18.6 0.039 38.0 128.0 0.9985 3.37 0.57 10.2 6 0 white 3 58 5.0 0.455 0.18 1.9 0.036 33.0 106.0 0.98746 3.21 0.83 14.0 7 1 white 4 59 5.0 0.55 0.14 8.3 0.032 35.0 164.0 0.9918 3.53 0.51 12.5 8 1 white 3 60 5.0 0.61 0.12 1.3 0.009 65.0 100.0 0.9874 3.26 0.37 13.5 5 0 white 0 61 5.0 0.74 0.0 1.2 0.041 16.0 46.0 0.99258 4.01 0.59 12.5 6 0 red 7 62 5.0 1.02 0.04 1.4 0.045 41.0 85.0 0.9938 3.75 0.48 10.5 4 0 red 3 63 5.0 1.04 0.24 1.6 0.05 32.0 96.0 0.9934 3.74 0.62 11.5 5 0 red 7 64 5.1 0.11 0.32 1.6 0.028 12.0 90.0 0.99008 3.57 0.52 12.2 6 0 white 3 65 5.1 0.14 0.25 0.7 0.039 15.0 89.0 0.9919 3.22 0.43 9.2 6 0 white 6 66 5.1 0.165 0.22 5.7 0.047 42.0 146.0 0.9934 3.18 0.55 9.9 6 0 white 3 67 5.1 0.21 0.28 1.4 0.047 48.0 148.0 0.99168 3.5 0.49 10.4 5 0 white 3 68 5.1 0.23 0.18 1.0 0.053 13.0 99.0 0.98956 3.22 0.39 11.5 5 0 white 0 69 5.1 0.25 0.36 1.3 0.035 40.0 78.0 0.9891 3.23 0.64 12.1 7 1 white 7 70 5.1 0.26 0.33 1.1 0.027 46.0 113.0 0.98946 3.35 0.43 11.4 7 1 white 6 71 5.1 0.26 0.34 6.4 0.034 26.0 99.0 0.99449 3.23 0.41 9.2 6 0 white 6 72 5.1 0.29 0.28 8.3 0.026 27.0 107.0 0.99308 3.36 0.37 11.0 6 0 white 0 73 5.1 0.29 0.28 8.3 0.026 27.0 107.0 0.99308 3.36 0.37 11.0 6 0 white 0 74 5.1 0.3 0.3 2.3 0.048 40.0 150.0 0.98944 3.29 0.46 12.2 6 0 white 6 75 5.1 0.305 0.13 1.75 0.036 17.0 73.0 0.99 3.4 0.51 12.3333333333333 5 0 white 3 76 5.1 0.31 0.3 0.9 0.037 28.0 152.0 0.992 3.54 0.56 10.1 6 0 white 3 77 5.1 0.33 0.22 1.6 0.027 18.0 89.0 0.9893 3.51 0.38 12.5 7 1 white 0 78 5.1 0.33 0.22 1.6 0.027 18.0 89.0 0.9893 3.51 0.38 12.5 7 1 white 0 79 5.1 0.33 0.22 1.6 0.027 18.0 89.0 0.9893 3.51 0.38 12.5 7 1 white 0 80 5.1 0.33 0.27 6.7 0.022 44.0 129.0 0.99221 3.36 0.39 11.0 7 1 white 0 81 5.1 0.35 0.26 6.8 0.034 36.0 120.0 0.99188 3.38 0.4 11.5 6 0 white 6 82 5.1 0.35 0.26 6.8 0.034 36.0 120.0 0.99188 3.38 0.4 11.5 6 0 white 6 83 5.1 0.35 0.26 6.8 0.034 36.0 120.0 0.99188 3.38 0.4 11.5 6 0 white 6 84 5.1 0.39 0.21 1.7 0.027 15.0 72.0 0.9894 3.5 0.45 12.5 6 0 white 6 85 5.1 0.42 0.0 1.8 0.044 18.0 88.0 0.99157 3.68 0.73 13.6 7 1 red 4 86 5.1 0.42 0.01 1.5 0.017 25.0 102.0 0.9894 3.38 0.36 12.3 7 1 white 0 87 5.1 0.47 0.02 1.3 0.034 18.0 44.0 0.9921 3.9 0.62 12.8 6 0 red 7 88 5.1 0.51 0.18 2.1 0.042 16.0 101.0 0.9924 3.46 0.87 12.9 7 1 red 4 89 5.1 0.52 0.06 2.7 0.052 30.0 79.0 0.9932 3.32 0.43 9.3 5 0 white 6 90 5.1 0.585 0.0 1.7 0.044 14.0 86.0 0.99264 3.56 0.94 12.9 7 1 red 2 91 5.2 0.155 0.33 1.6 0.028 13.0 59.0 0.98975 3.3 0.84 11.9 8 1 white 4 92 5.2 0.155 0.33 1.6 0.028 13.0 59.0 0.98975 3.3 0.84 11.9 8 1 white 4 93 5.2 0.16 0.34 0.8 0.029 26.0 77.0 0.99155 3.25 0.51 10.1 6 0 white 3 94 5.2 0.17 0.27 0.7 0.03 11.0 68.0 0.99218 3.3 0.41 9.8 5 0 white 6 95 5.2 0.185 0.22 1.0 0.03 47.0 123.0 0.99218 3.55 0.44 10.15 6 0 white 6 96 5.2 0.2 0.27 3.2 0.047 16.0 93.0 0.99235 3.44 0.53 10.1 7 1 white 3 97 5.2 0.21 0.31 1.7 0.048 17.0 61.0 0.98953 3.24 0.37 12.0 7 1 white 0 98 5.2 0.22 0.46 6.2 0.066 41.0 187.0 0.99362 3.19 0.42 9.73333333333333 5 0 white 6 99 5.2 0.24 0.15 7.1 0.043 32.0 134.0 0.99378 3.24 0.48 9.9 6 0 white 3 100 5.2 0.24 0.45 3.8 0.027 21.0 128.0 0.992 3.55 0.49 11.2 8 1 white 3 Rows: 1-100 | Columns: 15As shown above, a new column has been created, containing the clusters.
Hint
The name of the new column is optional. If not provided, it is randomly assigned.
Plots - Cluster Plot#
Plots highlighting the different clusters can be easily drawn using:
model.plot()
Plots - Voronoi#
KMeans
models can be visualized by drawing their voronoi plots. For more examples, check out Machine Learning - Voronoi Plots.model.plot_voronoi()
Plots - Contour#
In order to understand the parameter space, we can also look at the contour plots:
model.contour()