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verticapy.machine_learning.vertica.cluster.BisectingKMeans

class verticapy.machine_learning.vertica.cluster.BisectingKMeans(name: str = None, overwrite_model: bool = False, n_cluster: int = 8, bisection_iterations: int = 1, split_method: Literal['size', 'sum_squares'] = 'sum_squares', min_divisible_cluster_size: int = 2, distance_method: Literal['euclidean'] = 'euclidean', init: Literal['kmeanspp', 'pseudo', 'random'] | list = 'kmeanspp', max_iter: int = 300, tol: float = 0.0001)

Creates a BisectingKMeans object using the Vertica bisecting 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. Each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), which serves as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. Bisecting k-means combines k-means and hierarchical clustering.

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

bisection_iterations: int, optional

The number of iterations the bisecting KMeans algorithm performs for each bisection step. This corresponds to how many times a standalone KMeans algorithm runs in each bisection step. Setting to a value greater than 1 allows the algorithm to run and choose the best KMeans run within each bisection step. If you are using kmeanspp, the bisection_iterations value is always 1 because kmeanspp is more costly to run but also better than the alternatives, so it does not require multiple runs.

split_method: str, optional

The method used to choose a cluster to bisect/split.

• size:

  Choose the largest cluster to bisect.

• sum_squares:

  Choose the cluster with the largest withInSS to bisect.

min_divisible_cluster_size: int, optional

The minimum number of points of a divisible cluster. Must be greater than or equal to 2.

distance_method: str, optional

The distance measure between two data points. Only Euclidean distance is supported at this time.

init: str | list, optional

The method used to find the initial KMeans cluster centers.

• kmeanspp:

  Uses the KMeans++ method to initialize the centers.

• pseudo:

  Uses “pseudo center” approach used by Spark, bisects given center without iterating over points.

You can also provide a list with the initial cluster centers.

max_iter: int, optional

The maximum number of iterations the KMeans algorithm performs.

tol: float, optional

Determines whether the KMeans 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.

“children_left_”, “children_right_”,

tree_:

clusters_: numpy.array

Cluster centers.

p_: int

The p of the p-distances.

children_left_: numpy.array

A list of node IDs, where children_left[i] is the node ID of the left child of node i.

children_right_: numpy.array

A list of node IDs, where children_right[i] is the node ID of the right child of node i.

cluster_score_: numpy.array

The array containing the sizes for each cluster in a clustering analysis.

cluster_score_: numpy.array

The array containing the cluster scores for each cluster in a clustering analysis.

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.

cluster_i_ss_: numpy.array

The array containing the sum of squares (SS) for each cluster in a clustering analysis.

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 from verticapy 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()

	123 fixed_acidity Numeric(8)	123 volatile_acidity Numeric(9)	123 citric_acid Numeric(8)	123 residual_sugar Numeric(9)	123 chlorides Float(22)	123 free_sulfur_dioxide Numeric(9)	123 total_sulfur_dioxide Numeric(9)	123 density Float(22)	123 pH Numeric(8)	123 sulphates Numeric(8)	123 alcohol Float(22)	123 quality Integer	123 good Integer	Abc color Varchar(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: 14

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.

Model Initialization

First we import the BisectingKMeans model:

from verticapy.machine_learning.vertica import BisectingKMeans

Then we can create the model:

model = BisectingKMeans(
    n_cluster = 8,
    bisection_iterations = 1,
    split_method = 'sum_squares',
    min_divisible_cluster_size = 2,
    distance_method = "euclidean",
    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. In verticapy, we don’t work using X matrices and y 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([[0.99469663, 0.53126828],
       [0.9957307 , 0.73314636],
       [0.99437236, 0.46796199],
       [0.99489568, 0.52428219],
       [0.99366957, 0.39232591],
       [0.99487069, 0.49384431],
       [0.99493149, 0.56791416],
       [0.99299846, 0.33970859],
       [0.99396948, 0.41583962],
       [0.99485888, 0.48064574],
       [0.99489441, 0.52036036],
       [0.99624909, 1.02443182],
       [0.99566435, 0.69586182],
       [0.99363829, 0.39346041],
       [0.99426018, 0.43548263]])

In order to get the size of each cluster, you can use:

model.cluster_size_
Out[5]: 
array([6497, 1551, 4946, 2835, 2111, 1670, 1165,  652, 1459, 1115,  555,
        176, 1375,  682,  777])

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[6]: 128.553655

model.total_within_cluster_ss_
Out[7]: 15.346907

model.total_ss_
Out[8]: 143.900562

You also have access to the sum of squares of each cluster.

model.cluster_i_ss_
Out[9]: 
array([7.485924, 6.341603, 0.254458, 0.039501, 0.509403, 0.522764,
       0.092198, 0.101056])

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[10]: 89.3350611097683

Prediction

Predicting or ranking the dataset is straight-forward:

model.predict(data, ["density", "sulphates"])

	123 fixed_acidity Numeric(8)	123 volatile_acidity Numeric(9)	123 citric_acid Numeric(8)	123 residual_sugar Numeric(9)	123 chlorides Float(22)	123 free_sulfur_dioxide Numeric(9)	123 total_sulfur_dioxide Numeric(9)	123 density Float(22)	123 pH Numeric(8)	123 sulphates Numeric(8)	123 alcohol Float(22)	123 quality Integer	123 good Integer	Abc color Varchar(20)	123 Integer
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: 15

As shown above, a new column has been created, containing the bisected clusters.

Plots - Cluster Plot

Plots highlighting the different clusters can be easily drawn using:

model.plot()

Plots - Tree

Tree models can be visualized by drawing their tree plots. For more examples, check out Machine Learning - Tree Plots.

model.plot_tree()

Note

The above example may not render properly in the doc because of the huge size of the tree. But it should render nicely in jupyter environment.

In order to plot graph using graphviz separately, you can extract the graphviz DOT file code as follows:

model.to_graphviz()
Out[11]: 'digraph Tree {\ngraph [rankdir = "LR"];\n0 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#87cefa"><b> cluster_id: 0 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 6497 </td></tr><tr><td port="port3" border="1" align="left"> score: 1.0 </td></tr></table>>, shape="none"]\n0 -> 1 [label=""]\n0 -> 2 [label=""]\n1 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#87cefa"><b> cluster_id: 1 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 1551 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.5 </td></tr></table>>, shape="none"]\n1 -> 11 [label=""]\n1 -> 12 [label=""]\n2 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#87cefa"><b> cluster_id: 2 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 4946 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.5 </td></tr></table>>, shape="none"]\n2 -> 3 [label=""]\n2 -> 4 [label=""]\n3 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#87cefa"><b> cluster_id: 3 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 2835 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.13 </td></tr></table>>, shape="none"]\n3 -> 5 [label=""]\n3 -> 6 [label=""]\n4 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#87cefa"><b> cluster_id: 4 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 2111 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.1 </td></tr></table>>, shape="none"]\n4 -> 7 [label=""]\n4 -> 8 [label=""]\n5 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#87cefa"><b> cluster_id: 5 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 1670 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.02 </td></tr></table>>, shape="none"]\n5 -> 9 [label=""]\n5 -> 10 [label=""]\n6 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 6 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 1165 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.01 </td></tr></table>>, shape="none"]\n7 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 7 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 652 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.02 </td></tr></table>>, shape="none"]\n8 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#87cefa"><b> cluster_id: 8 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 1459 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.02 </td></tr></table>>, shape="none"]\n8 -> 13 [label=""]\n8 -> 14 [label=""]\n9 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 9 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 1115 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.01 </td></tr></table>>, shape="none"]\n10 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 10 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 555 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.0 </td></tr></table>>, shape="none"]\n11 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 11 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 176 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.47 </td></tr></table>>, shape="none"]\n12 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 12 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 1375 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.4 </td></tr></table>>, shape="none"]\n13 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 13 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 682 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.01 </td></tr></table>>, shape="none"]\n14 [label=<<table border="0" cellspacing="0"> <tr><td port="port1" border="1" bgcolor="#efc5b5"><b> cluster_id: 14 </b></td></tr><tr><td port="port2" border="1" align="left"> size: 777 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.01 </td></tr></table>>, shape="none"]\n}'

This string can then be copied into a DOT file which can be parsed by graphviz.

Plots - Contour

In order to understand the parameter space, we can also look at the contour plots:

model.contour()

Note

Machine learning models with two predictors can usually benefit from their own contour plot. This visual representation aids in exploring predictions and gaining a deeper understanding of how these models perform in different scenarios. Please refer to chart_gallery.contour_plot for more examples.

Parameter Modification

In order to see the parameters:

model.get_params()
Out[12]: 
{'n_cluster': 8,
 'bisection_iterations': 1,
 'split_method': 'sum_squares',
 'min_divisible_cluster_size': 2,
 'distance_method': 'euclidean',
 'init': 'kmeanspp',
 'max_iter': 300,
 'tol': 0.0001}

And to manually change some of the parameters:

model.set_params({'n_cluster': 5})

Model Register

In order to register the model for tracking and versioning:

model.register("model_v1")

Please refer to Model Tracking and Versioning for more details on model tracking and versioning.

Model Exporting

To Memmodel

model.to_memmodel()

Note

MemModel objects serve as in-memory representations of machine learning models. They can be used for both in-database and in-memory prediction tasks. These objects can be pickled in the same way that you would pickle a scikit-learn model.

The preceding methods for exporting the model use MemModel, and it is recommended to use MemModel directly.

To SQL

You can get the SQL query equivalent of the XGB model by:

model.to_sql()
Out[14]: '(CASE WHEN "density" IS NULL OR "sulphates" IS NULL THEN NULL ELSE (CASE WHEN POWER(POWER("density" - 0.995730702772405, 2) + POWER("sulphates" - 0.73314635718891, 2), 1/2) < POWER(POWER("density" - 0.994372363526082, 2) + POWER("sulphates" - 0.467961989486454, 2), 1/2) THEN (CASE WHEN POWER(POWER("density" - 0.996249090909091, 2) + POWER("sulphates" - 1.02443181818182, 2), 1/2) < POWER(POWER("density" - 0.995664349090909, 2) + POWER("sulphates" - 0.695861818181818, 2), 1/2) THEN 11 ELSE 12 END) ELSE (CASE WHEN POWER(POWER("density" - 0.994895675485009, 2) + POWER("sulphates" - 0.524282186948854, 2), 1/2) < POWER(POWER("density" - 0.993669573661772, 2) + POWER("sulphates" - 0.3923259118901, 2), 1/2) THEN (CASE WHEN POWER(POWER("density" - 0.994870691616766, 2) + POWER("sulphates" - 0.493844311377245, 2), 1/2) < POWER(POWER("density" - 0.994931489270386, 2) + POWER("sulphates" - 0.567914163090129, 2), 1/2) THEN (CASE WHEN POWER(POWER("density" - 0.994858883408072, 2) + POWER("sulphates" - 0.480645739910314, 2), 1/2) < POWER(POWER("density" - 0.994894414414414, 2) + POWER("sulphates" - 0.52036036036036, 2), 1/2) THEN 9 ELSE 10 END) ELSE 6 END) ELSE (CASE WHEN POWER(POWER("density" - 0.992998458588957, 2) + POWER("sulphates" - 0.339708588957055, 2), 1/2) < POWER(POWER("density" - 0.993969482522276, 2) + POWER("sulphates" - 0.415839616175463, 2), 1/2) THEN 7 ELSE (CASE WHEN POWER(POWER("density" - 0.993638291788856, 2) + POWER("sulphates" - 0.393460410557185, 2), 1/2) < POWER(POWER("density" - 0.99426018018018, 2) + POWER("sulphates" - 0.435482625482626, 2), 1/2) THEN 13 ELSE 14 END) END) END) END) END)'

Note

This SQL query can be directly used in any database.

Deploy SQL

To get the SQL query which uses Vertica functions use below:

model.deploySQL()
Out[15]: 'APPLY_BISECTING_KMEANS("density", "sulphates" USING PARAMETERS model_name = \'"public"."_verticapy_tmp_bisectingkmeans_v_demo_1a1a3fa6e22c11eea3a80242ac120002_"\', match_by_pos = \'true\')'

To Python

To obtain the prediction function in Python syntax, use the following code:

X = [[0.9, 0.5]]

model.to_python()(X)
Out[17]: array([9])

Hint

The to_python() method is used to retrieve the anomaly score. For specific details on how to use this method for different model types, refer to the relevant documentation for each model.

__init__(name: str = None, overwrite_model: bool = False, n_cluster: int = 8, bisection_iterations: int = 1, split_method: Literal['size', 'sum_squares'] = 'sum_squares', min_divisible_cluster_size: int = 2, distance_method: Literal['euclidean'] = 'euclidean', init: Literal['kmeanspp', 'pseudo', 'random'] | list = 'kmeanspp', max_iter: int = 300, tol: float = 0.0001) → None

Must be overridden in the child class

Methods

__init__([name, overwrite_model, n_cluster, ...])	Must be overridden in the child class
contour([nbins, chart])	Draws the model's contour plot.
deploySQL([X])	Returns the SQL code needed to deploy the model.
does_model_exists(name[, raise_error, ...])	Checks whether the model is stored in the Vertica database.
drop()	Drops the model from the Vertica database.
export_models(name, path[, kind])	Exports machine learning models.
features_importance([tree_id, show, chart])	Computes the model's features importance.
fit(input_relation[, X, return_report])	Trains the model.
get_attributes([attr_name])	Returns the model attributes.
get_match_index(x, col_list[, str_check])	Returns the matching index.
get_params()	Returns the parameters of the model.
get_plotting_lib([class_name, chart, ...])	Returns the first available library (Plotly, Matplotlib, or Highcharts) to draw a specific graphic.
get_score([tree_id])	Returns the feature importance metrics for the input tree.
get_tree()	Returns a table containing information about the BK-tree.
get_vertica_attributes([attr_name])	Returns the model Vertica attributes.
import_models(path[, schema, kind])	Imports machine learning models.
plot([max_nb_points, chart])	Draws the model.
plot_tree([pic_path])	Draws the input tree.
plot_voronoi([max_nb_points, plot_crosses, ...])	Draws the Voronoi Graph of the model.
predict(vdf[, X, name, inplace])	Makes predictions using the input relation.
register(registered_name[, raise_error])	Registers the model and adds it to in-DB Model versioning environment with a status of 'under_review'.
set_params([parameters])	Sets the parameters of the model.
summarize()	Summarizes the model.
to_binary(path)	Exports the model to the Vertica Binary format.
to_graphviz([round_score, percent, ...])	Returns the code for a Graphviz tree.
to_memmodel()	Converts the model to an InMemory object that can be used for different types of predictions.
to_pmml(path)	Exports the model to PMML.
to_python([return_proba, ...])	Returns the Python function needed for in-memory scoring without using built-in Vertica functions.
to_sql([X, return_proba, ...])	Returns the SQL code needed to deploy the model without using built-in Vertica functions.
to_tf(path)	Exports the model to the Frozen Graph format (TensorFlow).

Attributes

object_type