Loading...

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.

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)
13.90.2250.44.20.0329.0118.00.9893.570.3612.881white
24.70.3350.141.30.03669.0168.00.992123.470.4610.550white
34.70.4550.181.90.03633.0106.00.987463.210.8314.071white
44.70.7850.03.40.03623.0134.00.989813.530.9213.860white
54.90.3450.341.00.06832.0143.00.991383.240.410.150white
64.90.3450.341.00.06832.0143.00.991383.240.410.150white
74.90.420.02.10.04816.042.00.991543.710.7414.071red
85.00.270.41.20.07642.0124.00.992043.320.4710.160white
95.00.310.06.40.04643.0166.00.9943.30.639.960white
105.00.40.54.30.04629.080.00.99023.490.6613.660red
115.00.440.0418.60.03938.0128.00.99853.370.5710.260white
125.10.110.321.60.02812.090.00.990083.570.5212.260white
135.10.140.250.70.03915.089.00.99193.220.439.260white
145.10.1650.225.70.04742.0146.00.99343.180.559.960white
155.10.330.221.60.02718.089.00.98933.510.3812.571white
165.10.330.221.60.02718.089.00.98933.510.3812.571white
175.10.330.221.60.02718.089.00.98933.510.3812.571white
185.10.390.211.70.02715.072.00.98943.50.4512.560white
195.20.20.273.20.04716.093.00.992353.440.5310.171white
205.20.210.311.70.04817.061.00.989533.240.3712.071white
215.20.220.466.20.06641.0187.00.993623.190.429.7333333333333350white
225.20.310.22.40.02727.0117.00.988863.560.4513.071white
235.20.320.251.80.10313.050.00.99573.380.559.250red
245.20.340.376.20.03142.0133.00.990763.250.4112.560white
255.20.360.021.60.03124.0104.00.98963.440.3512.260white
265.20.3650.0813.50.04137.0142.00.9973.460.399.960white
275.20.480.041.60.05419.0106.00.99273.540.6212.271red
285.20.50.182.00.03623.0129.00.989493.360.7713.471white
295.30.160.391.00.02840.0101.00.991563.570.5910.660white
305.30.160.391.00.02840.0101.00.991563.570.5910.660white
315.30.1650.241.10.05125.0105.00.99253.320.479.150white
325.30.230.560.90.04146.0141.00.991193.160.629.750white
335.30.30.31.20.02925.093.00.987423.310.413.671white
345.30.330.31.20.04825.0119.00.990453.320.6211.360white
355.30.360.276.30.02840.0132.00.991863.370.411.660white
365.30.360.276.30.02840.0132.00.991863.370.411.660white
375.30.40.253.90.03145.0130.00.990723.310.5811.7571white
385.30.470.112.20.04816.089.00.991823.540.8813.671red
395.30.470.112.20.04816.089.00.991823.540.8813.566666666666771red
405.30.7150.191.50.1617.062.00.993953.620.6111.050red
415.40.220.291.20.04569.0152.00.991783.760.6311.071white
425.40.5950.12.80.04226.080.00.99323.360.389.350white
435.40.740.091.70.08916.026.00.994023.670.5611.660red
445.50.120.331.00.03823.0131.00.991643.250.459.850white
455.50.120.331.00.03823.0131.00.991643.250.459.850white
465.50.140.274.60.02922.0104.00.99493.340.449.050white
475.50.140.274.60.02922.0104.00.99493.340.449.050white
485.50.160.311.20.02631.068.00.98983.330.4411.6560white
495.50.160.311.20.02631.068.00.98983.330.4411.633333333333360white
505.50.180.225.50.03710.086.00.991563.460.4412.250white
515.50.240.451.70.04622.0113.00.992243.220.4810.050white
525.50.290.31.10.02220.0110.00.988693.340.3812.871white
535.50.310.293.00.02716.0102.00.990673.230.5611.260white
545.50.320.454.90.02825.0191.00.99223.510.4911.571white
555.50.350.351.10.04514.0167.00.9923.340.689.960white
565.50.3750.381.70.03617.098.00.991423.290.3910.560white
575.60.150.265.550.05151.0139.00.993363.470.511.060white
585.60.150.315.30.0388.079.00.99233.30.3910.560white
595.60.160.271.40.04453.0168.00.99183.280.3710.160white
605.60.1750.290.80.04320.067.00.991123.280.489.960white
615.60.1850.197.10.04836.0110.00.994383.260.419.560white
625.60.1850.197.10.04836.0110.00.994383.260.419.560white
635.60.220.321.20.02429.097.00.988233.20.4613.0571white
645.60.260.181.40.03418.0135.00.991743.320.3510.260white
655.60.260.265.70.03112.080.00.99233.250.3810.850white
665.60.260.511.40.02925.093.00.994283.230.4910.560white
675.60.280.284.20.04452.0158.00.9923.350.4410.771white
685.60.30.16.40.04334.0142.00.993823.140.489.850white
695.60.350.145.00.04648.0198.00.99373.30.7110.350white
705.60.490.134.50.03917.0116.00.99073.420.913.771white
715.60.490.134.50.03917.0116.00.99073.420.913.771white
725.60.660.02.20.0873.011.00.993783.710.6312.871red
735.60.660.02.20.0873.011.00.993783.710.6312.871red
745.70.150.4711.40.03549.0128.00.994563.030.3410.581white
755.70.180.262.20.02321.095.00.98933.070.5412.360white
765.70.180.361.20.0469.071.00.991993.70.6810.971white
775.70.20.32.50.04638.0125.00.992763.340.59.960white
785.70.210.320.90.03838.0121.00.990743.240.4610.660white
795.70.210.374.50.0458.0140.00.993323.290.6210.660white
805.70.220.216.00.04441.0113.00.998623.220.468.960white
815.70.220.216.00.04441.0113.00.998623.220.468.960white
825.70.220.216.00.04441.0113.00.998623.220.468.960white
835.70.220.216.00.04441.0113.00.998623.220.468.960white
845.70.220.216.00.04441.0113.00.998623.220.468.960white
855.70.220.293.50.0427.0146.00.989993.170.3612.160white
865.70.230.289.650.02526.0121.00.99253.280.3811.360white
875.70.250.2612.50.04952.5106.00.996913.080.459.460white
885.70.250.2612.50.04952.5120.00.996913.080.459.460white
895.70.250.2711.50.0424.0120.00.994113.330.3110.860white
905.70.260.2417.80.05923.0124.00.997733.30.510.150white
915.70.260.2417.80.05923.0124.00.997733.30.510.150white
925.70.260.2417.80.05923.0124.00.997733.30.510.150white
935.70.270.321.20.04620.0155.00.99343.80.4110.260white
945.70.280.2417.50.04460.0167.00.99893.310.449.450white
955.70.320.181.40.02926.0104.00.99063.440.3711.060white
965.70.320.384.750.03323.094.00.9913.420.4211.871white
975.70.360.344.20.02621.077.00.99073.410.4511.960white
985.80.140.156.10.04227.0123.00.993623.060.69.960white
995.80.150.321.20.03714.0119.00.991373.190.510.260white
1005.80.170.341.80.04596.0170.00.990353.380.911.881white
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"])


======
BKTree
======
center_id|density |sulphates|withinss |totWithinss|bisection_level|cluster_size|parent|left_child|right_child
---------+--------+---------+---------+-----------+---------------+------------+------+----------+-----------
    0    | 0.99470| 0.53127 |143.90056| 143.90056 |       0       |    6497    |      |    1     |     2     
    1    | 0.99437| 0.46796 |30.19361 | 60.86574  |       1       |    4946    |  0   |    3     |     4     
    2    | 0.99573| 0.73315 |30.67213 | 60.86574  |       1       |    1551    |  0   |    11    |    12     
    3    | 0.99490| 0.52428 | 5.15288 | 39.79475  |       2       |    2835    |  1   |    5     |     6     
    4    | 0.99367| 0.39233 | 3.96974 | 39.79475  |       2       |    2111    |  1   |    7     |     8     
    5    | 0.99487| 0.49384 | 0.87842 | 36.02969  |       3       |    1670    |  3   |    9     |    10     
    6    | 0.99493| 0.56791 | 0.50940 | 36.02969  |       3       |    1165    |  3   |          |           
    7    | 0.99300| 0.33971 | 0.52276 | 33.41748  |       4       |    652     |  4   |          |           
    8    | 0.99397| 0.41584 | 0.83476 | 33.41748  |       4       |    1459    |  4   |    13    |    14     
    9    | 0.99475| 0.47428 | 0.11483 | 32.77201  |       5       |    839     |  5   |          |           
   10    | 0.99499| 0.51360 | 0.11812 | 32.77201  |       5       |    831     |  5   |          |           
   11    | 0.99566| 0.69586 | 6.34160 | 15.92741  |       6       |    1375    |  2   |          |           
   12    | 0.99625| 1.02443 | 7.48592 | 15.92741  |       6       |    176     |  2   |          |           
   13    | 0.99426| 0.43548 | 0.10106 | 15.28590  |       7       |    777     |  8   |          |           
   14    | 0.99364| 0.39346 | 0.09220 | 15.28590  |       7       |    682     |  8   |          |           


=======
Metrics
=======
                       Measure                       |  Value  
-----------------------------------------------------+---------
                Total sum of squares                 |143.90056
         Total within-cluster sum of squares         |15.28590 
           Between-cluster sum of squares            |128.61466
Between-cluster sum of squares / Total sum of squares|89.37746 
      Sum of squares for cluster 1, center_id 9      | 0.11483 
     Sum of squares for cluster 2, center_id 10      | 0.11812 
      Sum of squares for cluster 3, center_id 6      | 0.50940 
      Sum of squares for cluster 4, center_id 7      | 0.52276 
     Sum of squares for cluster 5, center_id 13      | 0.10106 
     Sum of squares for cluster 6, center_id 14      | 0.09220 
     Sum of squares for cluster 7, center_id 11      | 6.34160 
     Sum of squares for cluster 8, center_id 12      | 7.48592 


===========
call_string
===========
bisecting_kmeans('"public"."_verticapy_tmp_bisectingkmeans_v_mldb_0b1588e2979611efa8720242ac120002_"', '"public"."_verticapy_tmp_view_v_mldb_0b46199e979611efa8720242ac120002_"', '"density", "sulphates"', 8
USING PARAMETERS bisection_iterations=1, split_method='SUM_SQUARES', min_divisible_cluster_size=2, distance_method='euclidean', kmeans_center_init_method='kmeanspp', kmeans_epsilon=0.0001, kmeans_max_iterations=300, key_columns=''"density", "sulphates"'')

===============
Additional Info
===============
        Name         |Value
---------------------+-----
   num_of_clusters   |  8  
dimensions_of_dataset|  2  
num_of_clusters_found|  8  
  height_of_BKTree   |  5  

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],
       [0.99437236, 0.46796199],
       [0.9957307 , 0.73314636],
       [0.99489568, 0.52428219],
       [0.99366957, 0.39232591],
       [0.99487069, 0.49384431],
       [0.99493149, 0.56791416],
       [0.99299846, 0.33970859],
       [0.99396948, 0.41583962],
       [0.99475134, 0.4742789 ],
       [0.99499119, 0.51359807],
       [0.99566435, 0.69586182],
       [0.99624909, 1.02443182],
       [0.99426018, 0.43548263],
       [0.99363829, 0.39346041]])

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

model.cluster_size_
Out[5]: 
array([6497, 4946, 1551, 2835, 2111, 1670, 1165,  652, 1459,  839,  831,
       1375,  176,  777,  682])

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]: 128.614661

model.total_within_cluster_ss_
Out[7]: 15.285901

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([0.114831, 0.118122, 0.509403, 0.522764, 0.101056, 0.092198,
       6.341603, 7.485924])

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]: 89.3774556627513

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
14.40.320.394.30.0331.0127.00.989043.460.3612.881white
24.40.460.12.80.02431.0111.00.988163.480.3413.160white
34.40.540.095.10.03852.097.00.990223.410.412.271white
44.70.60.172.30.05817.0106.00.99323.850.612.960red
54.70.670.091.00.025.09.00.987223.30.3413.650white
64.80.330.06.50.02834.0163.00.99373.350.619.950white
74.80.340.06.50.02833.0163.00.99393.360.619.960white
84.90.470.171.90.03560.0148.00.989643.270.3511.560white
95.00.270.324.50.03258.0178.00.989563.450.3112.671white
105.00.270.324.50.03258.0178.00.989563.450.3112.671white
115.00.290.545.70.03554.0155.00.989763.270.3412.981white
125.00.330.184.60.03240.0124.00.991143.180.411.060white
135.00.380.011.60.04826.060.00.990843.70.7514.060red
145.00.550.148.30.03235.0164.00.99183.530.5112.581white
155.00.610.121.30.00965.0100.00.98743.260.3713.550white
165.10.210.281.40.04748.0148.00.991683.50.4910.450white
175.10.230.181.00.05313.099.00.989563.220.3911.550white
185.10.250.361.30.03540.078.00.98913.230.6412.171white
195.10.260.346.40.03426.099.00.994493.230.419.260white
205.10.350.266.80.03436.0120.00.991883.380.411.560white
215.10.350.266.80.03436.0120.00.991883.380.411.560white
225.10.350.266.80.03436.0120.00.991883.380.411.560white
235.10.470.021.30.03418.044.00.99213.90.6212.860red
245.10.5850.01.70.04414.086.00.992643.560.9412.971red
255.20.1850.221.00.0347.0123.00.992183.550.4410.1560white
265.20.240.453.80.02721.0128.00.9923.550.4911.281white
275.20.240.453.80.02721.0128.00.9923.550.4911.281white
285.20.280.291.10.02818.069.00.991683.240.5410.060white
295.20.340.01.80.0527.063.00.99163.680.7914.060red
305.20.340.01.80.0527.063.00.99163.680.7914.060red
315.20.4050.151.450.03810.044.00.991253.520.411.640white
325.20.60.077.00.04433.0147.00.99443.330.589.750white
335.20.6450.02.150.0815.028.00.994443.780.6112.560red
345.30.20.313.60.03622.091.00.992783.410.59.860white
355.30.240.331.30.03325.097.00.99063.590.3811.081white
365.30.310.3810.50.03153.0140.00.993213.340.4611.760white
375.30.310.3810.50.03153.0140.00.993213.340.4611.760white
385.30.3950.071.30.03526.0102.00.9923.50.3510.660white
395.30.430.111.10.0296.051.00.990763.510.4811.240white
405.30.580.076.90.04334.0149.00.99443.340.579.750white
415.30.5850.077.10.04434.0145.00.99453.340.579.760white
425.30.760.032.70.04327.093.00.99323.340.389.250white
435.40.180.244.80.04130.0113.00.994453.420.49.460white
445.40.2050.1612.550.05131.0115.00.995643.40.3810.860white
455.40.2550.331.20.05129.0122.00.990483.370.6611.360white
465.40.290.381.20.02931.0132.00.988953.280.3612.460white
475.40.290.381.20.02931.0132.00.988953.280.3612.460white
485.40.450.276.40.03320.0102.00.989443.220.2713.481white
495.40.50.135.00.02812.0107.00.990793.480.8813.571white
505.40.530.162.70.03634.0128.00.988563.20.5313.281white
515.40.530.162.70.03634.0128.00.988563.20.5313.281white
525.40.590.077.00.04536.0147.00.99443.340.579.760white
535.50.160.261.50.03235.0100.00.990763.430.7712.060white
545.50.190.270.90.0452.0103.00.990263.50.3911.250white
555.50.230.192.20.04439.0161.00.992093.190.4310.460white
565.50.240.328.70.0619.0102.00.9943.270.3110.450white
575.60.180.271.70.0331.0103.00.988923.350.3712.960white
585.60.180.292.30.045.047.00.991263.070.4510.140white
595.60.180.310.20.02828.0131.00.99543.490.4210.871white
605.60.180.311.50.03816.084.00.99243.340.5810.160white
615.60.1850.491.10.0328.0117.00.99183.550.4510.360white
625.60.190.261.40.0312.076.00.99053.250.3710.971white
635.60.190.270.90.0452.0103.00.990263.50.3911.250white
645.60.190.312.70.02711.0100.00.989643.460.413.271white
655.60.190.461.10.03233.0115.00.99093.360.510.460white
665.60.20.6610.20.04378.0175.00.99452.980.4310.471white
675.60.2050.1612.550.05131.0115.00.995643.40.3810.860white
685.60.2250.249.80.05459.0140.00.995453.170.3910.260white
695.60.230.258.00.04331.0101.00.994293.190.4210.460white
705.60.230.293.10.02319.089.00.990683.250.5111.260white
715.60.2350.291.20.04733.0127.00.9913.340.511.071white
725.60.270.370.90.02511.049.00.988453.290.3313.160white
735.60.280.273.90.04352.0158.00.992023.350.4410.771white
745.60.290.050.80.03811.030.00.99243.360.359.250white
755.60.2950.22.20.04918.0134.00.993783.210.6810.050white
765.60.310.371.40.07412.096.00.99543.320.589.250red
775.60.330.281.20.03133.097.00.991263.490.5810.960white
785.60.340.11.30.03120.068.00.99063.360.5111.271white
795.60.340.252.50.04647.0182.00.990933.210.411.350white
805.60.390.244.70.03427.077.00.99063.280.3612.750white
815.60.410.227.10.0544.0154.00.99313.30.410.550white
825.60.460.244.80.04224.072.00.99083.290.3712.660white
835.60.50.092.30.04917.099.00.99373.630.6313.050red
845.60.50.092.30.04917.099.00.99373.630.6313.050red
855.60.6050.052.40.07319.025.00.992583.560.5512.950red
865.60.6950.066.80.0429.084.00.994323.440.4410.250white
875.70.1350.34.60.04219.0101.00.99463.310.429.360white
885.70.140.35.40.04526.0105.00.994693.320.459.350white
895.70.180.224.20.04225.0111.00.9943.350.399.450white
905.70.220.2216.650.04439.0110.00.998553.240.489.060white
915.70.220.2216.650.04439.0110.00.998553.240.489.060white
925.70.220.2216.650.04439.0110.00.998553.240.489.060white
935.70.220.2216.650.04439.0110.00.998553.240.489.060white
945.70.220.281.30.02726.0101.00.989483.350.3812.571white
955.70.2450.331.10.04928.0150.00.99273.130.429.350white
965.70.250.211.50.04421.0108.00.991423.30.5911.060white
975.70.2550.651.20.07917.0137.00.993073.20.429.450white
985.70.2550.651.20.07917.0137.00.993073.20.429.450white
995.70.280.33.90.02636.0105.00.989633.260.5812.7560white
1005.70.310.297.30.0533.0143.00.993323.310.511.066666666666760white
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()
../_images/machine_learning_vertica_tree_bisect_km_.png

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: 4946 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.5 </td></tr></table>>, shape="none"]\n1 -> 3 [label=""]\n1 -> 4 [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: 1551 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.5 </td></tr></table>>, shape="none"]\n2 -> 11 [label=""]\n2 -> 12 [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: 839 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.0 </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: 831 </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: 1375 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.4 </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: 176 </td></tr><tr><td port="port3" border="1" align="left"> score: 0.47 </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: 777 </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: 682 </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 /notebooks/ml/model_tracking_versioning/index.ipynb 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" - 0.994372363526082, 2) + POWER("sulphates" - 0.467961989486454, 2), 1/2) < POWER(POWER("density" - 0.995730702772405, 2) + POWER("sulphates" - 0.73314635718891, 2), 1/2) THEN (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" - 0.994751340882002, 2) + POWER("sulphates" - 0.474278903456496, 2), 1/2) < POWER(POWER("density" - 0.99499119133574, 2) + POWER("sulphates" - 0.513598074608905, 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" - 0.99426018018018, 2) + POWER("sulphates" - 0.435482625482626, 2), 1/2) < POWER(POWER("density" - 0.993638291788856, 2) + POWER("sulphates" - 0.393460410557185, 2), 1/2) THEN 13 ELSE 14 END) END) END) ELSE (CASE WHEN POWER(POWER("density" - 0.995664349090909, 2) + POWER("sulphates" - 0.695861818181818, 2), 1/2) < POWER(POWER("density" - 0.996249090909091, 2) + POWER("sulphates" - 1.02443181818182, 2), 1/2) THEN 11 ELSE 12 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_mldb_0b1588e2979611efa8720242ac120002_"\', 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([10])

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