Iris¶

This example uses the 'iris' dataset to predict the species of various flowers based on their physical features. You can download the Jupyter Notebook of the study here.

PetalLengthCm: Petal Length in cm
PetalWidthCm: Petal Width in cm
SepalLengthCm: Sepal Length in cm
SepalWidthCm: Sepal Width in cm
Species: The Flower Species (Setosa, Virginica, Versicolor)

We will follow the data science cycle (Data Exploration - Data Preparation - Data Modeling - Model Evaluation - Model Deployment) to solve this problem.

Initialization¶

This example uses the following version of VerticaPy:

In [24]:

import verticapy as vp
vp.__version__

Out[24]:

'0.9.0'

Connect to Vertica. This example uses an existing connection called "VerticaDSN." For details on how to create a connection, use see the connection tutorial.

In [1]:

vp.connect("VerticaDSN")

Let's create a Virtual DataFrame of the dataset.

In [11]:

from verticapy.datasets import load_iris
import verticapy.stats as st
iris = load_iris()
iris.head(5)

Out[11]:

	123 SepalLengthCm Numeric(5,2)	123 SepalWidthCm Numeric(5,2)	123 PetalLengthCm Numeric(5,2)	123 PetalWidthCm Numeric(5,2)	Abc Species Varchar(30)
1	4.3	3.0	1.1	0.1	Iris-setosa
2	4.4	2.9	1.4	0.2	Iris-setosa
3	4.4	3.0	1.3	0.2	Iris-setosa
4	4.4	3.2	1.3	0.2	Iris-setosa
5	4.5	2.3	1.3	0.3	Iris-setosa

Rows: 1-5 | Columns: 5

Data Exploration and Preparation¶

Let's explore the data by displaying descriptive statistics of all the columns.

In [12]:

iris.describe(method = "categorical", unique=True)

Out[12]:

	dtype	count	top	top_percent	unique
"SepalLengthCm"	numeric(5,2)	150	5.0	6.667	35.0
"SepalWidthCm"	numeric(5,2)	150	3.0	17.333	23.0
"PetalLengthCm"	numeric(5,2)	150	1.5	9.333	43.0
"PetalWidthCm"	numeric(5,2)	150	0.2	18.667	22.0
"Species"	varchar(30)	150	Iris-setosa	33.333	3.0

Rows: 1-5 | Columns: 6

We don't have much data here, but that's okay; since different flower species have different proportions and ratios between those proportions, we can start by making ratios between each feature.

We'll need to use the One-Hot Encoder on the 'Species' to get information about each species.

In [13]:

iris["Species"].one_hot_encode(drop_first = False)
iris["ratio_pwl"] = iris["PetalWidthCm"] / iris["PetalLengthCm"]
iris["ratio_swl"] = iris["SepalWidthCm"] / iris["SepalLengthCm"]

We can draw the correlation matrix (Pearson correlation coefficient) of the new features to see if there are some linear links.

In [14]:

%matplotlib inline
iris.corr()

Out[14]:

	"SepalLengthCm"	"SepalWidthCm"	"PetalLengthCm"	"PetalWidthCm"	"Species_Iris-setosa"	"Species_Iris-versicolor"	"Species_Iris-virginica"	"ratio_pwl"	"ratio_swl"
"SepalLengthCm"	1.0	-0.109369249950656	0.871754157304886	0.817953633369181	-0.717415668686111	0.0793955238434444	0.63802014484266	0.645854809352185	-0.724085081370438
"SepalWidthCm"	-0.109369249950656	1.0	-0.420516096401169	-0.356544089613812	0.595600845226849	-0.464699560561606	-0.13090128466524	-0.339854865893446	0.755415996230207
"PetalLengthCm"	0.871754157304886	-0.420516096401169	1.0	0.962757097050968	-0.922688332883109	0.201586759537506	0.721101573345601	0.8129592586072	-0.867296724293694
"PetalWidthCm"	0.817953633369181	-0.356544089613812	0.962757097050968	1.0	-0.887509958782658	0.118375979139307	0.76913397964335	0.910838299356941	-0.796309230951869
"Species_Iris-setosa"	-0.717415668686111	0.595600845226849	-0.922688332883109	-0.887509958782658	1.0	-0.5	-0.5	-0.825149778706552	0.907112624976622
"Species_Iris-versicolor"	0.0793955238434444	-0.464699560561606	0.201586759537506	0.118375979139307	-0.5	1.0	-0.5	0.212967593449348	-0.409714538856098
"Species_Iris-virginica"	0.63802014484266	-0.13090128466524	0.721101573345601	0.76913397964335	-0.5	-0.5	1.0	0.612182185257205	-0.497398086120528
"ratio_pwl"	0.645854809352185	-0.339854865893446	0.8129592586072	0.910838299356941	-0.825149778706552	0.212967593449348	0.612182185257205	1.0	-0.689720454015874
"ratio_swl"	-0.724085081370438	0.755415996230207	-0.867296724293694	-0.796309230951869	0.907112624976622	-0.409714538856098	-0.497398086120528	-0.689720454015874	1.0

Rows: 1-9 | Columns: 10

The Iris setosa is highly linearly correlated with the petal length and the sepal ratio. We can see a perfect separation using the two features (though we can also see this separation the petal length alone).

In [15]:

iris.scatter(columns = ["PetalLengthCm", "ratio_swl"], 
             catcol = "Species")

Out[15]:

<AxesSubplot:xlabel='"PetalLengthCm"', ylabel='"ratio_swl"'>

We can we a clear linear separation between the Iris setosa and the other species, but we'll need more features to identify the differences between Iris virginica and Iris versicolor.

In [16]:

iris.scatter(columns = ["PetalLengthCm", 
                        "PetalWidthCm", 
                        "SepalLengthCm"], 
             catcol = "Species")

Out[16]:

<Axes3DSubplot:xlabel='"PetalLengthCm"', ylabel='"PetalWidthCm"'>

Our strategy is simple: we'll use two Linear Support Vector Classification (SVC): one to classify the Iris setosa and another to classify the Iris versicolor.

Machine Learning¶

Let's build the first Linear SVC to predict if a flower is an Iris setosa.

In [17]:

from verticapy.learn.svm import LinearSVC
from verticapy.learn.model_selection import cross_validate

predictors = ["PetalLengthCm", "ratio_swl"]
response = "Species_Iris-setosa"
model = LinearSVC("svc_setosa_iris")
cross_validate(model, iris, predictors, response)

Out[17]:

	auc	prc_auc	accuracy	log_loss	precision	recall	f1_score	mcc	informedness	markedness	csi	time
1-fold	1.0	0.9999999999999999	1.0	0.0852135991098265	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.638392686843872
2-fold	1.0	0.9999999999999999	1.0	0.0808943478921133	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.5792129039764404
3-fold	0.9999999999999999	1.0	1.0	0.0744378576492842	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.4164810180664062
avg	1.0	0.9999999999999999	1.0	0.08018193488374134	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.544695536295573
std	6.409875621278546e-17	6.409875621278546e-17	0.0	0.005423080326436787	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.11491206937746823

Rows: 1-5 | Columns: 13

Our model is excellent. Let's build it using the entire dataset.

In [18]:

model.fit(iris, predictors, response)

Out[18]:


=======
details
=======
  predictor  |coefficient
-------------+-----------
  Intercept  |  1.38349  
petallengthcm| -0.84012  
  ratio_swl  |  1.32517  


===========
call_string
===========
SELECT svm_classifier('public.svc_setosa_iris', '"public"."_verticapy_tmp_view_dbadmin_40328_9186882012_"', '"species_iris-setosa"', '"PetalLengthCm", "ratio_swl"'
USING PARAMETERS class_weights='1,1', C=1, max_iterations=100, intercept_mode='regularized', intercept_scaling=1, epsilon=0.0001);

===============
Additional Info
===============
       Name       |Value
------------------+-----
accepted_row_count| 150 
rejected_row_count|  0  
 iteration_count  |  7

Let's plot the model to see the perfect separation.

In [19]:

model.plot()

Out[19]:

<AxesSubplot:xlabel='"PetalLengthCm"', ylabel='"ratio_swl"'>

We can add this probability to the vDataFrame.

In [20]:

model.predict_proba(iris, name = "setosa", pos_label=1)

Out[20]:

	123 SepalLengthCm Numeric(5,2)	123 SepalWidthCm Numeric(5,2)	123 PetalLengthCm Numeric(5,2)	123 PetalWidthCm Numeric(5,2)	Abc Species Varchar(30)	123 Species_Iris-setosa Bool	123 Species_Iris-versicolor Bool	123 Species_Iris-virginica Bool	123 ratio_pwl Numeric(20,15)	123 ratio_swl Numeric(20,15)	123 setosa Float
1	4.3	3.0	1.1	0.1	Iris-setosa	1	0	0	0.090909090909091	0.697674418604651	0.799616133475824
2	4.4	2.9	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.659090909090909	0.746632427676863
3	4.4	3.0	1.3	0.2	Iris-setosa	1	0	0	0.153846153846154	0.681818181818182	0.767609329878423
4	4.4	3.2	1.3	0.2	Iris-setosa	1	0	0	0.153846153846154	0.727272727272727	0.778180760876583
5	4.5	2.3	1.3	0.3	Iris-setosa	1	0	0	0.230769230769231	0.511111111111111	0.724849376339106
6	4.6	3.1	1.5	0.2	Iris-setosa	1	0	0	0.133333333333333	0.673913043478261	0.734263300128653
7	4.6	3.2	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.695652173913043	0.755687832710383
8	4.6	3.4	1.4	0.3	Iris-setosa	1	0	0	0.214285714285714	0.739130434782609	0.766167839545688
9	4.6	3.6	1.0	0.2	Iris-setosa	1	0	0	0.2	0.782608695652174	0.82926980908022
10	4.7	3.2	1.3	0.2	Iris-setosa	1	0	0	0.153846153846154	0.680851063829787	0.76738063375719
11	4.7	3.2	1.6	0.2	Iris-setosa	1	0	0	0.125	0.680851063829787	0.719411418945644
12	4.8	3.0	1.4	0.1	Iris-setosa	1	0	0	0.071428571428571	0.625	0.737991521269184
13	4.8	3.0	1.4	0.3	Iris-setosa	1	0	0	0.214285714285714	0.625	0.737991521269184
14	4.8	3.1	1.6	0.2	Iris-setosa	1	0	0	0.125	0.645833333333333	0.709949644614095
15	4.8	3.4	1.6	0.2	Iris-setosa	1	0	0	0.125	0.708333333333333	0.726703765068597
16	4.8	3.4	1.9	0.2	Iris-setosa	1	0	0	0.105263157894737	0.708333333333333	0.673910864793945
17	4.9	2.4	3.3	1.0	Iris-versicolor	0	1	0	0.303030303030303	0.489795918367347	0.323039614860416
18	4.9	2.5	4.5	1.7	Iris-virginica	0	0	1	0.377777777777778	0.510204081632653	0.151750696077398
19	4.9	3.0	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.612244897959184	0.734710097493698
20	4.9	3.1	1.5	0.1	Iris-setosa	1	0	0	0.066666666666667	0.63265306122449	0.723459090938328
21	4.9	3.1	1.5	0.1	Iris-setosa	1	0	0	0.066666666666667	0.63265306122449	0.723459090938328
22	4.9	3.1	1.5	0.1	Iris-setosa	1	0	0	0.066666666666667	0.63265306122449	0.723459090938328
23	5.0	2.0	3.5	1.0	Iris-versicolor	0	1	0	0.285714285714286	0.4	0.263694030318376
24	5.0	2.3	3.3	1.0	Iris-versicolor	0	1	0	0.303030303030303	0.46	0.314465933883348
25	5.0	3.0	1.6	0.2	Iris-setosa	1	0	0	0.125	0.6	0.697285021121722
26	5.0	3.2	1.2	0.2	Iris-setosa	1	0	0	0.166666666666667	0.64	0.772671290753683
27	5.0	3.3	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.66	0.746860255947267
28	5.0	3.4	1.5	0.2	Iris-setosa	1	0	0	0.133333333333333	0.68	0.735834215605851
29	5.0	3.4	1.6	0.4	Iris-setosa	1	0	0	0.25	0.68	0.719183705655739
30	5.0	3.5	1.3	0.3	Iris-setosa	1	0	0	0.230769230769231	0.7	0.771879602615583
31	5.0	3.5	1.6	0.6	Iris-setosa	1	0	0	0.375	0.7	0.724505067474212
32	5.0	3.6	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.72	0.761595468468724
33	5.1	2.5	3.0	1.1	Iris-versicolor	0	1	0	0.366666666666667	0.490196078431373	0.380536424820992
34	5.1	3.3	1.7	0.5	Iris-setosa	1	0	0	0.294117647058824	0.647058823529412	0.692695552384892
35	5.1	3.4	1.5	0.2	Iris-setosa	1	0	0	0.133333333333333	0.666666666666667	0.732385408664398
36	5.1	3.5	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.686274509803922	0.753386230741964
37	5.1	3.5	1.4	0.3	Iris-setosa	1	0	0	0.214285714285714	0.686274509803922	0.753386230741964
38	5.1	3.7	1.5	0.4	Iris-setosa	1	0	0	0.266666666666667	0.725490196078431	0.747384308490649
39	5.1	3.8	1.5	0.3	Iris-setosa	1	0	0	0.2	0.745098039215686	0.752258455681401
40	5.1	3.8	1.6	0.2	Iris-setosa	1	0	0	0.125	0.745098039215686	0.736272141535994
41	5.1	3.8	1.9	0.4	Iris-setosa	1	0	0	0.210526315789474	0.745098039215686	0.68452518034775
42	5.2	2.7	3.9	1.4	Iris-versicolor	0	1	0	0.358974358974359	0.519230769230769	0.230604211159528
43	5.2	3.4	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.653846153846154	0.745315390833046
44	5.2	3.5	1.5	0.2	Iris-setosa	1	0	0	0.133333333333333	0.673076923076923	0.734047050003793
45	5.2	4.1	1.5	0.1	Iris-setosa	1	0	0	0.066666666666667	0.788461538461538	0.762811887474022
46	5.3	3.7	1.5	0.2	Iris-setosa	1	0	0	0.133333333333333	0.69811320754717	0.740473501806866
47	5.4	3.0	4.5	1.5	Iris-versicolor	0	1	0	0.333333333333333	0.555555555555556	0.159649649102876
48	5.4	3.4	1.5	0.4	Iris-setosa	1	0	0	0.266666666666667	0.62962962962963	0.722656797169744
49	5.4	3.4	1.7	0.2	Iris-setosa	1	0	0	0.117647058823529	0.62962962962963	0.687757248197022
50	5.4	3.7	1.5	0.2	Iris-setosa	1	0	0	0.133333333333333	0.685185185185185	0.737167698365962
51	5.4	3.9	1.3	0.4	Iris-setosa	1	0	0	0.307692307692308	0.722222222222222	0.777023333634539
52	5.4	3.9	1.7	0.4	Iris-setosa	1	0	0	0.235294117647059	0.722222222222222	0.713482010522215
53	5.5	2.3	4.0	1.3	Iris-versicolor	0	1	0	0.325	0.418181818181818	0.194219643823906
54	5.5	2.4	3.7	1.0	Iris-versicolor	0	1	0	0.27027027027027	0.436363636363636	0.241093824269382
55	5.5	2.4	3.8	1.1	Iris-versicolor	0	1	0	0.289473684210526	0.436363636363636	0.226058264210938
56	5.5	2.5	4.0	1.3	Iris-versicolor	0	1	0	0.325	0.454545454545455	0.201872265775898
57	5.5	2.6	4.4	1.2	Iris-versicolor	0	1	0	0.272727272727273	0.472727272727273	0.156225228875569
58	5.5	3.5	1.3	0.2	Iris-setosa	1	0	0	0.153846153846154	0.636363636363636	0.756691610416908
59	5.5	4.2	1.4	0.2	Iris-setosa	1	0	0	0.142857142857143	0.763636363636364	0.771935440609133
60	5.6	2.5	3.9	1.1	Iris-versicolor	0	1	0	0.282051282051282	0.446428571428571	0.213933207860434
61	5.6	2.7	4.2	1.3	Iris-versicolor	0	1	0	0.30952380952381	0.482142857142857	0.181519581637256
62	5.6	2.8	4.9	2.0	Iris-virginica	0	0	1	0.408163265306122	0.5	0.111996799091321
63	5.6	2.9	3.6	1.3	Iris-versicolor	0	1	0	0.361111111111111	0.517857142857143	0.277943121171659
64	5.6	3.0	4.1	1.3	Iris-versicolor	0	1	0	0.317073170731707	0.535714285714286	0.205693392743854
65	5.6	3.0	4.5	1.5	Iris-versicolor	0	1	0	0.333333333333333	0.535714285714286	0.156153617405426
66	5.7	2.5	5.0	2.0	Iris-virginica	0	0	1	0.4	0.43859649122807	0.0965737982202029
67	5.7	2.6	3.5	1.0	Iris-versicolor	0	1	0	0.285714285714286	0.456140350877193	0.278390203317582
68	5.7	2.8	4.1	1.3	Iris-versicolor	0	1	0	0.317073170731707	0.491228070175439	0.196228591121515
69	5.7	2.8	4.5	1.3	Iris-versicolor	0	1	0	0.288888888888889	0.491228070175439	0.148542053943545
70	5.7	2.9	4.2	1.3	Iris-versicolor	0	1	0	0.30952380952381	0.508771929824561	0.186821367793599
71	5.7	3.0	4.2	1.2	Iris-versicolor	0	1	0	0.285714285714286	0.526315789473684	0.190379016686771
72	5.7	3.8	1.7	0.3	Iris-setosa	1	0	0	0.176470588235294	0.666666666666667	0.698198801634805
73	5.7	4.4	1.5	0.4	Iris-setosa	1	0	0	0.266666666666667	0.771929824561404	0.758825404150609
74	5.8	2.6	4.0	1.2	Iris-versicolor	0	1	0	0.3	0.448275862068966	0.200536953059694
75	5.8	2.7	3.9	1.2	Iris-versicolor	0	1	0	0.307692307692308	0.46551724137931	0.218217860142616
76	5.8	2.7	4.1	1.0	Iris-versicolor	0	1	0	0.24390243902439	0.46551724137931	0.190910337541694
77	5.8	2.7	5.1	1.9	Iris-virginica	0	0	1	0.372549019607843	0.46551724137931	0.0924379577314657
78	5.8	2.7	5.1	1.9	Iris-virginica	0	0	1	0.372549019607843	0.46551724137931	0.0924379577314657
79	5.8	2.8	5.1	2.4	Iris-virginica	0	0	1	0.470588235294118	0.482758620689655	0.0943726599781477
80	5.8	4.0	1.2	0.2	Iris-setosa	1	0	0	0.166666666666667	0.689655172413793	0.784021608790257
81	5.9	3.0	4.2	1.5	Iris-versicolor	0	1	0	0.357142857142857	0.508474576271186	0.186761512366878
82	5.9	3.0	5.1	1.8	Iris-virginica	0	0	1	0.352941176470588	0.508474576271186	0.0973257207195747
83	5.9	3.2	4.8	1.8	Iris-versicolor	0	1	0	0.375	0.542372881355932	0.126712735034151
84	6.0	2.2	4.0	1.0	Iris-versicolor	0	1	0	0.25	0.366666666666667	0.183758509548148
85	6.0	2.2	5.0	1.5	Iris-virginica	0	0	1	0.3	0.366666666666667	0.0885712440311769
86	6.0	2.7	5.1	1.6	Iris-versicolor	0	1	0	0.313725490196078	0.45	0.0907272611961409
87	6.0	2.9	4.5	1.5	Iris-versicolor	0	1	0	0.333333333333333	0.483333333333333	0.147223724664182
88	6.0	3.0	4.8	1.8	Iris-virginica	0	0	1	0.375	0.5	0.120628357257542
89	6.0	3.4	4.5	1.6	Iris-versicolor	0	1	0	0.355555555555556	0.566666666666667	0.16163497279113
90	6.1	2.6	5.6	1.4	Iris-virginica	0	0	1	0.25	0.426229508196721	0.0597292318554775
91	6.1	2.8	4.0	1.3	Iris-versicolor	0	1	0	0.325	0.459016393442623	0.202828547374176
92	6.1	2.8	4.7	1.2	Iris-versicolor	0	1	0	0.25531914893617	0.459016393442623	0.123814688224948
93	6.1	2.9	4.7	1.4	Iris-versicolor	0	1	0	0.297872340425532	0.475409836065574	0.126190742362697
94	6.1	3.0	4.6	1.4	Iris-versicolor	0	1	0	0.304347826086957	0.491803278688525	0.138317919091645
95	6.1	3.0	4.9	1.8	Iris-virginica	0	0	1	0.36734693877551	0.491803278688525	0.110921074597917
96	6.2	2.2	4.5	1.5	Iris-versicolor	0	1	0	0.333333333333333	0.354838709677419	0.127102859928249
97	6.2	2.8	4.8	1.8	Iris-virginica	0	0	1	0.375	0.451612903225806	0.113990321158717
98	6.2	2.9	4.3	1.3	Iris-versicolor	0	1	0	0.302325581395349	0.467741935483871	0.166702290969475
99	6.2	3.4	5.4	2.3	Iris-virginica	0	0	1	0.425925925925926	0.548387096774194	0.0811783736332713
100	6.3	2.3	4.4	1.3	Iris-versicolor	0	1	0	0.295454545454545	0.365079365079365	0.138329002279972

Rows: 1-100 of 150 | Columns: 11

Let's create a model to classify the Iris virginica.

In [21]:

predictors = ["PetalLengthCm", "SepalLengthCm", "SepalWidthCm", 
              "PetalWidthCm", "ratio_pwl", "ratio_swl"]
response = "Species_Iris-virginica"
model = LinearSVC("svc_virginica_iris")
cross_validate(model, iris, predictors, response)

Out[21]:

	auc	prc_auc	accuracy	log_loss	precision	recall	f1_score	mcc	informedness	markedness	csi	time
1-fold	0.9883333333333334	0.9809541204839196	0.96	0.124753596556893	0.9090909090909091	1.0	0.9523809523809523	0.9211323729436766	0.9333333333333333	0.9090909090909092	0.9090909090909091	1.9328792095184326
2-fold	0.9961904761904762	0.9910912698412698	0.98	0.0803143364420691	0.9375	1.0	0.967741935483871	0.9543135154205278	0.9714285714285715	0.9375	0.9375	1.7381629943847656
3-fold	1.0	0.9999999999999999	1.0	0.0850368152073147