In this example, we use VerticaPy to detect fraudulent credit card transactions. You can download the Jupyter notebook here.

The Credit Card Fraud Detection dataset contains credit card transactions from September 2013 by European cardholders. It contains numerical input variables from a principal component analysis (PCA) transformation.

To preserve the cardholders' confidentiality, we cannot access the original features and background information about the data.

"Time" and "Amount" are the only features that have not been transformed with PCA.

V1, V2,..., V28 : principal components from PCA
Time : Number of seconds elapsed between this transaction and the first transaction in the dataset
Amount : Transaction amount
Class : Response variable, where a value of 1 indicates fraudulent activity

"Amount" will be useful for example-dependent cost-sensitive learning.

We will follow the entire 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 [1]:

import verticapy as vp
vp.__version__

Out[1]:

'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 [2]:

vp.connect("VerticaDSN")

Let's create a Virtual DataFrame of the dataset.

In [3]:

creditcard = vp.read_csv('data/creditcard.csv', 
                         parse_nrows = 1000)
display(creditcard)

	123 Time Int	123 V1 Float	123 V2 Float	123 V3 Float	123 V4 Float	123 V5 Float	123 V6 Float	123 V7 Float	123 V8 Float	123 V9 Float	123 V10 Float	123 V11 Float	123 V12 Float	123 V13 Float	123 V14 Float	123 V15 Float	123 V16 Float	123 V17 Float	123 V18 Float	123 V19 Float	123 V20 Float	123 V21 Float	123 V22 Float	123 V23 Float	123 V24 Float	123 V25 Float	123 V26 Float	123 V27 Float	123 V28 Float	123 Amount Numeric(9,3)	123 Class Int
1	0	-1.3598071336738	-0.0727811733098497	2.53634673796914	1.37815522427443	-0.338320769942518	0.462387777762292	0.239598554061257	0.0986979012610507	0.363786969611213	0.0907941719789316	-0.551599533260813	-0.617800855762348	-0.991389847235408	-0.311169353699879	1.46817697209427	-0.470400525259478	0.207971241929242	0.0257905801985591	0.403992960255733	0.251412098239705	-0.018306777944153	0.277837575558899	-0.110473910188767	0.0669280749146731	0.128539358273528	-0.189114843888824	0.133558376740387	-0.0210530534538215	149.62	0
2	0	1.19185711131486	0.26615071205963	0.16648011335321	0.448154078460911	0.0600176492822243	-0.0823608088155687	-0.0788029833323113	0.0851016549148104	-0.255425128109186	-0.166974414004614	1.61272666105479	1.06523531137287	0.48909501589608	-0.143772296441519	0.635558093258208	0.463917041022171	-0.114804663102346	-0.183361270123994	-0.145783041325259	-0.0690831352230203	-0.225775248033138	-0.638671952771851	0.101288021253234	-0.339846475529127	0.167170404418143	0.125894532368176	-0.00898309914322813	0.0147241691924927	2.69	0
3	1	-1.35835406159823	-1.34016307473609	1.77320934263119	0.379779593034328	-0.503198133318193	1.80049938079263	0.791460956450422	0.247675786588991	-1.51465432260583	0.207642865216696	0.624501459424895	0.066083685268831	0.717292731410831	-0.165945922763554	2.34586494901581	-2.89008319444231	1.10996937869599	-0.121359313195888	-2.26185709530414	0.524979725224404	0.247998153469754	0.771679401917229	0.909412262347719	-0.689280956490685	-0.327641833735251	-0.139096571514147	-0.0553527940384261	-0.0597518405929204	378.66	0
4	1	-0.966271711572087	-0.185226008082898	1.79299333957872	-0.863291275036453	-0.0103088796030823	1.24720316752486	0.23760893977178	0.377435874652262	-1.38702406270197	-0.0549519224713749	-0.226487263835401	0.178228225877303	0.507756869957169	-0.28792374549456	-0.631418117709045	-1.0596472454325	-0.684092786345479	1.96577500349538	-1.2326219700892	-0.208037781160366	-0.108300452035545	0.00527359678253453	-0.190320518742841	-1.17557533186321	0.647376034602038	-0.221928844458407	0.0627228487293033	0.0614576285006353	123.5	0
5	2	-1.15823309349523	0.877736754848451	1.548717846511	0.403033933955121	-0.407193377311653	0.0959214624684256	0.592940745385545	-0.270532677192282	0.817739308235294	0.753074431976354	-0.822842877946363	0.53819555014995	1.3458515932154	-1.11966983471731	0.175121130008994	-0.451449182813529	-0.237033239362776	-0.0381947870352842	0.803486924960175	0.408542360392758	-0.00943069713232919	0.79827849458971	-0.137458079619063	0.141266983824769	-0.206009587619756	0.502292224181569	0.219422229513348	0.215153147499206	69.99	0
6	2	-0.425965884412454	0.960523044882985	1.14110934232219	-0.168252079760302	0.42098688077219	-0.0297275516639742	0.476200948720027	0.260314333074874	-0.56867137571251	-0.371407196834471	1.34126198001957	0.359893837038039	-0.358090652573631	-0.137133700217612	0.517616806555742	0.401725895589603	-0.0581328233640131	0.0686531494425432	-0.0331937877876282	0.0849676720682049	-0.208253514656728	-0.559824796253248	-0.0263976679795373	-0.371426583174346	-0.232793816737034	0.105914779097957	0.253844224739337	0.0810802569229443	3.67	0
7	4	1.22965763450793	0.141003507049326	0.0453707735899449	1.20261273673594	0.191880988597645	0.272708122899098	-0.00515900288250983	0.0812129398830894	0.464959994783886	-0.0992543211289237	-1.41690724314928	-0.153825826253651	-0.75106271556262	0.16737196252175	0.0501435942254188	-0.443586797916727	0.00282051247234708	-0.61198733994012	-0.0455750446637976	-0.21963255278686	-0.167716265815783	-0.270709726172363	-0.154103786809305	-0.780055415004671	0.75013693580659	-0.257236845917139	0.0345074297438413	0.00516776890624916	4.99	0
8	7	-0.89428608220282	0.286157196276544	-0.113192212729871	-0.271526130088604	2.6695986595986	3.72181806112751	0.370145127676916	0.851084443200905	-0.392047586798604	-0.410430432848439	-0.705116586646536	-0.110452261733098	-0.286253632470583	0.0743553603016731	-0.328783050303565	-0.210077268148783	-0.499767968800267	0.118764861004217	0.57032816746536	0.0527356691149697	-0.0734251001059225	-0.268091632235551	-0.204232669947878	1.0115918018785	0.373204680146282	-0.384157307702294	0.0117473564581996	0.14240432992147	93.2	0
9	7	-0.644269442348146	1.41796354547385	1.0743803763556	-0.492199018495015	0.948934094764157	0.428118462833089	1.12063135838353	-3.80786423873589	0.615374730667027	1.24937617815176	-0.619467796121913	0.291474353088705	1.75796421396042	-1.32386521970526	0.686132504394383	-0.0761269994382006	-1.2221273453247	-0.358221569869078	0.324504731321494	-0.156741852488285	1.94346533978412	-1.01545470979971	0.057503529867291	-0.649709005559993	-0.415266566234811	-0.0516342969262494	-1.20692108094258	-1.08533918832377	40.8	0
10	9	-0.33826175242575	1.11959337641566	1.04436655157316	-0.222187276738296	0.49936080649727	-0.24676110061991	0.651583206489972	0.0695385865186387	-0.736727316364109	-0.366845639206541	1.01761446783262	0.836389570307029	1.00684351373408	-0.443522816876142	0.150219101422635	0.739452777052119	-0.540979921943059	0.47667726004282	0.451772964394125	0.203711454727929	-0.246913936910008	-0.633752642406113	-0.12079408408185	-0.385049925313426	-0.0697330460416923	0.0941988339514961	0.246219304619926	0.0830756493473326	3.68	0
11	10	0.38497821518095	0.616109459176472	-0.874299702595052	-0.0940186259679115	2.92458437838817	3.31702716826156	0.470454671805879	0.53824722837695	-0.558894612428441	0.30975539423728	-0.259115563735702	-0.326143233995877	-0.0900467227020648	0.362832368569793	0.928903660629178	-0.129486811402759	-0.809978925963589	0.359985390219981	0.70766382644648	0.12599157561542	0.049923685888971	0.238421512225103	0.00912986861262866	0.996710209581086	-0.767314827174801	-0.492208295340017	0.042472441919027	-0.0543373883732122	9.99	0
12	10	1.249998742053	-1.22163680921816	0.383930151282291	-1.23489868766892	-1.48541947377961	-0.753230164566149	-0.689404975426345	-0.227487227519552	-2.09401057344842	1.32372927445937	0.227666231237246	-0.242681998944186	1.20541680770748	-0.317630527025074	0.725674990179153	-0.815612186027305	0.873936447614439	-0.847788598847099	-0.683192626267037	-0.102755941505071	-0.231809239223849	-0.483285330117712	0.0846676908596583	0.392830885335013	0.161134553588505	-0.354990039673962	0.0264155490776107	0.0424220887282304	121.5	0
13	10	1.44904378114715	-1.17633882535966	0.913859832832795	-1.37566665499943	-1.97138316545323	-0.62915213889734	-1.4232356010359	0.0484558879088564	-1.72040839292037	1.62665905834133	1.1996439495421	-0.671439778462005	-0.513947152539479	-0.0950450453999549	0.230930409124119	0.0319674667862076	0.253414715863197	0.854343814324194	-0.221365413645481	-0.387226474431156	-0.00930189652490052	0.313894410791098	0.0277401580170247	0.500512287104917	0.25136735874921	-0.129477953726618	0.0428498709381461	0.0162532619375515	7.8	0
14	11	1.0693735878819	0.287722129331455	0.828612726634281	2.71252042961718	-0.178398016248009	0.337543730282968	-0.0967168617395962	0.115981735546597	-0.221082566236194	0.460230444301678	-0.773656930526689	0.32338724546722	-0.0110758870883779	-0.178485175177916	-0.65556427824926	-0.19992517131173	0.1240054151819	-0.980496201537345	-0.982916082135047	-0.153197231044512	-0.0368755317335273	0.0744124028162195	-0.0714074332998586	0.104743752596029	0.548264725394119	0.104094153162781	0.0214910583643189	0.021293311477486	27.5	0
15	12	-2.7918547659339	-0.327770756658658	1.64175016056605	1.76747274389883	-0.136588446465306	0.80759646826532	-0.422911389711497	-1.90710747624096	0.755712908314791	1.1510869876677	0.844555470974377	0.7929439518176	0.370448092803246	-0.734975105820311	0.406795710431001	-0.303057623825763	-0.155868714793874	0.778265457041536	2.22186801373788	-1.58212204356551	1.15166304848789	0.222181966098225	1.02058620426601	0.0283166513238872	-0.232746324289105	-0.23555721754117	-0.16477751177654	-0.0301536365592253	58.8	0
16	12	-0.752417042956605	0.345485415344747	2.05732291276727	-1.46864329840046	-1.1583936804082	-0.0778498291166733	-0.608581418236123	0.00360348436201849	-0.436166983515744	0.747730827192802	-0.793980602837221	-0.770406728847129	1.04762699748088	-1.06660368148653	1.10695345662141	1.66011355713381	-0.279265373246772	-0.419994141181313	0.432535348618175	0.263450864446125	0.499624954671111	1.35365048557231	-0.256573280448308	-0.0650837078816517	-0.0391243535426488	-0.0870864732146962	-0.180997500092721	0.129394059390202	15.99	0
17	12	1.10321543528383	-0.0402962145973447	1.2673320885949	1.28909146962552	-0.735997163604068	0.288069162976262	-0.586056786337461	0.189379713679593	0.782332891785191	-0.267975066537173	-0.450311279515466	0.936707714991982	0.708380406186981	-0.468647287707221	0.354574063407955	-0.246634655717582	-0.00921237772707382	-0.595912405700819	-0.57568162226261	-0.113910176982092	-0.0246120063374677	0.196001952806192	0.0138016541409422	0.103758331023198	0.364297540595235	-0.382260574113217	0.092809187460487	0.0370505169810008	12.99	0
18	13	-0.436905071360625	0.918966212909322	0.92459077438817	-0.727219053596792	0.915678718106307	-0.127867352079254	0.707641607333935	0.0879623554672504	-0.66527135413364	-0.737979823596458	0.32409781346169	0.277192107214981	0.252624256310781	-0.291896460370468	-0.184520169327133	1.14317370716197	-0.92870926272403	0.680469592634687	0.0254364616880793	-0.0470212823165035	-0.194795823794671	-0.672637997017793	-0.156857514491897	-0.888386320943716	-0.342413218776576	-0.049026728633951	0.0796923991551505	0.131023789452311	0.89	0
19	14	-5.40125766315825	-5.45014783420644	1.18630463143652	1.73623880012095	3.04910587764025	-1.76340557365201	-1.55973769907953	0.160841747266769	1.23308974041888	0.345172827050629	0.917229867699146	0.970116716069048	-0.266567764915222	-0.479129929276704	-0.526608502569153	0.47200411177674	-0.725480944982201	0.075081351540202	-0.406866573198217	-2.19684802485647	-0.503600328973703	0.984459785590244	2.45858857639219	0.0421188969891572	-0.481630823956716	-0.621272013713977	0.392053289557744	0.949594245504846	46.8	0
20	15	1.4929359769862	-1.02934573189487	0.45479473374366	-1.43802587991702	-1.55543410136344	-0.720961147043557	-1.08066413038614	-0.0531271179483221	-1.9786815953872	1.63807603690446	1.07754241162743	-0.63204651464934	-0.41695716661602	0.0520105153724404	-0.0429789228232019	-0.166432496451972	0.304241418614353	0.554432499062278	0.0542295152184719	-0.387910172646258	-0.177649846438814	-0.175073809074822	0.0400022190621329	0.295813862676508	0.33293059939425	-0.220384850672322	0.0222984359135846	0.00760225559997897	5.0	0
21	16	0.694884775607337	-1.36181910308009	1.02922103956032	0.834159299216716	-1.19120879445965	1.30910881872952	-0.878585911450457	0.4452901278385	-0.446195831557423	0.568520735086962	1.01915061274695	1.29832870056251	0.420480265280796	-0.372650997239682	-0.807979512809369	-2.04455748288968	0.515663469043577	0.625847298442513	-1.30040816880609	-0.138333940419021	-0.295582931552029	-0.571955006812512	-0.0508807005036795	-0.304214501020644	0.0720010061385359	-0.422234430367677	0.0865533980909977	0.0634986493439305	231.71	0
22	17	0.962496069914852	0.32846102605212	-0.17147905415064	2.10920406774016	1.12956557126894	1.6960376856836	0.107711607311367	0.521502163844302	-1.19131110205143	0.724396314588903	1.6903299205808	0.406773575635315	-0.936421295934551	0.98373941913199	0.710910766068067	-0.602231772166344	0.402484375627273	-1.73716203452457	-2.02761232183279	-0.269320966548419	0.14399742335114	0.402491661406291	-0.0485082211745289	-1.37186629453889	0.390813885438659	0.199963657504328	0.0163706432842991	-0.01460532767228	34.09	0
23	18	0.247491127783665	0.277665627353681	1.18547084217971	-0.0926025498576041	-1.31439397897076	-0.150115997622665	-0.946364950111676	-1.61793505064675	1.54407140197844	-0.82988060074647	-0.583199526903095	0.524933232159904	-0.45337529664688	0.0813930875646215	1.55520419597553	-1.39689489286937	0.783130838324676	0.436621213910235	2.17780716839543	-0.230983142903519	1.65018036054154	0.200454090999037	-0.185352508080436	0.42307314795406	0.820591261750983	-0.227631863934761	0.336634446911129	0.250475352427605	22.75	0
24	18	1.16661638244228	0.502120087854101	-0.0673003143663533	2.26156923949128	0.428804194630708	0.0894735167274599	0.241146579907281	0.138081705243702	-0.989162395259052	0.922174967079328	0.744785789437272	-0.531377250104474	-2.1053464503177	1.12687010488156	0.00307532251490036	0.424424506356606	-0.454475291663708	-0.0988706272108058	-0.816597306905994	-0.307168508741084	0.0187018719918659	-0.0619722672279421	-0.103854921794533	-0.370415176650599	0.603200338674873	0.108555872801682	-0.0405207055560295	-0.0114178152991164	2.28	0
25	22	-2.0742946722629	-0.121481799450951	1.32202063048967	0.410007514171835	0.295197545759436	-0.95953722984438	0.543985491287656	-0.104626728092018	0.475664017945495	0.149450615348245	-0.856566363963256	-0.180523156037298	-0.655232930357476	-0.27979685563853	-0.21166795514315	-0.333320609694671	0.010751094250554	-0.488472666295676	0.505751034478604	-0.386693573241769	-0.403639498840125	-0.227404004096502	0.742434864076795	0.398534855447456	0.249212161486784	0.274404273874965	0.359969356358436	0.243231671798911	26.43	0
26	22	-1.94652513121534	-0.0449005054418194	-0.405570068378956	-1.01305733702394	2.94196769950545	2.95505339674562	-0.0630631473635638	0.855546309018146	0.0499669002270836	0.573742508037695	-0.0812565147381817	-0.215745003282808	0.0441606277765361	0.0338977566837455	1.19071767502074	0.578843475256385	-0.975667025451307	0.0440628177757039	0.488602868957758	-0.216715254448926	-0.579525934402369	-0.799228952914653	0.870300215304704	0.983421492506598	0.321201132609584	0.149649876930755	0.707518836410842	0.014599751533029	0.89	0
27	23	-0.414288810090829	0.905437322625407	1.72745294417921	1.47347126657189	0.00744274117322988	-0.200330677416199	0.740228319420026	-0.029247400012072	-0.593392019124765	-0.346188231273199	-0.0121421884961019	0.786796316060126	0.635953883297271	-0.0863244719500975	0.0768036871984215	-1.4059193336148	0.775591738395162	-0.94288892749919	0.543969461627011	0.0973075910928853	0.0772374339988386	0.457330598656119	-0.038499724582026	0.642521902774992	-0.183891335259639	-0.277464019495649	0.182687486490454	0.152664644968975	33.0	0
28	23	1.05938711501788	-0.175319186719244	1.26612964251002	1.18610995469348	-0.786001752758539	0.578435276462307	-0.767084276374229	0.401046149117525	0.699499675903727	-0.0647375556773487	1.04829248789913	1.00561836488785	-0.542001579163132	-0.0399145024672579	-0.218683247678604	0.00447568219903875	-0.193554038650394	0.0423879619548074	-0.277833720535009	-0.178023367448801	0.0136762939208399	0.213733610123234	0.0144618494665875	0.00295085991542244	0.294638014829328	-0.395069505138473	0.081461117248889	0.0242203485620962	12.99	0
29	23	1.17328461017079	0.353497876646456	0.28390506526532	1.1335633178795	-0.172577181842493	-0.916053706932115	0.36902484539083	-0.327260242196767	-0.24665102789456	-0.0461393022689538	-0.143418527309124	0.979350375717585	1.49228543545219	0.101417525935881	0.76147754528118	-0.014584082470356	-0.511640116553888	-0.32505635460906	-0.390933797720026	0.0278779087328671	0.0670033044874043	0.227811927638182	-0.150487224821759	0.43504510338369	0.724824579577241	-0.337082059875827	0.0163683792669046	0.0300411908366385	41.88	0
30	23	1.32270726911234	-0.17404083293642	0.434555031250987	0.576037652384661	-0.836758045983797	-0.831083411483829	-0.264904960791055	-0.220981942667704	-1.07142461772052	0.868558547570527	-0.641506289794406	-0.111315775017413	0.361485409760927	0.171945121866125	0.782166531823632	-1.35587072953395	-0.216935152965165	1.27176538520308	-1.24062193508556	-0.522950940722936	-0.284375572220815	-0.323357410638449	-0.0377099050596787	0.347150938808497	0.559639136527168	-0.280158165778367	0.042335257639718	0.0288223002307744	16.0	0
31	24	1.23742903021294	0.0610425841868962	0.380525879794222	0.761564111432371	-0.359770710369787	-0.494084149915291	0.00649421810779282	-0.133862379689891	0.438809736716666	-0.207358045517011	-0.92918211475144	0.5271060605933	0.348675901114132	-0.152535138608542	-0.218385629647018	-0.191551818259596	-0.116580602716053	-0.633790816521738	0.348415801097774	-0.0663513345433597	-0.245682498259096	-0.530900256150069	-0.0442653968237672	0.0791680288586917	0.50913568954621	0.288857833917937	-0.0227049816562784	0.0118362314304161	17.28	0
32	25	1.11400859541157	0.0855460896870318	0.493702487395368	1.33575998514475	-0.300188550950467	-0.0107537834263628	-0.11876001509605	0.188616695943139	0.20568684906514	0.0822622587556722	1.13355567149479	0.626699002489221	-1.49278039238295	0.520787893899183	-0.674592596871812	-0.529108241855907	0.158256197923207	-0.398751479349713	-0.1457089090445	-0.273832367278761	-0.0532336603921118	-0.0047601512119153	-0.0314701703936453	0.198053718143193	0.565007312878958	-0.337718126200803	0.0290574021222937	0.00445263143187997	4.45	0
33	26	-0.53538776309446	0.865267807575272	1.35107628772237	0.14757547449791	0.433680212077009	0.0869829381161816	0.693039311115721	0.179742260742556	-0.285641861230583	-0.482474471178567	0.871799580440785	0.853447434991487	-0.571821891415037	0.102252103048142	-1.51999120265821	-0.285912497081499	-0.309633386824141	-0.403901992939884	-0.823742994489464	-0.283263782156003	0.049525686687599	0.206536543024476	-0.18710806982075	0.000753014257497798	0.0981166059546266	-0.553470968822753	-0.0783055021726955	0.0254273775211197	1.77	0
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36	26	-0.529912284186556	0.873891581460326	1.34724732930113	0.145456676582257	0.414208858362661	0.10022309405219	0.711206082959649	0.1760659570625	-0.286716934699997	-0.484687683196852	0.872489590125871	0.851635859904339	-0.571745302934562	0.100974273045751	-1.51977183258512	-0.284375978261788	-0.310523584869201	-0.404247868800905	-0.823373523914155	-0.290347610865436	0.0469490671140629	0.208104855076299	-0.185548346773547	0.00103065983293288	0.0988157011025622	-0.552903603040518	-0.0732880835681738	0.0233070451077205	6.14	0
37	27	-1.45218727859439	1.76512373913739	0.611668540757038	1.17682498424561	-0.445979892057813	0.246826451919258	-0.257566155685306	1.0924724973132	-0.607524461211062	0.0471555530038123	0.783726853195604	1.0963856736135	-0.26809420573452	0.768648040128495	-0.524367354238622	-0.808816147106875	0.710386067439587	-0.11836878699997	0.979287835535805	0.00871333379747532	0.0822798172206588	0.325782190832103	-0.069107391080501	0.0209619966159794	-0.0446684875032122	-0.243441391677247	0.149180325186687	0.120556907850199	1.8	0
38	27	-0.246045948703835	0.47326690335701	1.69573755374059	0.262411487973117	-0.0108664136529745	-0.610835935296661	0.793936545512066	-0.247252830908628	0.138879113774066	-0.401007068346067	-0.812050381942678	-0.183524462361787	-0.630112887102238	-0.286217451066222	-0.337046323577501	-0.42810547355755	-0.0306021083323427	-0.504568166264421	0.355180278263647	0.0457211272611911	-0.194599935207223	-0.335132725895693	-0.0781796063470994	0.392783891527158	-0.0311571467736638	0.198036799472821	-0.175347300741823	-0.203616155701414	30.49	0
39	29	0.996369531566045	-0.12258878723806	0.546819472613086	0.706579541087689	0.134559557409452	1.15699511200606	-0.294561331432968	0.407429099419853	0.337862663634561	-0.408150492552647	0.682646123949549	1.25371968484033	0.391917044082342	-0.0375108583595551	0.795301519477008	-1.6682105913656	1.32299488209244	-2.83003522867318	-1.46343168833485	-0.203461209817417	-0.0763018365480559	0.108866913420892	0.162230940339532	-0.575624047818567	0.109794914589208	0.373813367278979	0.0505521972760614	0.00510555920011407	20.53	0
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45	34	-0.762255665726893	0.127767751953647	2.65005638571315	-1.87566277123804	-0.893356398126455	-0.268714889488759	-0.419863596621261	0.146233406715251	-0.869635290154597	-0.0386516694016891	-0.686124387103008	-0.502910878643487	1.38082632218495	-1.03912460633328	0.652842089032808	1.89874756257003	-0.458413549068005	-0.559803242547051	-0.295102639926884	0.359392905714987	0.433349641511561	1.26040266443393	-0.404700036155232	0.0949455232807396	0.480975976870017	-0.0906846797223101	0.319222972697776	0.135599924615913	15.99	0
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47	34	0.201685891430752	0.497483215432781	1.3739125741005	0.571405317647578	-0.630657750142243	-0.539659123772599	-0.0762702908119869	-0.917105750019037	0.270008406215231	-0.480280682110825	-0.512532739970476	0.680906258686799	0.089923036521968	-0.157405056857078	-0.588819331688659	-0.477908445696603	0.22538879557879	-0.668680159238467	-0.0235994213112055	-0.222302592236684	0.718961069869173	-0.17187687023179	-0.16620525458887	0.776471323845633	0.818460355548391	0.442547455443563	0.142757246943121	0.219237609708497	9.99	0
48	34	1.13831556625444	0.0569559699973862	0.649418964599217	0.873062040924213	-0.468466330715866	-0.410194552246249	-0.0138975543027732	-0.0724396093157116	0.306787909036459	-0.269952637390657	-0.00260184782303436	1.12430421589913	0.744206684168937	-0.188353421358499	-0.07566196255573	-0.70919227171914	0.381219102546287	-1.37208017404084	-0.273701149259017	-0.078354632808708	-0.16422241479465	-0.247400539229342	0.0594050645049741	0.456286465174056	0.361004003525112	0.274414145848337	-0.00249836244665451	0.017108846940255	21.34	0
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50	35	1.19935593362078	0.129953154513887	0.863584970776281	1.00263476869323	-0.783761014593659	-0.884679005672016	-0.0407432757589571	-0.208068511671504	0.392477871628745	-0.248177899888804	-0.0953627524727861	1.31413104809224	1.0916814094227	-0.409346352255035	-0.577994104632916	-0.581283742420706	0.212342679791527	-0.893181252962422	-0.0206528853522847	-0.0726201259267691	-0.0424680857272564	0.198474051899343	-0.0330099751170921	1.01329013084481	0.559097511348329	0.401817534390101	-0.00586465649000008	0.0179360319171187	0.99	0
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77	49	0.921543679723553	-0.0670837542257563	0.0774610275787093	0.953638217022313	0.0674124629108227	0.0161524649547512	0.32045155695341	0.0385340276125158	-0.391512665081147	0.0315602452397677	1.39169118010671	1.07936321996869	0.106267711683997	0.665985251334808	0.44225355774887	0.122646354959781	-0.492391586114359	-0.535140313996294	-0.0780818341113634	0.120050785637899	-0.333929581340575	-1.29991956674342	0.0843109903360168	-0.370397871198817	0.155101565371628	-0.834490365033198	0.000909065197964509	0.035546875724878	135.51	0
78	49	1.09860834614642	0.202423563829101	0.525455971945753	1.32343627201394	-0.130486421204476	0.0399243070766149	0.0283794159028238	0.0728410708847139	-0.0978693519806861	0.0195129951686423	1.47441332090063	1.68967421758435	0.506780523264567	0.125136664522659	-0.89270971177356	-0.621679133317781	0.0443402665913568	-0.642093954200622	-0.161986891000608	-0.128040892456864	-0.0249716784462107	0.154264260038072	-0.0631467432547598	0.253205307138793	0.629405434975953	-0.345344655387218	0.0404693378711826	0.010263750026757	13.18	0
79	50	-0.671708547741052	0.59450259438803	0.216415943954576	-0.867310638854276	2.96690830110092	3.63249487373809	0.563295074740477	0.673025596986071	-0.188766143762422	-0.404378291830518	-0.699710626192874	-0.184142608712838	-0.426813033653942	-0.183001108223398	-0.747731683219242	-0.0377075788937061	-0.866459638474451	-0.00725732026000804	-0.160432044223361	-0.00278433437563492	-0.136440966831564	-0.300362025601945	-0.331691623416602	0.996382470868604	0.502469492348796	-0.51804304841771	-0.208275755084745	-0.116048406394516	14.8	0
80	50	-0.571520749961747	1.07160044939815	1.28011024961142	0.542780003052458	0.574438986516567	-0.259359265830457	1.0611484151742	-0.410971967925814	-0.17913018113825	1.00350065764887	1.06238226849436	0.159422388058099	-0.2898603137468	0.00580474635482856	0.46044095320685	-0.22103526461389	-0.775852454545776	0.657023315008206	0.80758291868891	0.354730634765855	0.00355852008044498	0.561240486431022	-0.199286719692043	0.00138738938225278	-0.179529951929609	-0.374115725753305	0.0716414539902948	-0.175510468698003	9.79	0
81	51	1.25987313565004	0.25423957645842	0.51478862825195	0.620924297433486	-0.475930098771269	-0.992285839202021	0.0664165097996613	-0.209275058074655	0.0355715653783499	-0.0676158213568395	-0.204107263687151	0.402596690697874	0.376647694351449	0.227135013294715	1.02499612132291	0.29953171476471	-0.426046050892739	-0.550315065603572	-0.119898968647883	-0.0889700937046651	-0.256530535925767	-0.739211692487821	0.135732380872138	0.38198986620837	0.219301891750154	0.0942906925877441	-0.0286866677208069	0.019197591087878	1.98	0
82	52	-3.00523672241459	2.60013820219461	1.48369073726212	-2.41847295513682	0.306326406574465	-0.824574531939418	2.0654256392882	-1.82934658938092	4.00925851665725	6.05152135077273	2.57250018194268	0.0668507400137308	-0.353574309497439	-2.83713599830894	0.292226879668893	-0.303773839706442	-1.94230314485255	-0.435449716450276	-0.934016115189154	2.45672404561526	-0.852308858371298	-0.181268483843722	-0.163746504079237	0.515820525800135	0.13631843199517	0.460053967482399	-0.251258637837596	-1.10575115708552	1.46	0
83	52	1.14736892702922	0.0590346445535856	0.263632341401774	1.21102345823936	-0.0440955788263387	0.30106650133832	-0.132959855687363	0.227885136251461	0.252191237226831	0.083903938117339	0.645046450909254	0.413361748049543	-1.46803602930219	0.502861187887764	-0.626936022547138	-0.369716051829749	-0.0317992395701179	-0.215342173803487	0.0550196503583034	-0.255923874900886	-0.0878134178536766	-0.110756406773342	-0.0977707247600232	-0.323374178237458	0.633278881348768	-0.305327819106935	0.0273941237350875	-0.000580464688818191	6.67	0
84	53	-1.19896767411718	-1.47410047094211	1.8403259873066	-4.51582435488105	0.327567428246331	-0.174469282834848	0.959725705478786	-1.0264562279545	1.70043458447966	-0.0789417612044958	1.66266714493598	0.485619299748722	-0.93302495795613	-1.11878656487932	0.14125304079379	-2.81188754821512	-0.504745809870121	0.891222663154531	-1.51202243652326	-0.769854286810439	-0.453169416973525	0.334614040441455	-0.364541412466894	-0.310185782073785	-0.30259949355198	-1.24392415371264	-1.12345654520885	-0.73435108581633	89.17	0
85	54	1.20239832807905	0.321711386607054	0.281210894488001	0.643688582463962	-0.148668596204498	-0.589738666993022	0.0484125495667614	-0.0933612495778056	-0.042934036363588	-0.343245662317894	0.235106050512859	0.569881915499773	0.676330388590739	-0.351249746003609	1.29513005856263	0.164859782332548	0.246413935319911	-0.804462522225513	-0.561740542791253	-0.0707505670634631	-0.251113124454264	-0.680155165043549	0.148162526526488	0.0470615008737034	0.157049745885238	0.121934641489905	-0.00460789833531126	0.0294181090910756	7.53	0
86	55	-4.57509260816239	-4.42918377474876	3.40258500379828	0.903914679904333	3.00222377368078	-0.491077708080676	-2.70539316304114	0.666451302156469	1.92221617202329	-0.614312027380396	0.384926576987595	1.1944034523469	-1.02071845428099	-1.24682940571382	-2.34867343715332	-0.213437533486602	-0.100221744823898	-0.406073073481075	-1.63757251876291	-0.960962933953718	-0.0473650289231517	0.853359934678944	-0.971600429208365	-0.114861639404699	0.408300391838859	-0.304576465887789	0.547784788743973	-0.456296829036198	200.01	0
87	55	-0.773450000458189	0.85311249436819	0.818253541761677	-0.236070161217933	0.803462538724049	-1.43872833170719	0.799479364773059	-0.00798899962925418	-0.761089558526749	-1.04446403350044	1.50413489421274	-0.291634167856543	-1.61543302342075	-0.665286835592656	-0.292983045822984	0.803106054187593	0.462149366883927	0.83464109457954	-0.65179683321786	-0.10085848950269	0.0353615493510926	-0.116890316122963	-0.178926346760491	0.400155137444786	-0.0262306839064335	0.16515568350303	0.027761800392197	0.132979788496602	0.76	0
88	56	-0.847998365598453	1.04345933028073	1.26736889218816	1.13552949012637	0.0213621025987426	0.336914104132828	0.398479742797849	0.317399165838859	-0.0286579453593501	0.534033192472464	0.811280074910828	-0.0710028675857182	-1.96905159541282	0.450006443181567	-0.263173073378825	-0.968361412949194	0.459253723662508	0.0037711921426382	1.00071625183199	0.128621717056598	-0.0240461057456474	0.215006397493466	-0.131981589595316	-0.00741562681325391	-0.136578135429545	-0.242960778206656	0.38293084682331	0.276416935663384	20.22	0
89	56	0.0869961905163749	-0.0519887420255876	-0.497882441560081	-3.1519078565141	2.5584003623555	2.79667096978255	0.470283270790146	0.265332802943643	0.919513460198576	-0.735585687981152	0.208724948743441	0.0171306492463427	-0.110866963820059	-0.0426768695073913	1.65414036352275	-0.392648022607194	-0.875960217366143	0.183946189187007	1.25938002787067	0.167231088284993	-0.239425579903453	-0.437342143719405	0.0184257681232037	1.01303776342658	-0.258926558625905	-0.293189252573023	-0.394955581242805	-0.435995593150792	10.84	0
90	59	-0.773292609110981	-4.1460072502577	-0.932037567076045	0.0270936838890165	-1.69830732179181	0.460187805225441	0.737344474460422	-0.314215581514513	-0.84267253845447	0.0172757940177998	-0.617560331727886	-0.197503535476567	1.59495759349141	-0.259878797128783	1.22102546560587	1.32463951224473	0.120540185550046	-1.24864887121931	-0.00506979108522488	2.44278177400485	0.890977779336871	0.0261225750123657	-1.1347693370818	-0.654958249952389	0.0983862618989874	-0.209149914074031	-0.171709156383653	0.208056641158863	1142.02	0
91	59	0.921024018835922	-0.16244686110781	-0.0943313673869069	0.474083926327042	-0.0214859605972665	-0.397506306685279	0.482642978539503	-0.117495974844976	-0.577836031422653	-0.0186071371400667	1.83757918303173	1.45067106438787	0.679743972842061	0.593718449923865	0.249734697673045	-0.0843672205235	-0.25970727981991	-0.894995460456715	-0.0103739416854655	0.214510447897743	-0.209381106373359	-0.930107296377023	0.0285099107931845	0.0326820091099104	0.155130495109473	0.133250470013276	-0.0735342308160852	0.0223491449446096	149.9	0
92	60	1.06914138489519	0.0437859251672304	0.309867290850673	1.31669399295505	-0.462393623949898	-0.857887604269692	0.207903690796087	-0.191269941989371	0.0563978989012889	0.041567455076056	-0.507358124813112	-0.108666220084406	-0.473257348257937	0.452045889971559	1.00567481039881	0.185441397662765	-0.43997575238942	0.0125391476665563	-0.498587992492488	-0.00199825142437605	0.115775449915834	0.164781092368047	-0.177564054530198	0.391890569748269	0.624681738099145	-0.288376427654957	-0.00131183357960522	0.0358115192931624	89.4	0
93	60	1.10702937694843	0.216441000371351	0.538378149708233	1.47639799266774	-0.251941920499494	-0.340679706912496	0.154091744631261	-0.0865025456332286	0.144420201120718	-0.157374627687008	-0.107560297694088	1.0663256573792	0.620788366839222	-0.0708893376688794	-0.203857982828647	-0.853479419330768	0.336478013774869	-1.17953172110404	-0.501729107425755	-0.111852535538935	-0.0600374501076493	0.0598841227860989	-0.0475263664778327	0.443992418636119	0.640295758747984	-0.337657130668521	0.0421084838919154	0.024264710006858	26.72	0
94	62	-1.03510581776689	0.996013127817514	2.19247013559677	-0.170445302779918	-0.302319738525738	-0.142255767700287	0.223431774448596	0.289043410118421	0.0941408906153459	-0.157858732844487	-0.386373549409945	-0.628633662180404	-1.02395821122071	0.0984338746976314	1.56228876196439	0.168577701728536	-0.148826411284152	-0.285927210472601	-0.483363894151224	0.180287626805096	-0.098000008392506	-0.17024584412346	-0.13722752704315	0.0552282789358353	0.0793475542063078	0.302032602113411	0.391377349974797	0.196599880665289	5.99	0
95	64	-0.658304934095684	0.40679056737153	2.03746063876455	-0.291297974417195	0.147909808593845	-0.350857291958021	0.945373213135361	-0.172560016733978	0.0251333984849018	-0.778134723733662	-0.196289801937262	0.632955261826373	0.374025171567011	-0.531597207426503	-0.615062565100624	-0.518078459185166	0.00388089531948063	-1.2889540744158	-0.797804485217222	0.0641328738661188	-0.156095760618683	-0.238804964891445	0.0898771773985113	0.421195367129561	-0.352487134227907	0.0747827424634443	-0.0941921697507859	-0.0924931304008813	54.99	0
96	64	0.95960165851223	0.370711304613933	0.888613370045565	2.34324410302247	0.352490841084755	1.36551460619135	-0.277770730462741	0.516053179747465	-0.700929045055026	0.468216239367258	0.745611509947132	0.373531002993358	-0.223918285866667	0.417438142069896	1.67840014345469	-0.515701600237187	0.662478668271888	-2.5142351135941	-2.5896875748614	-0.298404520795831	-0.155547160729115	-0.403239315684771	0.356504034074842	-0.696881458915448	-0.198717970162506	-0.220267915515142	0.0685461961358583	0.0207973154161409	7.55	0
97	64	1.21251089095254	-0.0990542956039435	-1.19209409463426	0.286323561509755	2.16051625183209	3.61631350966622	-0.40420689806665	0.842330951647993	0.169360420742526	-0.0305221765721243	-0.541957258023106	0.237212014866616	-0.218129648703274	0.197436520971338	-0.147850245921019	-0.0978301417256899	-0.51005250120389	-0.0709392806421485	0.355170583653159	0.0147774396345371	-0.167496336516951	-0.494694569848075	-0.149785450968464	1.01122655467101	0.883547704730387	-0.329433810592075	0.020370145679431	0.0170370863505012	34.7	0
98	67	-1.49466784074271	0.837241399963629	2.62821061790607	3.14541437889465	-0.609098388854424	0.258495000688512	-0.0121886133587805	0.102136035246365	-0.286163596824287	1.19855632464938	-0.550295668711412	-0.106845988520745	0.208014288229433	-0.680510402769635	0.507763583158711	-0.260264022558778	0.246631323902287	0.00885550438424228	0.899415801359582	-0.0283519350532205	-0.140047358057139	0.355044183811602	0.332719988435228	0.718192517148152	-0.219366046114324	0.118926551385282	-0.317485702168288	-0.340783397650643	28.28	0
99	67	-0.653444627294995	0.160225076852038	1.59225555524082	1.29683228357565	0.997174923623236	-0.343000302409134	0.469936930779834	-0.132470081994361	-0.197794077439788	-0.105005538081425	-0.543662210926971	0.302233022635964	0.141211078726449	-0.207880443553101	0.0241083998795536	-1.20687659191564	0.39483638189259	-0.750955630206426	0.440558481170408	0.225920346918541	0.0383629679790368	0.336449012374641	-0.0148828328356718	0.102959010243	-0.265322060067868	-0.34863668662622	0.0112384491290326	-0.0494783399721492	19.85	0
100	68	-0.770196382647988	0.483572416412024	1.90107177893088	-0.00187625011618852	0.0242447851356973	-1.17190318158275	0.666483360897814	-0.0946029012075535	-0.136665621886762	-0.842507532652561	-0.408235097088101	0.503046644959921	-0.010588597193309	-0.200012764882671	-0.908689458907517	-0.323594882408827	-0.0221036727295719	-0.796683932841244	-0.479505428522999	-0.0338308901120332	-0.0573359108181297	-0.155801280763761	0.0181078020074367	0.941555368544963	-0.168581841126097	0.0561709969275176	0.0589793612903108	0.134187921277996	22.36	0

Rows: 1-100 | Columns: 31

Data Exploration

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

In [4]:

creditcard.describe()

Out[4]:

	count	mean	std	min	approx_25%	approx_50%	approx_75%	max
"Time"	284806	94813.8413657027	47488.2283297513	0.0	53836.3519125683	84348.356547619	139145.62236534	172792.0
"V1"	284806	4.94593944284826e-06	1.9586974640224	-56.407509631329	-0.922687561939835	-0.00402352156353561	1.31589044482424	2.45492999121121
"V2"	284806	5.70457762978566e-06	1.65130867214891	-72.7157275629303	-0.595755755649292	0.0648887280140533	0.806345971979393	22.0577289904909
"V3"	284806	-8.9455359328619e-06	1.51625015150494	-48.3255893623954	-0.889747862139421	0.179795003048091	1.02790240542886	9.38255843282114
"V4"	284806	-1.35415518936858e-06	1.4158708761878	-5.68317119816995	-0.850673053289735	-0.0227690960995851	0.742162498479369	16.8753440335975
"V5"	284806	-1.76537738534109e-06	1.38024883562916	-113.743306711146	-0.692237575696747	-0.054146987315591	0.612683911437621	34.8016658766686
"V6"	284806	-1.78084282248157e-06	1.33227308968888	-26.1605059358433	-0.767764777497726	-0.272073011134111	0.397409728991759	73.3016255459646
"V7"	284806	6.12498031875639e-06	1.23709145154523	-43.5572415712451	-0.553882847518934	0.0398145626467979	0.570420541346974	120.589493945238
"V8"	284806	-2.67056953047529e-06	1.19435414910998	-73.2167184552674	-0.208766182758203	0.022006162856551	0.328470871881628	20.0072083651213
"V9"	284806	-1.05394689850686e-05	1.09861961972555	-13.4340663182301	-0.641658431375348	-0.0516690117329882	0.59598968061615	15.5949946071278
"V10"	284806	4.08381472133854e-06	1.08884949581936	-24.5882624372475	-0.535699872562504	-0.0929203715980967	0.453282552509602	23.7451361206545
"V11"	284806	-1.38169915208807e-06	1.02071455331551	-4.79747346479757	-0.763765051282868	-0.0338218748537519	0.739841748427711	12.0189131816199
"V12"	284806	6.93843535334324e-06	0.999196282625864	-18.6837146333443	-0.404322288797075	0.141928630337509	0.618731149795737	7.8483920756446
"V13"	284806	-8.12075363651004e-07	0.995275883057862	-5.79188120632084	-0.649459842407078	-0.0133491049029432	0.661437168912665	7.12688295859376
"V14"	284806	-1.84962341608303e-06	0.95859678593258	-19.2143254902614	-0.426741184891107	0.0511643166509132	0.492764910455353	10.5267660517847
"V15"	284806	1.13497169209891e-05	0.91529757725878	-4.49894467676621	-0.583026504706252	0.0464760315849951	0.649751230006888	8.87774159774277
"V16"	284806	-7.66515009784341e-08	0.876254424770488	-14.1298545174931	-0.467552238700086	0.0662673912174244	0.523427807344667	17.3151115176278
"V17"	284806	-1.82546167118454e-06	0.849337996047683	-25.1627993693248	-0.483346901949957	-0.0660582514236486	0.399404850508734	9.25352625047285
"V18"	284806	-3.95506512618923e-06	0.838175023391719	-9.49874592104677	-0.499033588630568	-0.00326277745515932	0.500574214811809	5.04106918541184
"V19"	284806	-2.80927640719469e-07	0.81404191608048	-7.21352743017759	-0.454885031303711	0.00365240266736609	0.458694074365924	5.59197142733558
"V20"	284806	-7.33947797666482e-07	0.770926278808211	-54.497720494566	-0.211671047672314	-0.0624977050964054	0.133346175929553	39.4209042482199
"V21"	284806	-7.64172187575889e-07	0.734525190677675	-34.8303821448146	-0.2286085901976	-0.0293868910448687	0.186064488481304	27.2028391573154
"V22"	284806	-2.66232723466359e-06	0.725701443601768	-10.933143697655	-0.542158403990438	0.00674792105323886	0.528403121589584	10.5030900899454
"V23"	284806	-9.87528822847108e-07	0.624461169497999	-44.8077352037913	-0.161700875369553	-0.011133509692752	0.147758350823079	22.5284116897749
"V24"	284806	-2.58634991744588e-06	0.605646558279992	-2.83662691870341	-0.353468648185489	0.0409638594891091	0.438843291633271	4.58454913689817
"V25"	284806	2.60318278485781e-06	0.521277134452016	-10.2953970749851	-0.317398528013778	0.0169733881663996	0.349873011475687	7.51958867870916
"V26"	284806	-8.96574869783747e-07	0.482227622472413	-2.60455055280817	-0.327442353708538	-0.0538597392382451	0.24123393626275	3.5173456116238
"V27"	284806	-4.98388964024732e-07	0.403633115942523	-22.5656793207827	-0.0710228898328251	0.00143959250889526	0.0913103439918259	31.6121981061363
"V28"	284806	-8.01132016653443e-07	0.330083566760313	-15.4300839055349	-0.052949981732936	0.0112649959176305	0.0783476607706018	33.8478078188831
"Amount"	284806	88.3497556582376	250.120537753744	0.0	5.63722943722944	22.0010913705584	77.0284982935154	25691.16
"Class"	284806	0.00172749169610191	0.0415272624138428	0.0	0.0	0.0	0.0	1.0

Rows: 1-31 | Columns: 9

It'll be difficult to work on the principal components (V1 through V28) without knowing what they mean. The only features we can work on are Time and Amount.

Let's convert the number of seconds elapsed to the correct date and time. We know that the records were ingested in September 2013, so we'll use that to create the new feature.

In [5]:

creditcard["Time"].apply("TIMESTAMPADD(second, {}::int, '2013-09-01 00:00:00'::timestamp)")

Out[5]: