Cluster Analysis

Grupo de Pesquisa - Prof. Dirceu Reis, UnB

by Cássio Rampinelli

13 de Outubro de 2021

OBJETIVOS

Os objetivos deste post são:

• Apresentar um script inicial para uma análise de cluster para 63 bacias na bacia do rio São Francisco;

• Variáveis consideradas: Coordenadas Geográficas, Média(w), Média (E0/P); Média (Q/P); Média(Q3[Q/P]-Q1[Q/P])

CARREGANDO PACOTES

#Clean R memory
rm(list=ls(all=TRUE))
############################################
#Loading packages to deal with maps#
############################################
#install.packages(maps)
library(maps)
#install.packages(mapdata)
library(mapdata)
############################################

############################################
#Loading clustering packages#
############################################
#install.packages((cluster))
library(cluster)

## 
## Attaching package: 'cluster'

## The following object is masked from 'package:maps':
## 
##     votes.repub

#install.packages(devtools)
library(devtools)

## Loading required package: usethis

devtools::install_github("kassambara/factoextra")

## Skipping install of 'factoextra' from a github remote, the SHA1 (1689fc74) has not changed since last install.
##   Use `force = TRUE` to force installation

library("factoextra")

## Loading required package: ggplot2

## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

ACESSANDO O BANCO DE DADOS E EXTRAINDO AS INFORMAÇÕES

setwd("E:/GA_Dirceu/Felipe")
data.Set<-read.table(file="Tabela_RHSF.txt",header=T,sep="\t")
knitr::kable(data.Set, col.names = gsub("[.]", " ", names(data.Set)))

Região por aproximação	Estação	Código da estação	Latitude	Longitude	Mín w	Q1 w	Mediana w	Média w	Q3 w	Máx w	Q3 Q1 w	Mín E0 P	Q1 E0 P	Mediana E0 P	Média E0 P	Q3 E0 P	Máx E0 P	Q3 Q1 E0 P	Mín Q P	Q1 Q P	Mediana Q P	Média Q P	Q3 Q P	Máx Q P	Q3 Q1 Q P
5	1	40037000	-20.2156	-46.2322	1.514308	1.536707	1.579840	1.575616	1.607679	1.631433	0.0709723	0.9710513	0.9815990	0.9888933	0.9992123	1.015855	1.041346	0.0342563	0.5330215	0.5436427	0.5508239	0.5535076	0.5674175	0.5719827	0.0237748
5	2	40040000	-20.0953	-46.0622	1.619535	1.715655	1.741545	1.733955	1.754262	1.811112	0.0386071	1.0147138	1.0364808	1.0786599	1.0746477	1.103510	1.161930	0.0670288	0.4522004	0.4605616	0.4731951	0.4739446	0.4829042	0.5014871	0.0223427
5	3	40050000	-20.1700	-45.7158	1.705369	1.893871	1.953258	1.934295	2.000002	2.049997	0.1061315	0.9776253	1.0093356	1.0531283	1.0520865	1.073078	1.156257	0.0637420	0.3817590	0.3967063	0.4225908	0.4185116	0.4340151	0.4656242	0.0373088
5	4	40060001	-19.8875	-46.0169	1.989879	2.029046	2.313460	2.245233	2.406849	2.521074	0.3778029	0.8341509	0.8858713	0.9606404	0.9535782	1.019912	1.052831	0.1340403	0.3556270	0.3716833	0.3812388	0.3829062	0.3974917	0.4094330	0.0258084
5	5	40070000	-19.7761	-45.4792	1.910141	2.006979	2.066303	2.052491	2.093824	2.162296	0.0868446	0.9962446	1.0297097	1.0695675	1.0639161	1.083563	1.153334	0.0538529	0.3525980	0.3686143	0.3864845	0.3840770	0.4011784	0.4144422	0.0325641
5	6	40100000	-19.2814	-45.2753	1.982855	2.093417	2.150278	2.150088	2.217682	2.287789	0.1242646	1.0236328	1.0643297	1.1061220	1.1034485	1.127044	1.181647	0.0627146	0.3080925	0.3356518	0.3531145	0.3514682	0.3709236	0.3833278	0.0352718
5	7	40170000	-20.2169	-44.9181	2.095362	2.144747	2.290844	2.249889	2.335367	2.383232	0.1906203	1.0218082	1.0660717	1.1346429	1.1310330	1.183517	1.231119	0.1174454	0.2870190	0.2963476	0.3185987	0.3238982	0.3560507	0.3674961	0.0597032
5	8	40185000	-20.1847	-44.8933	2.101615	2.131448	2.315613	2.261954	2.370611	2.391608	0.2391628	1.0629806	1.1011511	1.1647353	1.1510392	1.191180	1.235631	0.0900285	0.2737914	0.2879834	0.2933297	0.3162593	0.3583206	0.3715590	0.0703372
5	9	40500000	-19.3317	-45.2214	2.434509	2.476277	2.516197	2.516847	2.542717	2.685808	0.0664392	1.1294491	1.1733024	1.2377641	1.2147470	1.245815	1.277073	0.0725126	0.2198984	0.2440026	0.2496291	0.2545899	0.2672528	0.2833291	0.0232503
5	10	40549998	-20.6039	-43.9086	1.911675	1.996725	2.184255	2.124448	2.245055	2.305338	0.2483296	1.0253092	1.0383729	1.0779720	1.0789612	1.112337	1.153791	0.0739642	0.3334946	0.3506574	0.3554934	0.3659193	0.3821844	0.4070809	0.0315270
5	11	40680000	-20.6611	-44.0722	1.786904	1.859932	1.978891	1.983275	2.055923	2.258575	0.1959914	0.9924341	1.0348249	1.0582386	1.0609784	1.086108	1.131769	0.0512826	0.3379897	0.3804245	0.4045835	0.4042459	0.4292902	0.4533129	0.0488657
5	12	40810350	-20.0942	-44.4936	2.334176	2.398727	2.481705	2.457067	2.510566	2.530437	0.1118387	1.0621306	1.0867832	1.1335631	1.1221612	1.154005	1.170884	0.0672219	0.2663502	0.2716938	0.2920581	0.2886778	0.3083017	0.3144959	0.0366079
5	13	40810800	-20.0869	-44.4381	2.243752	2.363645	2.437707	2.415805	2.467561	2.610738	0.1039152	1.0461397	1.1289098	1.1654396	1.1726441	1.201111	1.341734	0.0722009	0.2121116	0.2670024	0.2803145	0.2825989	0.3006141	0.3476788	0.0336117
5	14	40811100	-20.0475	-44.4089	2.354257	2.474307	2.518941	2.512879	2.577612	2.614108	0.1033058	1.0619492	1.1256531	1.1516081	1.1546558	1.178896	1.288485	0.0532424	0.2221193	0.2535258	0.2725484	0.2712882	0.2839606	0.3205327	0.0304349
5	15	40822995	-19.9850	-44.4389	2.846258	3.006445	3.072213	3.066218	3.175168	3.215936	0.1687228	1.0702626	1.1484539	1.1585635	1.1551734	1.165646	1.220968	0.0171919	0.1938964	0.1980361	0.2038756	0.2037303	0.2085280	0.2154808	0.0104918
5	16	40823500	-19.9614	-44.3661	2.231958	2.336278	2.436758	2.416162	2.521894	2.546832	0.1856156	1.0699792	1.1442133	1.1607895	1.1576522	1.171804	1.258683	0.0275903	0.2700190	0.2744489	0.2887116	0.2865738	0.2951240	0.3062768	0.0206750
5	17	41250000	-19.6875	-43.9206	2.108892	2.248207	2.376563	2.378434	2.487944	2.737786	0.2397365	1.1482069	1.1770942	1.1979084	1.2037977	1.224238	1.294013	0.0471441	0.2178118	0.2640819	0.2827658	0.2818165	0.3061328	0.3405824	0.0420509
5	18	41300000	-19.6536	-43.6875	1.904650	1.983605	2.125109	2.117803	2.247171	2.331037	0.2635658	1.0287058	1.0606989	1.0877581	1.0973767	1.129544	1.219204	0.0688450	0.2994813	0.3351561	0.3501586	0.3618233	0.3865687	0.4242917	0.0514126
5	19	41380000	-19.4619	-43.9036	2.140815	2.216303	2.312072	2.292173	2.357744	2.426671	0.1414404	1.1614035	1.2017107	1.2135837	1.2394606	1.259778	1.418617	0.0580672	0.2402201	0.2708004	0.2830931	0.2878840	0.3098751	0.3319541	0.0390747
5	20	41410000	-19.2311	-44.0247	2.193326	2.311757	2.351549	2.361852	2.407354	2.590115	0.0955962	1.0665885	1.0979739	1.1123550	1.1104888	1.122044	1.155116	0.0240704	0.2629945	0.3005322	0.3086743	0.3081567	0.3180335	0.3408165	0.0175014
5	21	41440005	-19.3714	-44.1528	2.191811	2.230237	2.239777	2.241930	2.248766	2.300257	0.0185288	1.1559190	1.1765961	1.2116910	1.2275920	1.254925	1.372477	0.0783290	0.2563367	0.2958097	0.3066496	0.3000981	0.3118148	0.3168879	0.0160051
5	22	41600000	-19.0111	-44.0383	2.221909	2.323748	2.367452	2.358921	2.394833	2.513205	0.0710845	1.0496923	1.0953074	1.1288377	1.1273712	1.150964	1.239782	0.0556562	0.2649687	0.2922425	0.3032259	0.3039077	0.3154021	0.3353028	0.0231596
5	23	41650002	-18.6728	-44.1939	2.298975	2.341423	2.378975	2.382701	2.408906	2.575260	0.0674827	1.0625463	1.1856270	1.2066755	1.1937121	1.222784	1.263692	0.0371572	0.2631533	0.2733676	0.2809910	0.2821308	0.2922887	0.2998254	0.0189211
5	24	41685000	-18.6042	-44.2847	2.439105	2.576166	2.654052	2.744172	2.972386	3.155575	0.3962196	1.3846444	1.4750933	1.5605683	1.5449299	1.608389	1.681457	0.1332961	0.0971907	0.1339512	0.1535039	0.1601713	0.1930586	0.2115293	0.0591074
5	25	41780002	-18.6450	-44.0506	1.663712	1.681722	1.700028	1.706406	1.725361	1.775812	0.0436388	1.0839505	1.2180279	1.2444975	1.2228430	1.258712	1.285038	0.0406840	0.4153381	0.4423792	0.4557255	0.4521717	0.4604370	0.4745437	0.0180578
5	26	41818000	-18.3061	-44.2258	2.221549	2.289974	2.323969	2.354570	2.418759	2.569612	0.1287854	1.0913363	1.1420048	1.2431647	1.2179510	1.268611	1.340268	0.1266066	0.2483141	0.2699008	0.2831574	0.2821658	0.2959835	0.3127786	0.0260827
5	27	41890000	-17.9964	-44.1775	1.505173	1.528945	1.580741	1.587310	1.628781	1.729148	0.0998366	1.4156376	1.5847562	1.6807927	1.6439816	1.739251	1.816555	0.1544951	0.3649021	0.4176105	0.4562867	0.4403152	0.4626616	0.4767280	0.0450511
5	28	41940000	-18.1908	-44.5556	2.057468	2.118544	2.171723	2.175578	2.189515	2.381318	0.0709707	1.5517847	1.5856979	1.6537796	1.6475256	1.701286	1.763775	0.1155882	0.2047873	0.2281686	0.2366753	0.2369349	0.2497933	0.2581432	0.0216246
5	29	41990000	-17.5961	-44.7133	2.048901	2.109099	2.162380	2.164503	2.228694	2.286264	0.1195950	1.1825618	1.2359782	1.3448563	1.3143586	1.372180	1.420743	0.1362015	0.2563092	0.2753206	0.2936344	0.2978712	0.3197810	0.3414997	0.0444604
4	30	42187000	-16.4669	-44.3761	2.803549	2.960975	3.044053	3.165465	3.316517	3.824952	0.3555414	1.2109087	1.4208002	1.6877790	1.6144071	1.801279	1.901557	0.3804793	0.0959398	0.1007321	0.1094364	0.1117385	0.1212790	0.1354252	0.0205469
4	31	42250000	-17.9150	-47.0108	1.759705	1.871084	2.017787	1.965856	2.058259	2.151770	0.1871751	1.0744705	1.1637799	1.1887995	1.1784629	1.208097	1.225254	0.0443173	0.3221079	0.3506077	0.3600251	0.3785874	0.4101080	0.4461181	0.0595004
4	32	42290000	-17.5025	-46.5711	2.326172	2.386720	2.541326	3.520066	4.979696	5.624542	2.5929762	0.8056469	0.8576098	1.1769600	1.0606651	1.219680	1.251033	0.3620704	0.1941090	0.2287885	0.2574404	0.2501165	0.2732785	0.2965104	0.0444899
4	33	42395000	-17.2550	-46.4728	2.231987	2.382786	2.499358	2.820177	3.447484	3.676991	1.0646984	0.8851943	0.9495739	1.1734189	1.1037237	1.217928	1.255022	0.2683542	0.2131885	0.2546480	0.2606980	0.2641674	0.2748538	0.3169062	0.0202058
4	34	42545500	-16.4925	-46.6686	2.148108	2.269585	2.399757	2.364695	2.435824	2.574133	0.1662394	1.1625366	1.2488323	1.3155713	1.2918215	1.336506	1.368799	0.0876737	0.2216459	0.2401188	0.2473997	0.2626503	0.2924071	0.3257587	0.0522883
4	35	42850000	-17.3506	-45.5325	1.973935	2.057805	2.148697	2.175229	2.296376	2.414711	0.2385713	1.1938066	1.2785651	1.3444988	1.3244732	1.385358	1.423222	0.1067927	0.2518607	0.2596138	0.2844879	0.2950978	0.3279781	0.3498327	0.0683643
4	36	43429998	-15.9178	-46.1192	2.176111	2.330913	2.396716	2.370069	2.449352	2.488509	0.1184392	1.1924039	1.2711702	1.3039207	1.3194054	1.371878	1.466439	0.1007078	0.2180381	0.2388239	0.2447706	0.2557020	0.2590814	0.3207860	0.0202575
4	37	43670000	-16.1331	-45.7417	2.143220	2.174365	2.394377	2.321714	2.441309	2.515792	0.2669440	1.2454935	1.3151364	1.3647082	1.3743657	1.426116	1.547877	0.1109798	0.1969771	0.2174281	0.2397954	0.2541605	0.2950561	0.3064042	0.0776280
4	38	43880000	-16.2811	-45.4142	2.131742	2.169285	2.276555	2.271624	2.373923	2.464526	0.2046379	1.2739936	1.3373391	1.4150484	1.4106048	1.469587	1.560664	0.1322482	0.2073884	0.2239410	0.2519424	0.2564434	0.2912866	0.3046215	0.0673456
3	39	45131000	-14.3136	-44.4594	1.665513	1.790494	2.146191	2.142952	2.411206	2.688815	0.6207127	1.1935463	1.2565536	1.4915576	1.4905064	1.678819	1.876982	0.4222652	0.2324815	0.2401407	0.2531564	0.2892216	0.3583853	0.3812054	0.1182446
3	40	45170001	-14.2642	-44.5225	1.630359	1.676468	1.704239	1.709900	1.730446	1.812601	0.0539777	1.7015457	1.7890147	1.9075050	1.8800405	1.961924	2.043961	0.1729093	0.2982958	0.3329458	0.3606038	0.3518615	0.3764750	0.3856534	0.0435292
3	41	45210000	-14.2808	-44.4097	1.749905	2.032102	2.182336	2.130017	2.300389	2.405188	0.2682876	1.3602291	1.3866542	1.4891758	1.5148809	1.614925	1.807869	0.2282704	0.2356783	0.2404171	0.2477178	0.2745861	0.3042772	0.3590583	0.0638601
3	42	45220000	-14.4236	-44.4831	2.470860	2.520062	2.555629	2.585864	2.652946	2.785651	0.1328834	1.5032007	1.6130636	1.8084487	1.7836743	1.886252	2.128338	0.2731881	0.1054233	0.1193607	0.1485695	0.1477808	0.1714351	0.1836208	0.0520744
3	43	45260000	-14.2600	-44.1522	1.870270	2.007008	2.215748	2.183693	2.325764	2.451793	0.3187557	1.4311951	1.4855888	1.6197847	1.6281422	1.732055	1.973120	0.2464662	0.2018244	0.2106444	0.2214075	0.2428125	0.2839807	0.3033746	0.0733363
2	44	45590000	-13.3406	-44.6386	2.062743	2.113210	2.138692	2.160351	2.225355	2.258837	0.1121448	1.4794173	1.6387350	1.6753068	1.6653616	1.715467	1.800450	0.0767319	0.2067417	0.2249801	0.2420105	0.2374772	0.2511937	0.2561981	0.0262136
2	45	45740001	-13.2853	-44.5617	2.548385	2.600731	2.647221	2.652476	2.679858	2.796913	0.0791275	1.4782666	1.6789165	1.7392901	1.7268287	1.781976	1.897780	0.1030591	0.1246298	0.1306465	0.1438269	0.1439483	0.1546699	0.1648175	0.0240233
2	46	45770000	-13.4528	-44.5689	1.867213	1.899723	1.912138	1.949033	2.003188	2.106252	0.1034659	1.4572503	1.6227370	1.6631854	1.6511241	1.691433	1.788270	0.0686963	0.2542405	0.2922527	0.3016133	0.2955246	0.3106238	0.3149410	0.0183711
2	47	45880000	-13.5586	-44.3031	1.864548	1.951984	2.008306	2.018202	2.092430	2.180514	0.1404462	1.5741052	1.7804613	1.8134898	1.7980465	1.839954	1.897572	0.0594932	0.2079219	0.2307568	0.2528259	0.2560917	0.2801553	0.2992697	0.0493985
2	48	45910001	-13.4006	-44.1989	2.242687	2.272755	2.295826	2.319680	2.368401	2.435912	0.0956463	1.4678998	1.6476290	1.7135022	1.6969020	1.763616	1.820660	0.1159867	0.1694414	0.1865364	0.2018562	0.2000571	0.2129062	0.2220193	0.0263699
2	49	45960001	-13.2914	-43.9089	2.257944	2.289650	2.304721	2.322550	2.347601	2.431273	0.0579511	1.4821512	1.6503227	1.7096058	1.6975752	1.769214	1.831012	0.1188918	0.1732228	0.1903574	0.2027041	0.1992312	0.2103161	0.2172976	0.0199587
1	50	46415000	-12.4306	-45.0856	2.552323	2.596106	2.637630	2.637881	2.660604	2.768277	0.0644981	1.4050008	1.5027074	1.5699464	1.5659530	1.640529	1.713869	0.1378217	0.1402341	0.1529638	0.1708958	0.1679395	0.1803428	0.1915442	0.0273789
1	51	46455000	-12.4106	-45.1222	2.347953	2.404361	2.596561	2.560382	2.697988	2.789708	0.2936262	1.2968585	1.3642780	1.4516226	1.4963121	1.621840	1.760965	0.2575622	0.1847375	0.1912866	0.1927485	0.1930110	0.1945153	0.2011608	0.0032287
1	52	46490000	-12.4044	-44.9531	3.635151	3.657063	3.692556	3.738067	3.814939	3.924747	0.1578756	1.7550477	1.9205472	1.9496876	1.9306663	1.984343	2.028442	0.0637956	0.0356145	0.0397720	0.0436643	0.0432425	0.0468768	0.0501672	0.0071048
1	53	46543000	-12.1358	-45.1033	2.309944	2.372440	2.403785	2.410527	2.434284	2.646361	0.0618435	1.2617681	1.3994531	1.4786166	1.4611177	1.539156	1.641932	0.1397028	0.2031773	0.2144883	0.2241529	0.2207324	0.2260715	0.2318241	0.0115832
1	54	46550000	-12.1525	-45.0094	2.964689	3.304702	3.353613	3.375623	3.451583	3.696462	0.1468815	1.3865526	1.4305749	1.5288948	1.5276515	1.610933	1.716522	0.1803580	0.0836955	0.0938716	0.1016092	0.1018720	0.1074592	0.1271868	0.0135876
1	55	46570000	-11.8953	-45.6081	3.448549	3.584449	3.712223	3.908116	4.193531	4.775177	0.6090821	1.1199757	1.2216202	1.3155380	1.2847388	1.358008	1.420500	0.1363879	0.1073133	0.1112881	0.1129394	0.1127737	0.1141148	0.1187805	0.0028267
1	56	46590000	-11.8561	-45.1200	2.497619	2.574294	2.620107	2.637440	2.684793	2.870494	0.1104987	1.3576027	1.4874201	1.5625869	1.5487977	1.624923	1.736735	0.1375034	0.1596200	0.1659452	0.1724848	0.1708757	0.1750351	0.1783061	0.0090899
1	57	46610000	-11.9794	-44.8772	2.656201	2.703562	2.733202	2.746495	2.765236	2.973240	0.0616740	1.4008771	1.5401697	1.5938861	1.5914007	1.672773	1.706997	0.1326032	0.1354397	0.1449634	0.1533130	0.1501381	0.1550218	0.1597645	0.0100585
1	58	46650000	-11.7208	-44.5022	2.707813	2.791443	2.852842	2.907103	3.021541	3.194093	0.2300988	1.4208014	1.4555698	1.5707097	1.5571878	1.644310	1.727508	0.1887401	0.1228230	0.1324660	0.1402007	0.1379248	0.1427256	0.1486539	0.0102596
1	59	46675000	-11.6106	-44.1567	2.782719	2.874605	2.934703	2.992835	3.131709	3.289594	0.2571034	1.4467090	1.4837984	1.6062790	1.5988230	1.687761	1.834545	0.2039629	0.1138691	0.1187160	0.1242287	0.1235812	0.1274820	0.1332269	0.0087661
1	60	46770000	-10.9936	-45.5278	2.219139	2.340967	2.492865	2.492633	2.540961	2.976663	0.1999939	1.6219831	1.7461938	1.8423587	1.8570552	1.990415	2.106780	0.2442210	0.1200686	0.1460980	0.1580429	0.1543102	0.1666259	0.1769410	0.0205279
1	61	46790000	-11.0514	-45.1969	1.942036	2.033424	2.124634	2.159790	2.184040	2.601803	0.1506161	1.6225127	1.7748936	1.8671018	1.8796119	2.020546	2.206691	0.2456526	0.1630395	0.2054144	0.2205263	0.2147308	0.2300581	0.2463092	0.0246437
1	62	46870000	-11.2356	-43.9494	2.265423	2.306601	2.392867	2.424634	2.497968	2.726866	0.1913664	1.7988364	1.8892153	1.9896523	1.9713547	2.049252	2.103254	0.1600365	0.1253737	0.1417972	0.1543022	0.1506524	0.1609103	0.1650709	0.0191131
1	63	46902000	-11.3450	-43.8261	2.790458	2.898036	2.981696	3.047905	3.200795	3.385257	0.3027596	1.4572261	1.4914865	1.6192059	1.6091154	1.703505	1.835663	0.2120181	0.1048976	0.1143988	0.1180859	0.1172190	0.1204625	0.1249270	0.0060637

VISUALIZANDO DADOS

############################################
#Plotting map of Brazil
############################################
map('worldHires','Brazil', xlim=c(-75.6,-33.6), ylim=c(-34.3,6), col='gray90', fill=TRUE)

############################################
#Plotting sites
############################################
coordinates<-cbind(data.Set$Longitude,data.Set$Latitude)
colnames(coordinates)<-c("long","lat")
coordinates<-as.data.frame(coordinates)
points(coordinates$long, coordinates$lat, pch=19, col="red", cex=0.5)  #plot my sample sites

CLUSTER ANALYSIS

Cluster by coordinates

Scaling data

df.scaled<-cbind(data.Set$Longitude,data.Set$Latitude)
col1<-(df.scaled[,1]-min(df.scaled[,1]))/(max(df.scaled[,1])-min(df.scaled[,1]))
col2<-(df.scaled[,2]-min(df.scaled[,2]))/(max(df.scaled[,2])-min(df.scaled[,2]))

df.scaled[,1]=col1
df.scaled[,2]=col2

df.scaled<-as.data.frame(df.scaled)
colnames(df.scaled)<-c("long","lat")
head(df.scaled)

##        long        lat
## 1 0.2342852 0.04608223
## 2 0.2854392 0.05852599
## 3 0.3896729 0.05079907
## 4 0.2990702 0.08002069
## 5 0.4608672 0.09154383
## 6 0.5222219 0.14271528

Scaling data

df.scaled<-cbind(data.Set$Longitude,data.Set$Latitude)
col1<-(df.scaled[,1]-min(df.scaled[,1]))/(max(df.scaled[,1])-min(df.scaled[,1]))
col2<-(df.scaled[,2]-min(df.scaled[,2]))/(max(df.scaled[,2])-min(df.scaled[,2]))

df.scaled[,1]=col1
df.scaled[,2]=col2

df.scaled<-as.data.frame(df.scaled)
colnames(df.scaled)<-c("scaled.long","scaled.lat")
head(df.scaled)

##   scaled.long scaled.lat
## 1   0.2342852 0.04608223
## 2   0.2854392 0.05852599
## 3   0.3896729 0.05079907
## 4   0.2990702 0.08002069
## 5   0.4608672 0.09154383
## 6   0.5222219 0.14271528

Dissimilarity Matrix - Euclidian Distance

#Euclidean Distance
#################################################
dist.eucl<-dist(df.scaled,method="euclidean")
#Visualizing the distance matrices
fviz_dist(dist.eucl)

K-Means - Number of Clusters

#Number of Clusters: Elbow method
fviz_nbclust(df.scaled,kmeans,method="wss")+geom_vline(xintercept=3,linetype=2)+labs(subtitle="Elbow method")

K-Means - 3 Clusters

#Compute k-means k=3
km.res<-kmeans(df.scaled,3,nstart=15)
km.res

## K-means clustering with 3 clusters of sizes 15, 23, 25
## 
## Cluster means:
##   scaled.long scaled.lat
## 1   0.3135057  0.2504012
## 2   0.8242933  0.1460240
## 3   0.7104384  0.8251742
## 
## Clustering vector:
##  [1] 1 1 1 1 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1
## [39] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 
## Within cluster sum of squares by cluster:
## [1] 0.7810200 0.4592320 0.8504986
##  (between_SS / total_SS =  80.7 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

clusters<-km.res$cluster

fviz_cluster(km.res, data = df.scaled)

df.scaled.cluster<-cbind(clusters,coordinates$long, coordinates$lat)

colnames(df.scaled.cluster)<-c("clusters","long","lat")

df.scaled.cluster<-as.data.frame(df.scaled.cluster)

head(df.scaled.cluster)

##   clusters     long      lat
## 1        1 -46.2322 -20.2156
## 2        1 -46.0622 -20.0953
## 3        1 -45.7158 -20.1700
## 4        1 -46.0169 -19.8875
## 5        1 -45.4792 -19.7761
## 6        1 -45.2753 -19.2814

points.cluster.1<-df.scaled.cluster[which(df.scaled.cluster$clusters==1),]
colnames(points.cluster.1)<-c("cluster","long","lat")
points.cluster.1<-as.data.frame(points.cluster.1)

points.cluster.2<-df.scaled.cluster[which(df.scaled.cluster$clusters==2),]
colnames(points.cluster.2)<-c("cluster","long","lat")
points.cluster.2<-as.data.frame(points.cluster.2)


points.cluster.3<-df.scaled.cluster[which(df.scaled.cluster$clusters==3),]
colnames(points.cluster.3)<-c("cluster","long","lat")
points.cluster.3<-as.data.frame(points.cluster.3)

map('worldHires','Brazil', xlim=c(-75.6,-33.6), ylim=c(-34.3,6), col='gray90', fill=TRUE)
points(points.cluster.1$long, points.cluster.1$lat, pch=19, col="blue", cex=0.5)  #plot my sample sites
points(points.cluster.2$long, points.cluster.2$lat, pch=21, col="red", cex=0.5)  #plot my sample sites
points(points.cluster.3$long, points.cluster.3$lat, pch=22, col="green", cex=0.5)  #plot my sample sites


#Configurando a legenda
legend("topright", c("Cluster 1", "Cluster 2","Cluster 3"), col = c("blue","red","green"),
       pch = c(19,21,22))

K-Means - 2 Clusters

#Compute k-means k=2
km.res<-kmeans(df.scaled,2,nstart=15)
km.res

## K-means clustering with 2 clusters of sizes 25, 38
## 
## Cluster means:
##   scaled.long scaled.lat
## 1   0.7104384  0.8251742
## 2   0.6226666  0.1872255
## 
## Clustering vector:
##  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [39] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 
## Within cluster sum of squares by cluster:
## [1] 0.8504986 3.7078972
##  (between_SS / total_SS =  57.8 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

clusters<-km.res$cluster

fviz_cluster(km.res, data = df.scaled)

df.scaled.cluster<-cbind(clusters,coordinates$long, coordinates$lat)

colnames(df.scaled.cluster)<-c("clusters","long","lat")

df.scaled.cluster<-as.data.frame(df.scaled.cluster)

head(df.scaled.cluster)

##   clusters     long      lat
## 1        2 -46.2322 -20.2156
## 2        2 -46.0622 -20.0953
## 3        2 -45.7158 -20.1700
## 4        2 -46.0169 -19.8875
## 5        2 -45.4792 -19.7761
## 6        2 -45.2753 -19.2814

points.cluster.1<-df.scaled.cluster[which(df.scaled.cluster$clusters==1),]
colnames(points.cluster.1)<-c("cluster","long","lat")
points.cluster.1<-as.data.frame(points.cluster.1)

points.cluster.2<-df.scaled.cluster[which(df.scaled.cluster$clusters==2),]
colnames(points.cluster.2)<-c("cluster","long","lat")
points.cluster.2<-as.data.frame(points.cluster.2)

map('worldHires','Brazil', xlim=c(-75.6,-33.6), ylim=c(-34.3,6), col='gray90', fill=TRUE)
points(points.cluster.1$long, points.cluster.1$lat, pch=19, col="blue", cex=0.5)  #plot my sample sites
points(points.cluster.2$long, points.cluster.2$lat, pch=21, col="red", cex=0.5)  #plot my sample sites


#Configurando a legenda
legend("topright", c("Cluster 1", "Cluster 2"), col = c("blue","red"),
       pch = c(19,21))

Cluster by w; E0/P; Q/P

Scaling data

subs.set<-cbind(data.Set$Média..w.,data.Set$Média..E0.P.,data.Set$Média..Q.P.)

df.scaled<-0

df.scaled<-subs.set

col1=col2=col3=0

col1<-(df.scaled[,1]-min(df.scaled[,1]))/(max(df.scaled[,1])-min(df.scaled[,1]))
col2<-(df.scaled[,2]-min(df.scaled[,2]))/(max(df.scaled[,2])-min(df.scaled[,2]))
col3<-(df.scaled[,3]-min(df.scaled[,3]))/(max(df.scaled[,3])-min(df.scaled[,3]))


df.scaled[,1]=col1
df.scaled[,2]=col2
df.scaled[,3]=col3

colnames(df.scaled)<-c("w","E0/P","Q0/P")

head(df.scaled)

##               w       E0/P      Q0/P
## [1,] 0.00000000 0.04483707 1.0000000
## [2,] 0.06788383 0.11895490 0.8440751
## [3,] 0.15377450 0.09678773 0.7354396
## [4,] 0.28708123 0.00000000 0.6656613
## [5,] 0.20444814 0.10841078 0.6679557
## [6,] 0.24629062 0.14725268 0.6040502

Dissimilarity Matrix - Euclidian Distance

#Euclidean Distance
#################################################
dist.eucl<-dist(df.scaled,method="euclidean")
#Visualizing the distance matrices
fviz_dist(dist.eucl)

K-Means - Number of Clusters

#Number of Clusters: Elbow method
fviz_nbclust(df.scaled,kmeans,method="wss")+geom_vline(xintercept=3,linetype=2)+labs(subtitle="Elbow method")

K-Means - 3 Clusters

#Compute k-means k=3
km.res<-kmeans(df.scaled,3,nstart=15)
km.res

## K-means clustering with 3 clusters of sizes 15, 34, 14
## 
## Cluster means:
##           w      E0/P      Q0/P
## 1 0.2444478 0.7322860 0.4070958
## 2 0.3063365 0.2093014 0.5456739
## 3 0.6014762 0.6337619 0.1787336
## 
## Clustering vector:
##  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 1 2 3 2 2 2 2 2 2 2 2
## [39] 1 1 1 3 1 1 3 1 1 1 1 3 3 3 1 3 3 3 3 3 3 1 1 1 3
## 
## Within cluster sum of squares by cluster:
## [1] 0.7720936 1.8391153 0.7871033
##  (between_SS / total_SS =  64.1 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

clusters<-km.res$cluster

fviz_cluster(km.res, data = df.scaled)

df.scaled.cluster<-cbind(clusters,coordinates$long, coordinates$lat)

colnames(df.scaled.cluster)<-c("clusters","long","lat")

df.scaled.cluster<-as.data.frame(df.scaled.cluster)

head(df.scaled.cluster)

##   clusters     long      lat
## 1        2 -46.2322 -20.2156
## 2        2 -46.0622 -20.0953
## 3        2 -45.7158 -20.1700
## 4        2 -46.0169 -19.8875
## 5        2 -45.4792 -19.7761
## 6        2 -45.2753 -19.2814

points.cluster.1<-df.scaled.cluster[which(df.scaled.cluster$clusters==1),]
colnames(points.cluster.1)<-c("cluster","long","lat")
points.cluster.1<-as.data.frame(points.cluster.1)

points.cluster.2<-df.scaled.cluster[which(df.scaled.cluster$clusters==2),]
colnames(points.cluster.2)<-c("cluster","long","lat")
points.cluster.2<-as.data.frame(points.cluster.2)


points.cluster.3<-df.scaled.cluster[which(df.scaled.cluster$clusters==3),]
colnames(points.cluster.3)<-c("cluster","long","lat")
points.cluster.3<-as.data.frame(points.cluster.3)

map('worldHires','Brazil', xlim=c(-75.6,-33.6), ylim=c(-34.3,6), col='gray90', fill=TRUE)
points(points.cluster.1$long, points.cluster.1$lat, pch=19, col="blue", cex=0.5)  #plot my sample sites
points(points.cluster.2$long, points.cluster.2$lat, pch=21, col="red", cex=0.5)  #plot my sample sites
points(points.cluster.3$long, points.cluster.3$lat, pch=22, col="green", cex=0.5)  #plot my sample sites


#Configurando a legenda
legend("topright", c("Cluster 1", "Cluster 2","Cluster 3"), col = c("blue","red","green"),
       pch = c(19,21,22))

K-Means - 2 Clusters

#Compute k-means k=2
km.res<-kmeans(df.scaled,2,nstart=15)
km.res

## K-means clustering with 2 clusters of sizes 27, 36
## 
## Cluster means:
##           w      E0/P      Q0/P
## 1 0.4384866 0.6907801 0.2721658
## 2 0.2962135 0.2311706 0.5503650
## 
## Clustering vector:
##  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2
## [39] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 
## Within cluster sum of squares by cluster:
## [1] 2.409625 2.291579
##  (between_SS / total_SS =  50.3 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

clusters<-km.res$cluster

fviz_cluster(km.res, data = df.scaled)

df.scaled.cluster<-cbind(clusters,coordinates$long, coordinates$lat)

colnames(df.scaled.cluster)<-c("clusters","long","lat")

df.scaled.cluster<-as.data.frame(df.scaled.cluster)

head(df.scaled.cluster)

##   clusters     long      lat
## 1        2 -46.2322 -20.2156
## 2        2 -46.0622 -20.0953
## 3        2 -45.7158 -20.1700
## 4        2 -46.0169 -19.8875
## 5        2 -45.4792 -19.7761
## 6        2 -45.2753 -19.2814

points.cluster.1<-df.scaled.cluster[which(df.scaled.cluster$clusters==1),]
colnames(points.cluster.1)<-c("cluster","long","lat")
points.cluster.1<-as.data.frame(points.cluster.1)

points.cluster.2<-df.scaled.cluster[which(df.scaled.cluster$clusters==2),]
colnames(points.cluster.2)<-c("cluster","long","lat")
points.cluster.2<-as.data.frame(points.cluster.2)

map('worldHires','Brazil', xlim=c(-75.6,-33.6), ylim=c(-34.3,6), col='gray90', fill=TRUE)
points(points.cluster.1$long, points.cluster.1$lat, pch=19, col="blue", cex=0.5)  #plot my sample sites
points(points.cluster.2$long, points.cluster.2$lat, pch=21, col="red", cex=0.5)  #plot my sample sites


#Configurando a legenda
legend("topright", c("Cluster 1", "Cluster 2"), col = c("blue","red"),
       pch = c(19,21))

Cluster by w; E0/P; Q/P; Q3(Q/P)-Q2(Q/P)

Scaling data

subs.set<-cbind(data.Set$Média..w.,data.Set$Média..E0.P.,data.Set$Média..Q.P.,data.Set$Q3.Q1..Q.P.)


df.scaled<-0

df.scaled<-subs.set

col1=col2=col3=0

col1<-(df.scaled[,1]-min(df.scaled[,1]))/(max(df.scaled[,1])-min(df.scaled[,1]))
col2<-(df.scaled[,2]-min(df.scaled[,2]))/(max(df.scaled[,2])-min(df.scaled[,2]))
col3<-(df.scaled[,3]-min(df.scaled[,3]))/(max(df.scaled[,3])-min(df.scaled[,3]))
col4<-(df.scaled[,4]-min(df.scaled[,4]))/(max(df.scaled[,4])-min(df.scaled[,4]))


df.scaled[,1]=col1
df.scaled[,2]=col2
df.scaled[,3]=col3
df.scaled[,4]=col4

colnames(df.scaled)<-c("w","E0/P","Q0/P","Q3-Q1")

head(df.scaled)

##               w       E0/P      Q0/P     Q3-Q1
## [1,] 0.00000000 0.04483707 1.0000000 0.1814977
## [2,] 0.06788383 0.11895490 0.8440751 0.1690895
## [3,] 0.15377450 0.09678773 0.7354396 0.2987587
## [4,] 0.28708123 0.00000000 0.6656613 0.1991175
## [5,] 0.20444814 0.10841078 0.6679557 0.2576499
## [6,] 0.24629062 0.14725268 0.6040502 0.2811095

Dissimilarity Matrix - Euclidian Distance

#Euclidean Distance
#################################################
dist.eucl<-dist(df.scaled,method="euclidean")
#Visualizing the distance matrices
fviz_dist(dist.eucl)

K-Means - Number of Clusters

#Number of Clusters: Elbow method
fviz_nbclust(df.scaled,kmeans,method="wss")+geom_vline(xintercept=3,linetype=2)+labs(subtitle="Elbow method")

K-Means - 3 Clusters

#Compute k-means k=3
km.res<-kmeans(df.scaled,3,nstart=15)
km.res

## K-means clustering with 3 clusters of sizes 10, 31, 22
## 
## Cluster means:
##           w      E0/P      Q0/P     Q3-Q1
## 1 0.2029375 0.6072437 0.4945840 0.5171310
## 2 0.3077453 0.1899790 0.5557471 0.2650719
## 3 0.4969702 0.6823372 0.2267099 0.1425506
## 
## Clustering vector:
##  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 3 2 3 2 2 2 2 1 2 1 1
## [39] 1 1 1 3 1 3 3 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## 
## Within cluster sum of squares by cluster:
## [1] 0.9770914 2.1588440 1.9312151
##  (between_SS / total_SS =  56.8 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

clusters<-km.res$cluster

fviz_cluster(km.res, data = df.scaled)

df.scaled.cluster<-cbind(clusters,coordinates$long, coordinates$lat)

colnames(df.scaled.cluster)<-c("clusters","long","lat")

df.scaled.cluster<-as.data.frame(df.scaled.cluster)

head(df.scaled.cluster)

##   clusters     long      lat
## 1        2 -46.2322 -20.2156
## 2        2 -46.0622 -20.0953
## 3        2 -45.7158 -20.1700
## 4        2 -46.0169 -19.8875
## 5        2 -45.4792 -19.7761
## 6        2 -45.2753 -19.2814

points.cluster.1<-df.scaled.cluster[which(df.scaled.cluster$clusters==1),]
colnames(points.cluster.1)<-c("cluster","long","lat")
points.cluster.1<-as.data.frame(points.cluster.1)

points.cluster.2<-df.scaled.cluster[which(df.scaled.cluster$clusters==2),]
colnames(points.cluster.2)<-c("cluster","long","lat")
points.cluster.2<-as.data.frame(points.cluster.2)


points.cluster.3<-df.scaled.cluster[which(df.scaled.cluster$clusters==3),]
colnames(points.cluster.3)<-c("cluster","long","lat")
points.cluster.3<-as.data.frame(points.cluster.3)

map('worldHires','Brazil', xlim=c(-75.6,-33.6), ylim=c(-34.3,6), col='gray90', fill=TRUE)
points(points.cluster.1$long, points.cluster.1$lat, pch=19, col="blue", cex=0.5)  #plot my sample sites
points(points.cluster.2$long, points.cluster.2$lat, pch=21, col="red", cex=0.5)  #plot my sample sites
points(points.cluster.3$long, points.cluster.3$lat, pch=22, col="green", cex=0.5)  #plot my sample sites


#Configurando a legenda
legend("topright", c("Cluster 1", "Cluster 2","Cluster 3"), col = c("blue","red","green"),
       pch = c(19,21,22))

K-Means - 2 Clusters

#Compute k-means k=2
km.res<-kmeans(df.scaled,2,nstart=15)
km.res

## K-means clustering with 2 clusters of sizes 26, 37
## 
## Cluster means:
##           w      E0/P      Q0/P     Q3-Q1
## 1 0.4462097 0.6961370 0.2651960 0.1783792
## 2 0.2946316 0.2398282 0.5477438 0.3212647
## 
## Clustering vector:
##  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2
## [39] 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 
## Within cluster sum of squares by cluster:
## [1] 2.927807 3.728618
##  (between_SS / total_SS =  43.2 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

clusters<-km.res$cluster

fviz_cluster(km.res, data = df.scaled)

df.scaled.cluster<-cbind(clusters,coordinates$long, coordinates$lat)

colnames(df.scaled.cluster)<-c("clusters","long","lat")

df.scaled.cluster<-as.data.frame(df.scaled.cluster)

head(df.scaled.cluster)

##   clusters     long      lat
## 1        2 -46.2322 -20.2156
## 2        2 -46.0622 -20.0953
## 3        2 -45.7158 -20.1700
## 4        2 -46.0169 -19.8875
## 5        2 -45.4792 -19.7761
## 6        2 -45.2753 -19.2814

points.cluster.1<-df.scaled.cluster[which(df.scaled.cluster$clusters==1),]
colnames(points.cluster.1)<-c("cluster","long","lat")
points.cluster.1<-as.data.frame(points.cluster.1)

points.cluster.2<-df.scaled.cluster[which(df.scaled.cluster$clusters==2),]
colnames(points.cluster.2)<-c("cluster","long","lat")
points.cluster.2<-as.data.frame(points.cluster.2)

map('worldHires','Brazil', xlim=c(-75.6,-33.6), ylim=c(-34.3,6), col='gray90', fill=TRUE)
points(points.cluster.1$long, points.cluster.1$lat, pch=19, col="blue", cex=0.5)  #plot my sample sites
points(points.cluster.2$long, points.cluster.2$lat, pch=21, col="red", cex=0.5)  #plot my sample sites


#Configurando a legenda
legend("topright", c("Cluster 1", "Cluster 2"), col = c("blue","red"),
       pch = c(19,21))

```