Reducción de Dimensiones

PCA

Datos

Tenemos datos sobre un encuesta muy grande, donde se hicieron preguntas sobre 8 temas principales: gustos musicales, gustos cinematográficos, hobbies, miedos o fobias, salud y bienestar, personalidad, gastos y aspectos demográficos.

Importamos los datos a R, limpiamos los nombres y quitamos los NAs. Una vez que tenemos nuestros datos completos vamos a convertir las 11 columnas categóricas que tenemos en numéricas, asignandoles valores entre 1 y el número de categorias o niveles que tenga dicha columna para poder tener todas nuestras columnas numéricas.

library(tidyverse)
library(janitor)
library(factoextra)
library(corrplot)
library(formattable)
datos <- read.csv("C:/Users/luisa/Downloads/respuestas_encuesta.csv",
                  fileEncoding = "UTF-8-BOM")
datos <- datos %>% clean_names()

datos <- datos
datos <- datos %>%
  mutate_all(~ifelse(. %in% c("N/A", "null", ""), NA, .)) %>% 
  na.omit()

datos$smoking <- factor(datos$smoking, levels = c("never smoked", 
                                                    "tried smoking",
                                                    "former smoker",
                                                    "current smoker"))
datos$smoking <- as.numeric(datos$smoking)
datos$alcohol <- factor(datos$alcohol, levels = c("never", 
                                                    "social drinker",
                                                    "drink a lot"))
datos$alcohol <- as.numeric(datos$alcohol)
datos$punctuality <- factor(datos$punctuality, levels = c("i am often early", 
                                                    "i am always on time",
                                                    "i am often running late"))
datos$punctuality <- as.numeric(datos$punctuality)
datos$lying <- factor(datos$lying, levels = c("never", 
                                                "only to avoid hurting someone",
                                                "sometimes",
                                                "everytime it suits me"))
datos$lying <- as.numeric(datos$lying)
datos$internet_usage <- factor(datos$internet_usage, 
                                levels = c("no time at all", 
                                           "less than an hour a day",
                                           "few hours a day",
                                           "most of the day"))
datos$internet_usage <- as.numeric(datos$internet_usage)
datos$gender <- factor(datos$gender, levels = c("female", "male"))
datos$gender <- as.numeric(datos$gender)
datos$left_right_handed <- factor(datos$left_right_handed, 
                                   levels = c("left handed", "right handed"))
datos$left_right_handed <- as.numeric(datos$left_right_handed)
datos$education <- factor(datos$education)
datos$education <- factor(datos$education, 
                                levels = c("currently a primary school pupil", 
                                           "primary school",
                                           "secondary school",
                                           "college/bachelor degree",
                                           "masters degree",
                                           "doctorate degree"))
datos$education <- as.numeric(datos$education)
datos$only_child <- factor(datos$only_child, levels = c("no", "yes"))
datos$only_child <- as.numeric(datos$only_child)
datos$village_town <- factor(datos$village_town, levels = c("city", 
                                                              "village"))
datos$village_town <- as.numeric(datos$village_town)
datos$house_block_of_flats <- factor(datos$house_block_of_flats, 
                                      levels = c("house/bungalow", 
                                                 "block of flats"))
datos$house_block_of_flats <- as.numeric(datos$house_block_of_flats)

Para mantener en cuenta los temas principales de la encuesta, formaremos variables que guarden las columnas de cada tema. Y veremos la correlación entre las categorias de cada tema.

musica <- datos[,1:19]
peliculas <- datos[,20:31]
hobbies <- datos[,32:63]
fobias <- datos[,64:73]
salud <- datos[,74:76]
personalidad <- datos[,77:133]
gastos <- datos[,134:140]
demografia <- datos[,141:150]
corrplot(cor(musica), method="color", tl.cex = 0.5)

corrplot(cor(peliculas), method="color", tl.cex = 0.5)

corrplot(cor(hobbies), method="color", tl.cex = 0.5)

corrplot(cor(fobias), method="color", tl.cex = 0.5)

corrplot(cor(salud), method="color", tl.cex = 0.5)

corrplot(cor(personalidad), method="color", tl.cex = 0.5)

corrplot(cor(gastos), method="color", tl.cex = 0.5)

corrplot(cor(demografia), method="color", tl.cex = 0.5)

Componentes Principales

Ya teniendo una idea de como son estas variables y como se relacionan entre ellas dentro de cada tema veremos cuantos componentes necesitamos para cubrir el 50% de la varianza (al tener un conjunto de datos tan diverso no podemos esperar explicar una gran parte de la varianza ya que eso nos daría una cantidad grande de componentes y estaríamos reduciendo muy pocas dimensiones).

i <- 1
acum <- c()
prop_varianza <- 0
pca <- NULL
prop_varianza_acum <- 0
while(prop_varianza_acum[i] <= 0.51){
  pca <- prcomp(datos, center = T, scale. = T, rank. = i)
  prop_varianza <- pca$sdev^2 / sum(pca$sdev^2)
  prop_varianza_acum <- cumsum(prop_varianza)
  acum[i] <- prop_varianza_acum[i]
  i <- i + 1
}

pc <- 1:(i-1)
df <- data.frame(Dimensions = pc, Variance_Explained = prop_varianza_acum[1:(i-1)])
ggplot(df, aes(Dimensions, Variance_Explained)) + geom_point() + 
  geom_line() + theme_minimal() + geom_point(aes(26, 0.50686), col = 'red') + 
  annotate(geom="text", x=28.5, y=0.49, label="50% Variance", color="red") + 
  scale_y_continuous(labels = scales::percent)

(componentes <- i-1)

## [1] 26

Podemos ver que alcanzamos explicar el 50% cuando tenemos 26 componentes. Por lo que con este número ajustaremos el modelo y veremos el porcentaje que explica cada uno de los primeros 10 componentes

pca <- prcomp(datos, center = T, scale. = T, rank. = 26)
fviz_eig(pca)

vect <- as.data.frame(pca$rotation)

Podemos ver además, usando la información dentro de las primeras dos dimensiones respecto a la colaboración de las variables en los componentes.

fviz_pca_var(pca,
             col.var = "contrib", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE
             )

Aquí se ven los vectores propios asociados a cada dimensión en una tabla donde los colores más obscuros representan un mayor peso de la variable en dicho componente.

#area(col = 2:7) ~ color_tile("#DeF7E9", "#71CA97")
vect <- as.data.frame(pca$rotation)
round_df <- function(x, digits) {
  numeric_columns <- sapply(x, mode) == 'numeric'
  x[numeric_columns] <-  round(x[numeric_columns], digits)
  return(x)
}
vect <- round_df(vect, 6)
unit.scale = function(x) (x - min(x)) / (max(x) - min(x))
formattable(vect, align = c(rep('r', 26)), 
            list(PC1 = color_tile("#edf8fb", "#006d2c"),
                 PC2 = color_tile("#feedde", "#a63603"),
                 PC3 = color_tile("#eff3ff", "#08519c"),
                 PC4 = color_tile("#f2f0f7", "#54278f"),
                 PC5 = color_tile("#edf8fb", "#006d2c"),
                 PC6 = color_tile("#feedde", "#a63603"),
                 PC7 = color_tile("#eff3ff", "#08519c"),
                 PC8 = color_tile("#f2f0f7", "#54278f"),
                 PC9 = color_tile("#edf8fb", "#006d2c"),
                 PC10 = color_tile("#feedde", "#a63603"),
                 PC11 = color_tile("#eff3ff", "#08519c"),
                 PC12 = color_tile("#f2f0f7", "#54278f"),
                 PC13 = color_tile("#edf8fb", "#006d2c"),
                 PC14 = color_tile("#feedde", "#a63603"),
                 PC15 = color_tile("#eff3ff", "#08519c"),
                 PC16 = color_tile("#f2f0f7", "#54278f"),
                 PC17 = color_tile("#edf8fb", "#006d2c"),
                 PC18 = color_tile("#feedde", "#a63603"),
                 PC19 = color_tile("#eff3ff", "#08519c"),
                 PC20 = color_tile("#f2f0f7", "#54278f"),
                 PC21 = color_tile("#edf8fb", "#006d2c"),
                 PC22 = color_tile("#feedde", "#a63603"),
                 PC23 = color_tile("#eff3ff", "#08519c"),
                 PC24 = color_tile("#f2f0f7", "#54278f"),
                 PC25 = color_tile("#edf8fb", "#006d2c"),
                 PC26 = color_tile("#feedde", "#a63603"))
)

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	PC11	PC12	PC13	PC14	PC15	PC16	PC17	PC18	PC19	PC20	PC21	PC22	PC23	PC24	PC25	PC26
music	-0.039196	0.044246	-0.040506	0.102683	-0.014533	0.101198	-0.015239	0.065659	-0.002312	0.049699	-0.007860	0.029130	-0.056255	0.099615	-0.008343	0.002749	0.124652	0.035781	-0.029233	0.099231	-0.101554	0.153825	-0.031358	0.171162	-0.072657	0.031846
slow_songs_or_fast_songs	0.060574	0.001965	-0.056144	-0.022438	-0.034128	0.034134	0.042493	0.008572	-0.051054	-0.056265	-0.121418	0.002028	-0.088398	0.102511	-0.058368	0.182382	0.135076	-0.075951	0.089714	0.098500	-0.054572	0.146168	-0.041470	0.093130	0.061914	-0.036628
dance	-0.046431	0.036156	-0.169435	-0.071686	0.072809	0.133423	-0.028357	-0.107991	0.086371	-0.116044	-0.079379	0.128923	-0.148296	-0.037335	-0.021184	0.077020	-0.080983	-0.013579	-0.027641	0.055163	-0.004324	0.061101	-0.037900	0.155946	-0.060705	0.044003
folk	-0.066773	0.136976	0.083259	-0.014789	-0.029357	0.062555	-0.099237	-0.160292	0.053845	-0.082743	-0.017111	0.081579	0.026440	0.032713	0.112103	-0.066737	-0.061799	0.043399	0.062514	0.036168	0.013764	-0.058982	0.014055	0.115924	0.037820	-0.026674
country	0.002499	0.125112	0.077947	-0.029822	0.048130	0.079415	-0.121375	-0.081673	0.066705	-0.112592	0.009826	-0.000661	0.081885	-0.046452	0.037285	-0.001497	-0.177421	0.090745	0.016301	-0.157898	-0.011014	-0.035040	0.070639	0.150233	0.042989	0.064059
classical_music	-0.050311	0.176310	0.144976	0.099591	0.054867	-0.019804	-0.026574	-0.037130	0.123798	-0.068909	0.060161	0.001854	-0.003974	-0.007890	0.150366	-0.080368	0.021254	0.086342	-0.051929	0.082321	-0.008866	0.003551	-0.003113	-0.005155	-0.101201	-0.065496
musical	-0.129083	0.116851	0.012797	0.032041	0.024378	0.061245	-0.029055	0.007592	0.141187	-0.152009	0.032608	-0.068107	0.060012	-0.099001	0.041727	0.002642	-0.014543	0.155840	0.027058	0.049236	0.122829	-0.009475	-0.035803	-0.014289	-0.045701	-0.146295
pop	-0.083715	-0.018213	-0.143871	-0.057249	0.104569	0.103021	-0.040178	0.002448	0.162518	-0.148895	-0.008822	0.094887	-0.078347	0.011522	-0.021704	0.070727	-0.014605	0.017323	0.074925	0.064231	0.014332	-0.059108	-0.089682	0.073613	-0.039439	-0.038636
rock	0.019070	0.076974	0.105519	0.177835	-0.017599	0.138145	-0.112181	0.135198	-0.132041	-0.021608	0.099176	0.022521	0.005676	0.097412	-0.085058	0.060675	-0.046965	0.045300	0.199660	-0.038548	-0.032658	0.020363	-0.108012	0.043383	-0.011882	-0.106010
metal_or_hardrock	0.091223	0.072070	0.143906	0.107152	-0.027468	0.085500	-0.035437	0.081032	-0.192567	-0.022060	0.010502	-0.024166	0.092896	0.087798	-0.112868	0.009560	-0.027261	-0.029597	0.172463	-0.054053	-0.089748	-0.007564	0.026616	-0.023212	-0.031019	-0.159740
punk	0.046644	0.061587	0.086280	0.129699	0.001595	0.112534	-0.080223	0.111250	-0.220708	0.012108	0.030882	-0.023040	0.094291	0.176480	-0.168184	0.069971	-0.068706	0.044171	0.181161	0.025794	0.000170	0.084946	0.023823	-0.011687	-0.086749	-0.133227
hiphop_rap	0.021958	0.016509	-0.198908	-0.022571	0.083881	0.064778	-0.006438	-0.055936	0.026199	-0.037504	-0.145220	0.045943	-0.103677	-0.027040	-0.010622	0.099757	-0.101745	-0.086231	-0.050034	0.052522	-0.009258	0.031290	0.042928	0.073512	-0.030244	-0.006633
reggae_ska	0.009904	0.102505	-0.031303	0.067112	-0.011688	0.119492	-0.102194	0.019911	-0.116788	-0.091640	-0.107794	0.093612	-0.072412	0.008578	-0.038780	0.101291	-0.194935	-0.061355	0.029522	-0.007841	0.123830	-0.007248	0.069442	-0.005699	-0.008934	-0.046908
swing_jazz	-0.052894	0.169382	0.062828	0.127883	0.003987	0.044936	-0.084566	0.013340	0.029655	-0.079269	-0.021868	0.094441	0.036229	-0.111451	0.094567	0.012841	-0.112546	-0.053329	-0.045746	0.004790	-0.015936	-0.101476	0.012447	0.100464	-0.054071	-0.002602
rock_n_roll	-0.016421	0.138416	0.068274	0.163189	-0.021319	0.107416	-0.138271	0.037356	-0.099737	-0.056519	0.018688	0.033978	0.070815	-0.011914	-0.062870	0.062374	-0.117934	0.017701	0.097087	0.004954	-0.027062	-0.055067	-0.028306	0.123830	0.005019	0.001375
alternative	-0.002264	0.108194	0.110464	0.206878	-0.057445	0.019347	-0.053536	0.045466	-0.077633	0.040401	0.050238	0.050463	0.007166	0.006016	-0.077950	0.083715	-0.008781	0.026583	-0.061038	0.075323	0.007484	0.054643	-0.013945	0.103190	-0.025249	-0.077793
latino	-0.126723	0.094001	-0.057704	-0.034586	-0.029396	0.061559	-0.034566	-0.070465	0.117844	-0.205662	-0.092241	0.095786	-0.052587	-0.044323	0.019055	-0.009631	-0.180244	-0.049104	-0.049535	-0.032876	0.045628	-0.007484	-0.060325	0.016665	0.060576	-0.113570
techno_trance	0.032340	0.032873	-0.097135	-0.015716	0.099025	0.139165	0.051714	-0.116727	0.045446	-0.072466	-0.109263	0.096540	-0.097352	0.056527	-0.040099	0.021519	0.023074	-0.120696	-0.172590	-0.031879	-0.085561	0.108221	-0.000865	0.089974	-0.084665	-0.059978
opera	-0.053001	0.172216	0.110165	0.047755	0.037239	-0.040798	-0.015387	-0.043393	0.061957	-0.128585	0.023860	-0.063800	0.015125	-0.052241	0.142899	-0.160776	-0.006223	0.147847	-0.016291	0.085578	-0.049030	0.018991	-0.020927	-0.042928	-0.092661	-0.112070
movies	-0.007968	0.045814	-0.059468	0.088624	0.059005	0.120015	-0.064963	0.101247	0.137479	0.087138	0.027202	-0.177015	-0.096014	-0.000506	0.012981	-0.056340	0.071334	0.020276	0.017809	0.142460	-0.020362	0.104426	-0.162351	-0.079953	-0.128105	0.245260
horror	0.080976	0.004478	-0.046472	0.056087	0.087942	0.047350	-0.032509	0.060425	-0.012122	0.015596	-0.224343	-0.118256	-0.104657	-0.076486	-0.146127	-0.095146	0.055654	0.134277	0.070101	-0.018657	-0.095132	-0.054936	0.128012	0.030583	-0.094579	0.182223
thriller	0.088125	0.018308	-0.019981	0.044403	0.141847	0.051702	-0.070123	0.044664	-0.003968	-0.001842	-0.134661	-0.141897	-0.170036	0.020518	-0.102880	-0.101570	-0.002087	0.197050	0.091472	0.059809	-0.139179	-0.042368	0.029925	0.084460	-0.031131	0.098008
comedy	-0.019407	0.016477	-0.109427	-0.046325	0.075197	0.156859	-0.052260	0.155722	0.053152	-0.017170	-0.055649	0.023804	-0.006407	-0.017140	0.069711	-0.017205	0.081808	-0.188062	0.064683	-0.020682	0.056227	-0.153702	-0.007637	-0.134386	-0.010336	0.082729
romantic	-0.179954	-0.000790	-0.087564	-0.018442	0.034511	0.087912	-0.056172	0.043381	0.104672	-0.034473	0.021512	0.027019	0.097442	-0.082235	-0.069572	-0.025369	-0.036863	-0.032387	0.064259	-0.089977	0.018574	-0.006238	-0.016722	-0.048309	0.051059	-0.052558
sci_fi	0.111181	0.077423	0.045799	0.028292	0.109001	0.175574	-0.027287	0.034188	0.111982	-0.031708	-0.023715	-0.047786	0.051053	-0.003035	-0.016252	-0.041997	-0.010562	-0.004903	-0.011710	-0.044194	-0.072442	0.100187	-0.089001	0.051650	-0.071124	0.111444
war	0.122110	0.087200	0.005371	0.059457	0.084398	0.025012	-0.045017	-0.099297	0.006466	0.089291	0.000172	-0.094521	-0.044607	0.112134	0.115042	-0.051488	-0.161148	0.050493	0.009142	-0.100318	-0.074349	0.016950	0.046005	0.005902	0.075557	0.153277
fantasy_fairy_tales	-0.141893	0.053721	-0.020438	0.030957	-0.013624	0.186012	-0.069868	0.069484	0.037398	-0.072500	0.015496	-0.018714	0.017927	-0.071889	0.212657	-0.143862	0.050811	-0.064814	0.124160	-0.104026	-0.012152	0.107857	0.026036	-0.072565	0.075309	-0.032352
animated	-0.094255	0.052008	-0.001147	0.059353	-0.002563	0.229654	-0.030382	0.115018	0.069908	-0.048058	0.025366	-0.033756	0.044382	-0.046888	0.172327	-0.124205	0.064175	-0.089382	0.113425	-0.084794	0.004047	0.139730	0.079138	-0.111936	0.039743	0.010220
documentary	0.023194	0.153040	0.085382	-0.020991	0.064813	0.011065	0.006315	0.022173	-0.053070	0.000481	0.013648	-0.015582	-0.065795	0.125607	0.206894	-0.087565	-0.058519	-0.084511	-0.131811	-0.047431	-0.041612	0.047320	-0.012169	-0.032684	0.182246	0.092451
western	0.112294	0.118373	0.041221	-0.000625	0.063343	0.077424	-0.057082	-0.081602	-0.002063	-0.067543	-0.026231	-0.086049	0.107103	-0.033412	0.071200	0.018610	-0.138385	0.030313	-0.021749	-0.136124	-0.077965	-0.003998	0.047909	0.028086	0.138103	0.060890
action	0.135363	0.058487	-0.050011	-0.028774	0.136754	0.079664	-0.084106	0.012167	0.063703	0.006130	-0.039141	-0.078163	-0.012885	0.075141	0.147016	-0.012796	0.005108	0.004338	-0.053624	0.003025	-0.029435	0.011372	-0.100423	-0.033235	-0.080931	-0.044509
history	0.018088	0.154126	0.057763	0.095888	0.029584	-0.153789	-0.000813	0.018840	0.012220	0.058591	-0.097457	-0.128057	-0.102563	0.106790	0.170698	-0.017672	-0.035658	-0.118366	-0.049944	-0.059650	-0.085382	0.038436	0.043878	-0.013406	-0.001653	0.013269
psychology	-0.071482	0.108573	0.023630	0.103120	-0.007366	-0.058676	0.057289	0.011365	0.061743	-0.029944	-0.090042	-0.024539	-0.111873	0.082961	-0.092899	0.081104	0.062317	0.001049	-0.111674	-0.208278	-0.007334	-0.020233	0.175652	-0.076574	0.036413	-0.016988
politics	0.061928	0.135441	-0.023236	0.045205	0.071714	-0.251060	-0.033605	0.022600	0.083460	0.066169	-0.012026	-0.108544	-0.122934	0.133694	0.013955	0.019717	-0.069167	-0.160136	0.060794	-0.059586	0.101242	-0.048318	-0.001879	-0.027786	-0.095215	-0.021423
mathematics	0.066096	0.106943	0.054498	-0.126175	0.086132	0.065205	0.008025	0.006552	0.064395	-0.128820	0.112414	0.043589	0.041183	-0.011642	-0.221249	0.012143	-0.041874	-0.109664	-0.056247	-0.074927	0.187723	0.094086	0.053733	-0.090646	-0.044977	0.110854
physics	0.088894	0.146115	0.074526	-0.115617	0.087628	0.079034	0.096740	-0.041580	-0.037638	-0.147962	0.143963	0.023796	-0.003904	-0.032331	-0.114781	-0.030749	0.043299	-0.071488	-0.102738	-0.124230	0.103730	0.053699	0.017983	-0.021011	-0.042159	0.045078
internet	0.062820	0.004624	-0.058812	0.001597	0.167556	0.086349	-0.102386	0.102279	0.124734	0.013135	0.083693	-0.020864	0.049993	0.107711	-0.151811	0.060731	0.158128	-0.077316	-0.119800	-0.007851	0.079600	-0.011570	0.007992	-0.062471	0.032458	-0.110707
pc	0.149289	0.081084	0.003691	-0.057438	0.174245	0.080338	-0.094244	0.040858	0.053267	-0.007601	0.013126	0.000255	0.082297	-0.014143	-0.184374	-0.028849	0.173545	-0.067472	-0.052884	0.012494	0.054681	0.016028	0.014418	0.016103	0.027852	-0.018900
economy_management	0.020781	0.061766	-0.103147	-0.032412	0.086405	-0.142691	-0.125062	0.103188	0.124742	-0.039336	-0.002120	0.018575	0.012499	0.051166	-0.151356	0.091544	-0.136960	-0.041392	0.011973	-0.095977	0.172698	0.054934	0.052614	-0.068190	0.032350	0.015809
biology	-0.096805	0.103067	0.038182	-0.060325	0.018767	0.161049	0.285565	-0.055731	-0.107128	-0.096317	0.118620	-0.065248	-0.207899	0.063414	-0.055377	0.004215	0.053089	-0.013205	0.029031	-0.019709	-0.061240	-0.105646	-0.058821	-0.040525	-0.002310	-0.006210
chemistry	-0.049291	0.083846	0.055546	-0.099507	0.009381	0.142445	0.277642	-0.047724	-0.109749	-0.136218	0.142646	-0.009299	-0.173091	0.088243	-0.039545	-0.039385	0.006514	-0.031753	0.066710	-0.023058	-0.061252	-0.089157	-0.062738	-0.030664	-0.032529	0.044596
reading	-0.134289	0.089110	0.100043	0.140402	-0.056733	-0.051693	0.026574	0.101536	0.035476	-0.033387	-0.013025	-0.053497	-0.037444	0.011636	0.086559	0.104134	0.072141	-0.008881	-0.005034	0.079245	0.047587	0.044033	-0.037029	-0.016194	-0.039284	0.000704
geography	0.016204	0.133062	0.000931	0.021208	0.025867	-0.090711	0.015749	0.027240	0.024370	0.093769	-0.011354	-0.090914	-0.029759	0.113191	0.002570	0.090479	-0.081264	-0.135564	-0.109539	0.197973	0.011497	0.042732	0.002320	-0.056940	0.034109	-0.079167
foreign_languages	-0.087395	0.111232	-0.017135	0.122519	-0.004146	-0.060789	-0.023339	0.079082	0.059464	0.010744	0.027282	0.011411	0.001121	0.118183	-0.098643	0.138095	-0.031709	-0.019406	-0.143672	0.074927	0.010413	0.055443	-0.063385	-0.110880	0.020876	0.054065
medicine	-0.078476	0.109717	0.035973	-0.046212	0.007327	0.088430	0.252755	-0.079173	-0.099881	-0.109342	0.099692	-0.071950	-0.213101	0.096715	-0.106978	-0.009995	0.027365	0.036605	0.057946	0.003076	-0.076508	-0.158846	-0.062132	-0.107795	0.015036	-0.023951
law	0.000270	0.108167	-0.075062	0.036322	0.070077	-0.193212	-0.003506	0.047988	0.048227	-0.030096	-0.089678	-0.160004	-0.084932	0.076612	-0.056972	0.043347	-0.131806	-0.065795	0.105430	-0.153408	0.107800	-0.052842	-0.046902	-0.106820	-0.054300	0.008420
cars	0.139155	0.076950	-0.113099	-0.076602	0.125244	0.071622	-0.033724	-0.046400	-0.037208	0.053659	-0.040395	-0.081405	0.036005	-0.028728	0.027460	-0.010399	-0.042523	-0.016653	0.028389	0.039699	0.051435	-0.049276	0.002263	-0.095377	-0.026008	-0.061730
art_exhibitions	-0.117359	0.151409	0.051291	0.144287	-0.026924	-0.048042	0.027809	-0.031405	-0.039203	0.030967	-0.005217	-0.086405	0.037033	-0.121709	-0.038714	0.044312	0.098665	0.020533	-0.136107	0.094579	0.036997	-0.024012	0.089004	-0.010131	-0.048680	0.011957
religion	-0.067985	0.120319	0.074791	-0.015091	-0.022964	-0.023884	0.014728	-0.236727	0.135188	0.130670	0.028256	-0.048120	-0.044655	0.106060	-0.047200	0.079901	0.025989	-0.025056	0.058936	-0.035029	-0.029619	0.042598	-0.020336	-0.104744	-0.153378	-0.100065
countryside_outdoors	-0.082003	0.117947	0.044002	-0.053667	-0.023093	0.072321	-0.004247	-0.069740	-0.030588	0.122976	-0.054149	-0.036722	0.100654	-0.056634	0.015587	0.057367	0.033523	-0.100418	-0.094412	0.150561	-0.013983	0.010921	0.093368	-0.083057	0.199976	0.076370
dancing	-0.141359	0.095304	-0.097229	0.015407	-0.050845	0.022090	0.073738	-0.120089	0.067170	-0.036162	-0.089640	-0.031513	-0.010507	-0.089045	-0.071282	0.064625	-0.037030	-0.092481	-0.110515	0.031674	0.009635	-0.040840	-0.031623	-0.042346	0.035272	0.023576
musical_instruments	-0.055593	0.135148	0.066231	0.074839	-0.012379	0.028489	-0.007986	-0.106489	0.016993	0.029509	-0.023012	-0.007690	0.179382	-0.084295	-0.079297	-0.045089	0.129754	-0.050079	0.002414	0.095943	-0.052117	-0.088498	0.044934	-0.011069	-0.126300	0.013470
writing	-0.065778	0.087223	0.077598	0.116977	0.024973	-0.072669	0.053665	-0.047915	0.052079	0.034140	-0.109932	-0.081732	0.106026	-0.096741	-0.038987	0.086338	0.223921	-0.070871	-0.039776	-0.070039	-0.009433	0.015191	0.044022	0.161616	-0.031381	0.006686
passive_sport	0.049836	0.048218	-0.079635	-0.016721	0.034240	0.112837	-0.031543	0.031347	-0.006329	0.131522	0.002783	-0.033603	-0.026865	0.041078	-0.027077	0.009245	-0.018527	-0.052411	0.064521	0.137971	0.166337	-0.273268	0.073502	-0.030995	0.044462	-0.098364
active_sport	0.051502	0.118692	-0.118316	-0.030483	-0.018458	0.056479	0.066388	-0.059794	-0.127859	0.051065	-0.113845	-0.056581	0.022842	-0.073085	-0.011137	0.017145	-0.119967	-0.109633	-0.049741	0.105052	-0.060055	-0.061137	0.008673	0.065869	0.035200	-0.034055
gardening	-0.093690	0.062695	0.016650	-0.093016	-0.013998	0.040208	0.097931	-0.081145	-0.035335	0.043238	-0.041285	-0.156379	0.010630	-0.099005	0.031890	0.061762	0.168647	-0.114065	0.039850	0.126571	0.145947	0.004462	0.113680	0.101596	0.016008	-0.003004
celebrities	-0.095988	-0.054818	-0.155596	0.027941	0.143459	-0.010382	-0.012558	0.022065	0.026127	-0.070783	-0.003576	-0.069786	0.039371	-0.017454	0.002254	0.137167	0.038625	0.001678	0.113295	0.035115	0.026125	-0.014856	0.102650	0.074305	-0.007523	-0.134125
shopping	-0.154653	-0.033224	-0.198703	0.043814	0.064292	0.012673	0.050820	0.050037	0.015476	-0.039109	0.056466	-0.122728	0.050439	0.018151	-0.018920	0.037047	0.037488	0.122167	0.015660	-0.000437	-0.020100	-0.004124	0.028779	0.076155	0.017035	0.026085
science_and_technology	0.103397	0.167502	0.025464	-0.031517	0.151876	0.075895	0.065642	0.021118	-0.057647	-0.023818	0.116768	-0.040459	-0.008465	0.051109	-0.011831	-0.048673	0.106167	0.052145	-0.094390	-0.035870	0.062553	0.038158	-0.058246	0.009185	0.040348	0.029233
theatre	-0.143822	0.131277	0.042362	0.123927	-0.045282	-0.038121	0.014951	0.042712	0.008439	-0.011248	0.012818	-0.053143	-0.026675	-0.150580	0.067062	0.002142	0.082487	0.106375	-0.067385	0.052717	0.133419	-0.079720	-0.035025	-0.053327	-0.007794	0.013968
fun_with_friends	-0.013994	0.081831	-0.151452	0.091617	-0.072356	0.105931	-0.049042	0.048399	-0.046684	0.070545	0.073033	0.093365	-0.095873	-0.066955	0.036332	0.036251	0.041797	-0.013828	-0.033819	0.042332	0.043517	-0.006643	-0.056828	0.049254	-0.097259	0.105891
adrenaline_sports	0.082047	0.126176	-0.131179	0.042463	-0.016561	0.060234	0.109087	-0.060542	-0.073084	0.084727	-0.100250	-0.012566	0.008761	-0.064583	-0.102465	0.023487	-0.087745	0.039229	-0.030546	0.115711	0.052903	0.069036	0.048379	-0.004852	0.149905	0.067953
pets	-0.062090	0.010530	-0.052613	0.001886	0.025733	0.113256	0.071825	0.105163	-0.158158	0.014368	-0.101448	-0.209825	-0.018476	-0.020939	0.119537	0.105351	0.037385	-0.066760	0.081933	-0.097246	0.106694	0.119973	0.039131	-0.031595	0.028827	0.065257
flying	-0.086038	-0.051116	0.026966	-0.043890	0.070823	-0.025362	-0.175309	-0.074248	-0.082133	-0.014513	-0.052736	-0.056924	-0.010085	-0.012689	0.014318	0.024134	0.026662	-0.218119	0.018842	-0.003956	-0.097390	-0.114969	0.046652	0.120365	-0.155535	-0.046872
storm	-0.137871	-0.050431	-0.037872	0.016196	0.028547	0.017129	-0.127926	-0.108015	-0.178108	-0.076770	0.022164	-0.054382	0.026480	0.023674	-0.026892	0.057543	0.102207	-0.104764	0.047024	-0.003804	-0.004244	-0.137480	-0.068276	-0.031075	0.056998	0.044400
darkness	-0.136022	-0.060520	-0.036301	0.098056	0.037463	0.026822	-0.089168	-0.062523	-0.121289	-0.073476	0.000780	-0.026235	0.029017	0.049638	-0.038565	0.046414	0.047883	-0.120347	-0.040050	-0.101330	-0.080573	-0.120933	-0.006811	-0.134867	0.096479	0.034841
heights	-0.047758	-0.060717	0.015177	0.024509	0.070798	-0.038888	-0.162644	-0.106029	-0.136714	-0.040436	0.016985	-0.036603	-0.000196	0.036841	0.059729	0.104855	0.144280	-0.156141	-0.090486	-0.117180	-0.119160	-0.110933	-0.000923	0.027365	-0.032297	0.083342
spiders	-0.113963	-0.067965	-0.056169	0.059468	0.088758	0.013888	-0.095389	0.018296	-0.081560	-0.087594	0.053945	-0.120858	0.034844	0.076430	0.009145	-0.066467	-0.012570	0.007989	-0.149045	-0.034709	-0.120340	0.032102	-0.066082	-0.139097	0.089545	0.007683
snakes	-0.107188	-0.065787	-0.068775	-0.008641	0.093143	-0.030991	-0.232155	-0.076721	-0.052555	-0.020501	0.072726	-0.118597	0.083995	0.096379	0.069311	-0.068618	-0.010774	-0.046564	-0.095818	0.061881	-0.045462	0.103527	-0.073041	-0.093092	0.127044	-0.003376
rats	-0.104972	-0.063823	-0.086434	0.023041	0.122787	-0.050703	-0.199993	-0.122421	-0.035758	-0.064021	0.020925	-0.099671	0.028962	0.137721	-0.045681	-0.093863	-0.016287	0.032074	-0.037054	0.055658	-0.033712	0.023809	-0.004611	-0.068703	0.065472	-0.004738
ageing	-0.068216	-0.043718	-0.053347	0.089404	0.107376	-0.040732	-0.008201	-0.018459	-0.161698	-0.002791	-0.009251	0.082833	0.040579	-0.010664	0.013587	-0.119632	-0.095976	0.009669	-0.108195	0.060877	0.055927	-0.102201	-0.009899	0.114755	0.030905	0.019461
dangerous_dogs	-0.119319	-0.066405	-0.010142	0.006428	0.111203	-0.016702	-0.138133	-0.125013	-0.065437	-0.013574	0.112044	0.017682	0.035245	0.116288	-0.016288	-0.057065	0.038803	0.029957	-0.053796	0.108614	-0.000848	0.040629	-0.070837	0.119706	-0.040686	0.030614
fear_of_public_speaking	-0.053416	-0.100978	0.092195	0.010931	0.137809	0.120481	-0.041511	0.011934	-0.051760	0.017357	0.043624	-0.060615	-0.104923	-0.075962	-0.030955	0.108017	-0.133019	-0.047514	-0.047545	0.229797	-0.084909	0.101641	0.124390	-0.063587	0.012443	-0.087370
smoking	0.035785	-0.027549	-0.085727	0.175319	-0.020137	-0.081549	-0.035831	-0.040864	-0.096445	-0.078862	-0.098761	0.052047	-0.110016	-0.004925	-0.005025	0.082569	0.081260	0.107455	0.009624	-0.100100	-0.079786	0.129858	0.088751	0.003864	-0.006717	0.026858
alcohol	0.056710	-0.001307	-0.043329	0.174531	-0.045449	-0.020063	-0.040576	-0.043151	-0.056345	-0.081696	0.079694	0.149037	-0.134334	-0.027951	-0.014283	0.148634	-0.017804	0.037582	0.057250	0.007241	0.024336	0.102337	0.102124	-0.095777	-0.027525	0.132650
healthy_eating	-0.065269	0.103465	-0.062247	-0.076124	0.021576	-0.041108	0.078207	0.026289	-0.101730	0.021996	0.056529	0.006299	0.013547	0.030443	-0.043662	0.034054	-0.054991	-0.037740	-0.072775	0.116910	-0.162532	0.067398	0.084361	0.036620	0.058706	-0.039955
daily_events	0.009769	0.109470	-0.051204	0.039314	0.115515	-0.205110	-0.036495	0.062475	0.063891	0.061341	-0.046779	-0.027495	-0.088408	0.096995	0.010399	0.025953	0.083368	-0.073468	0.097156	0.034750	0.096495	-0.036048	0.014759	0.083400	-0.018085	-0.077302
prioritising_workload	-0.074255	0.078452	-0.000418	-0.178095	0.053457	-0.114973	0.022362	0.055405	-0.183860	-0.057957	-0.092345	0.011563	0.127604	0.000973	-0.013966	-0.015716	-0.026197	0.053348	0.084192	0.058406	0.025955	0.026275	0.024680	-0.017810	-0.162702	0.156640
writing_notes	-0.136366	0.076838	0.005889	-0.073603	0.058773	-0.099917	-0.008487	0.036048	-0.063549	-0.028863	-0.035923	0.108468	0.050583	-0.044069	-0.011371	-0.057229	0.010239	-0.007338	0.029528	0.042846	0.064960	0.145217	-0.009378	-0.058597	-0.148159	0.139633
workaholism	-0.068771	0.139478	0.054905	-0.077672	0.061411	-0.143013	0.052290	0.052558	-0.117291	-0.088677	0.027580	0.048936	0.076820	0.039236	-0.049433	-0.022317	-0.026505	-0.027931	0.004377	0.064279	-0.003636	0.047848	-0.081891	0.021737	-0.069622	0.228378
thinking_ahead	-0.025216	0.071037	0.066078	-0.108086	0.158404	-0.093552	0.039201	0.086720	-0.058033	0.020605	-0.055554	0.188373	0.073288	0.073227	0.016940	0.075688	-0.023884	0.015813	0.006093	-0.082407	-0.078318	-0.038898	0.049807	-0.004066	-0.084860	0.075619
final_judgement	-0.071877	0.034796	-0.003151	-0.071037	0.057924	0.009412	-0.037289	-0.155216	0.090795	0.172575	0.070236	0.109696	-0.004600	-0.017711	0.006030	0.173708	-0.036871	0.040563	0.167916	-0.110772	-0.247492	-0.009989	0.003939	-0.178833	-0.085892	-0.024946
reliability	-0.051514	0.086627	-0.015007	-0.133260	0.073357	-0.077294	-0.059172	0.161958	-0.018255	-0.035626	-0.081233	0.136756	0.020167	-0.016599	0.075021	0.077846	0.061385	0.127519	-0.014719	0.086365	-0.096498	0.049190	0.084113	-0.118581	0.028448	0.065542
keeping_promises	-0.033948	0.086155	0.012488	-0.107572	0.065102	0.001433	-0.023049	0.077460	-0.074661	0.053432	-0.110092	0.196816	0.048481	-0.128749	0.032057	0.119288	0.019803	0.094231	0.021311	-0.007653	-0.068886	0.031625	0.046429	-0.148996	-0.044826	-0.087045
loss_of_interest	-0.001560	-0.009039	-0.038742	0.104163	0.061376	-0.051097	0.136256	-0.068424	0.080219	-0.134838	-0.042523	0.131348	0.082098	0.034282	0.043238	0.116759	0.011041	-0.008898	0.046500	0.104330	-0.125142	0.127559	-0.026314	-0.039722	0.146552	0.057888
friends_versus_money	-0.071145	0.070917	0.009859	-0.024952	-0.074446	0.067616	-0.113094	-0.046448	-0.039106	0.217030	0.027093	0.119855	-0.019657	-0.107891	-0.043895	0.064742	0.077384	-0.101320	0.020878	-0.059444	0.013602	-0.026969	-0.057999	-0.066875	0.002281	0.015264
funniness	0.067423	0.050190	-0.028347	0.085537	0.083601	0.042186	-0.012527	0.013798	-0.001830	0.064799	0.101675	0.115638	0.044564	0.004624	0.074895	-0.009652	0.164382	-0.132395	0.136851	0.095775	0.010632	-0.172669	0.033224	-0.072363	0.089670	0.239190
fake	0.020209	-0.040805	0.062185	0.117901	0.133012	-0.075987	0.145980	-0.111477	0.090574	-0.062517	0.019647	-0.051231	0.064494	-0.021613	0.091088	0.062002	0.035990	0.044252	0.140024	0.113442	-0.009252	-0.050981	0.149889	-0.046794	0.073250	0.033649
criminal_damage	0.070761	-0.033479	-0.035059	0.107811	0.125763	0.011302	0.106827	-0.084374	-0.108572	-0.009115	-0.135003	0.016396	0.014514	0.039312	0.041549	-0.145733	-0.026970	-0.080839	-0.034295	-0.000962	-0.010908	0.124609	0.000053	-0.018261	-0.093162	-0.014375
decision_making	-0.086432	-0.011649	0.082502	-0.063079	0.119199	0.025530	-0.019324	0.036417	-0.092119	0.092205	0.100314	0.134644	-0.066906	0.036703	0.105744	0.003650	0.021444	0.070177	-0.099405	0.026347	-0.025079	0.001058	0.117850	0.008418	-0.111491	0.104269
elections	-0.014662	0.099181	0.020405	-0.008148	-0.015162	-0.100622	-0.067073	0.069243	0.043328	0.038674	0.007177	0.088672	-0.208011	-0.069545	0.077217	0.032051	0.088185	-0.050941	0.154154	0.094828	0.123218	0.019590	-0.086785	0.019675	0.008227	0.073847
self_criticism	-0.052355	0.025884	0.106847	0.065722	0.132742	-0.027844	0.034107	0.037204	0.027591	0.108253	0.021850	0.258691	0.035475	0.051396	0.041493	0.028799	-0.062724	0.010596	-0.014718	-0.006034	0.040977	-0.056475	-0.006192	0.067102	0.162430	0.067643
judgment_calls	-0.023394	0.065658	-0.044579	0.065343	0.012600	0.019094	0.007299	0.026713	0.008369	-0.014995	-0.157306	0.132353	-0.003295	0.128349	0.046068	0.035964	0.156939	0.109952	-0.189698	-0.115515	-0.015655	-0.159905	0.122583	-0.213244	-0.002055	-0.147254
hypochondria	-0.046044	-0.032841	0.032706	0.091168	0.122285	-0.037695	0.002519	-0.114182	-0.090115	-0.000826	0.046392	-0.103130	0.150857	-0.002125	-0.173490	-0.023136	-0.048740	0.016530	0.004597	-0.043804	0.059415	-0.019242	0.092225	-0.004012	-0.003300	0.083460
empathy	-0.100539	0.042017	-0.002193	0.003388	-0.026350	0.081259	-0.061711	0.042431	-0.025855	0.074745	-0.141722	0.120631	-0.108970	0.080590	-0.043002	-0.079657	0.054003	0.109307	-0.150556	-0.213232	-0.059423	-0.097077	0.019958	-0.009185	-0.003274	-0.018120
eating_to_survive	0.012912	-0.012392	0.036791	-0.020519	0.104841	0.042961	-0.002738	-0.154414	0.011183	0.023670	-0.122091	-0.074545	0.140868	-0.101773	-0.108867	-0.001321	-0.075397	0.053643	0.020025	-0.029069	-0.006146	-0.001813	0.036213	-0.096923	-0.073543	0.109552
giving	-0.100552	0.056530	-0.086816	-0.060700	0.024133	0.015300	-0.060341	0.046476	-0.034543	0.141790	-0.033433	-0.051621	0.018870	-0.109780	-0.029157	-0.125283	-0.016674	0.032920	0.093892	-0.126913	0.079328	0.023507	0.031338	0.055192	-0.072913	0.047567
compassion_to_animals	-0.090373	-0.000247	-0.015068	0.024382	0.030332	0.064138	0.027481	0.138343	-0.116980	0.141500	-0.154968	-0.090610	-0.098153	-0.062018	0.063799	-0.044769	-0.004127	0.075050	-0.026550	-0.191189	0.052156	0.039905	-0.050467	0.024409	0.084470	0.080708
borrowed_stuff	-0.060638	0.045951	0.010097	-0.112391	0.100932	0.064778	0.001300	0.153719	-0.045320	0.132661	-0.152659	0.091078	-0.002424	-0.001768	0.059151	0.007406	0.006827	0.083586	-0.040369	0.023012	-0.079554	0.020158	-0.058768	-0.034825	-0.078552	-0.073548
loneliness	-0.047851	-0.060052	0.120320	0.101554	0.176052	0.038660	0.125925	-0.024306	0.048199	0.072022	-0.106831	0.062539	0.043623	-0.029393	-0.113841	0.009861	0.012057	0.000365	0.000980	0.000253	0.019858	0.064654	-0.064836	0.096008	0.120748	-0.109989
cheating_in_school	0.055306	-0.045710	-0.125868	0.146243	-0.040018	0.091823	-0.010622	-0.013766	0.020918	0.085334	-0.079720	0.014687	-0.081815	0.061937	0.068593	-0.073715	-0.058493	-0.004813	-0.018660	0.102497	0.070971	0.029886	0.038082	-0.059245	-0.004295	-0.119300
health	-0.095494	-0.003490	-0.057464	-0.026215	0.182812	-0.031573	-0.005428	-0.016104	-0.176162	0.108065	0.066972	0.050193	-0.016622	0.002788	-0.005355	-0.106856	-0.057370	-0.006705	-0.019073	0.067247	0.087522	-0.155986	-0.005438	0.006023	-0.086308	-0.107169
changing_the_past	-0.013617	-0.056896	0.029833	0.115090	0.172083	0.074263	0.108532	-0.057921	0.085468	0.156065	-0.060455	0.077940	0.070342	-0.085122	-0.038511	-0.062236	-0.065816	-0.038832	0.119354	0.027905	-0.011676	-0.032842	-0.047317	0.009748	0.051855	0.050858
god	-0.103616	0.035698	-0.004230	-0.064804	-0.010347	0.032603	-0.030603	-0.245021	0.146291	0.185500	0.049849	0.041394	-0.018132	0.059568	0.005571	0.088695	-0.044289	-0.014554	0.137449	-0.091601	-0.141785	0.025841	-0.068473	-0.110396	-0.136567	-0.067404
dreams	0.024231	0.038113	-0.060139	-0.068198	-0.081508	0.013174	0.004586	0.046254	0.097502	-0.037394	0.137621	-0.019000	0.049129	0.024904	0.065438	0.022313	-0.048339	-0.133295	0.108093	0.044674	-0.113705	0.046331	0.173598	0.038063	0.072534	0.034603
charity	-0.059235	0.129279	0.005085	0.024969	0.059546	-0.116131	0.012862	-0.056533	0.048874	0.126408	0.019837	-0.107892	-0.051192	-0.116984	-0.113013	0.006135	-0.083244	0.028388	0.114515	-0.060528	-0.166926	0.042013	0.003559	0.028751	0.091172	-0.046571
number_of_friends	0.001263	0.101901	-0.182098	0.038004	-0.129176	-0.001730	-0.118529	-0.081792	-0.068794	0.074900	0.057458	0.075541	0.051309	-0.043259	-0.028817	-0.041689	0.057639	-0.013835	0.063889	-0.013365	-0.093222	-0.020633	-0.053820	0.007951	-0.073259	0.057275
punctuality	0.001298	-0.000194	-0.039909	0.150662	-0.083543	-0.017335	-0.039125	-0.113593	0.043642	0.007762	0.153801	0.024948	-0.110578	-0.066542	-0.062413	-0.071052	-0.128312	-0.084019	-0.178025	0.004005	0.022524	0.065764	0.050176	0.073094	-0.064709	0.138247
lying	0.029800	-0.038049	0.003676	0.138327	0.009768	-0.003368	0.002961	0.003071	0.069498	-0.069252	-0.012253	-0.029196	-0.048583	0.088512	0.111161	0.024624	-0.030147	0.032194	0.162741	0.139755	-0.048970	-0.186390	0.108848	-0.054040	0.004035	0.095297
waiting	0.031012	0.056219	0.024571	-0.039616	-0.108369	0.041993	-0.006052	0.071869	0.148502	0.011605	0.033838	-0.056231	0.047297	-0.005613	-0.133025	-0.025166	0.072097	0.060603	-0.000421	-0.079562	-0.018805	-0.128090	0.014561	0.098446	0.116833	0.069821
new_environment	0.049725	0.087760	-0.099376	0.034174	-0.146627	0.016482	0.001528	-0.024818	0.072197	-0.027535	-0.052677	0.040050	0.128759	0.203779	-0.055509	-0.046450	0.045697	0.060264	-0.016825	0.029658	-0.066277	-0.038514	-0.072605	-0.062199	0.145673	0.055527
mood_swings	-0.085140	-0.071741	0.060719	0.096201	0.101006	-0.030704	0.160012	-0.078774	0.001381	0.002316	-0.076957	0.134114	0.065061	-0.022293	-0.010231	-0.096031	-0.028348	-0.144714	0.054320	-0.074041	0.107967	0.196939	-0.009467	-0.032251	-0.044911	0.018597
appearence_and_gestures	-0.078867	0.017184	-0.129766	0.050939	0.077973	-0.063281	0.095132	0.013496	0.018361	-0.006663	0.060537	0.092072	-0.020758	0.121781	0.077293	-0.054843	0.064448	0.068138	-0.018510	-0.088251	-0.069082	-0.109302	0.039447	0.168804	-0.018405	-0.001709
socializing	0.002220	0.108858	-0.155909	0.057894	-0.114392	-0.016321	0.071798	-0.053704	0.011835	0.037577	-0.057979	0.094280	0.096624	0.095372	-0.080370	-0.037441	0.040740	-0.012811	0.053134	-0.009241	-0.060888	0.012705	-0.047591	0.083197	0.064117	0.186923
achievements	0.016589	0.014424	-0.078865	0.048428	0.057564	-0.022178	0.048366	-0.002194	-0.037456	-0.048092	0.115049	0.043553	0.041319	-0.042462	0.101575	0.004798	0.042946	-0.137260	0.202131	-0.086919	0.020003	0.098185	0.157268	-0.056824	0.132583	-0.010724
responding_to_a_serious_letter	-0.005727	-0.021540	0.058978	0.031146	0.038443	0.012576	-0.026108	0.043567	-0.000441	0.073858	0.206961	0.061908	-0.145382	0.108183	0.051643	-0.002158	-0.016585	-0.074758	0.001116	-0.107342	0.138887	0.043101	0.212372	0.183711	0.043172	0.025526
children	-0.107056	0.051425	-0.055040	-0.065972	-0.034962	0.027462	-0.034858	-0.035879	0.069565	0.143815	-0.017822	-0.009606	-0.095589	0.033286	-0.049952	-0.142197	0.085123	-0.011692	0.117793	-0.047188	-0.044405	0.091334	0.081093	0.083288	0.153398	0.033551
assertiveness	0.038196	0.072924	-0.080723	0.031286	-0.013680	-0.075257	0.029800	0.033052	0.034874	-0.097962	-0.113044	0.056084	0.002251	0.107175	-0.031362	-0.210771	0.074822	-0.050603	0.059764	0.021020	-0.032540	0.023982	-0.197545	-0.049383	-0.007968	-0.151692
getting_angry	-0.044013	-0.081415	-0.025378	0.094590	0.121373	-0.090701	0.098778	-0.044186	-0.102817	-0.038893	-0.042998	0.104934	-0.017489	0.011359	0.045213	-0.162832	0.025519	-0.173363	0.143452	-0.060270	0.006266	0.208979	-0.157820	-0.016768	-0.045247	-0.060168
knowing_the_right_people	0.009850	0.079333	-0.147863	0.052288	0.095584	-0.093930	0.082447	0.011833	0.007639	-0.052063	0.067022	0.129592	0.173657	0.087844	0.051856	-0.086618	-0.025670	0.038176	0.077260	0.026305	0.095162	-0.119315	0.031126	-0.008677	0.011689	-0.003470
public_speaking	-0.068918	-0.119542	0.049788	-0.052279	0.145092	0.087762	-0.014035	0.063056	-0.003887	0.030118	0.073931	-0.015716	-0.128016	-0.047394	0.029738	0.092686	-0.069961	0.024237	-0.018992	0.152675	-0.075150	0.019751	0.095729	-0.109846	0.026915	-0.008007
unpopularity	-0.050618	0.013084	0.059704	0.010744	0.063475	-0.007133	0.003169	0.023174	0.091128	0.160473	-0.031516	0.086646	-0.049459	0.069142	-0.095826	-0.073322	-0.076313	-0.002695	0.057647	0.002066	0.045553	-0.111713	-0.116785	0.073619	0.212618	-0.024241
life_struggles	-0.204940	-0.062656	0.013482	0.026146	-0.003053	0.033313	0.031103	0.036446	-0.023154	0.013539	-0.049267	0.004798	-0.046629	-0.034530	-0.072125	-0.127476	0.025309	-0.068210	0.007417	-0.073612	0.100876	-0.079066	0.036817	0.036530	0.081260	-0.048733
happiness_in_life	0.017992	0.102318	-0.136730	-0.132718	-0.144410	-0.020141	-0.099318	0.035157	-0.046349	-0.051408	0.127216	0.026779	-0.004192	0.058552	0.068084	0.006668	-0.038005	0.009526	0.019471	0.022229	0.061701	0.071740	0.123206	-0.026422	-0.082360	0.001219
energy_levels	0.013440	0.114010	-0.185944	-0.072054	-0.161501	0.013525	0.000300	-0.016780	-0.098391	0.031399	0.012926	0.013000	0.059738	0.084317	0.009929	-0.120259	0.014873	-0.011549	0.072032	0.071346	-0.029453	0.018622	-0.018977	-0.040635	0.000278	-0.072036
small_big_dogs	0.117870	0.030087	-0.010380	0.083968	-0.068428	0.019392	0.091798	-0.070643	-0.090012	-0.003526	-0.161105	0.005884	0.024243	-0.101219	0.085638	-0.022598	-0.147962	-0.041452	0.021944	0.026512	0.010742	-0.061896	0.093049	-0.154054	0.058010	-0.026637
personality	0.031328	0.059534	-0.151780	-0.094334	-0.085959	-0.020881	-0.024624	0.005175	-0.057721	-0.030998	0.092328	-0.037219	0.047041	-0.021498	0.017040	0.054779	0.050213	-0.010503	-0.019435	-0.085342	-0.088063	0.093410	0.189701	0.079496	-0.018555	-0.088370
finding_lost_valuables	-0.083882	0.064315	0.039106	-0.054577	-0.009414	-0.041693	-0.002796	0.054491	0.021352	0.224468	0.153410	-0.083107	-0.019269	-0.088771	-0.051981	0.024098	-0.095219	-0.058622	-0.014578	-0.070334	-0.101028	0.119875	-0.216550	-0.011076	0.070842	-0.029371
getting_up	0.000541	-0.062969	-0.023216	0.179566	0.013130	0.089479	-0.032678	-0.030144	0.058364	0.091079	0.089504	0.037415	-0.124433	-0.106107	-0.020414	-0.013316	-0.021056	-0.077340	-0.095377	-0.050524	0.025894	-0.028352	0.033620	-0.015826	-0.108071	0.050240
interests_or_hobbies	0.018474	0.165435	-0.100833	0.004476	-0.094332	-0.000595	0.001005	-0.031463	-0.040574	0.067943	-0.027338	0.000527	0.146129	0.010156	-0.039760	-0.135162	0.079936	-0.086857	-0.053647	0.092706	-0.090394	0.021401	-0.005856	0.041006	-0.031184	-0.044264
parents_advice	-0.089722	0.052423	-0.005522	-0.078117	0.074169	-0.036696	0.016512	0.046795	0.003819	0.114296	0.050651	0.017639	-0.064503	0.056339	0.009183	-0.088305	-0.108447	-0.019891	0.072510	0.135266	-0.017076	-0.028318	0.057775	0.197510	0.037054	-0.068245
questionnaires_or_polls	-0.084802	0.024257	0.051384	-0.042252	0.021964	0.039035	0.053708	0.058078	0.099669	0.010506	-0.078278	-0.019607	0.096372	0.107544	0.000226	0.101985	0.077354	-0.047518	0.024367	-0.045314	-0.116342	0.034843	0.188765	0.158721	0.050247	-0.044797
internet_usage	0.071376	-0.042034	0.036902	0.108590	0.107507	0.017923	-0.027809	0.039586	0.110142	-0.058718	0.048619	0.093541	0.017175	0.024220	-0.070682	0.060110	0.174279	-0.005421	-0.010337	0.037141	-0.062799	0.065528	-0.022917	-0.045438	0.067719	-0.016844
finances	-0.058493	0.033240	0.081456	-0.179973	0.044576	0.013098	-0.011235	0.108839	0.055468	0.040218	-0.038836	-0.026978	0.013914	0.087123	-0.034158	0.060518	-0.075843	0.056315	0.007592	0.051898	-0.038258	-0.001933	0.038497	0.026660	0.002654	0.083168
shopping_centres	-0.095275	-0.016117	-0.186225	0.020919	0.087399	0.014203	0.091797	0.041655	0.069997	-0.024129	0.119933	-0.126206	0.117508	0.040521	-0.000313	0.099391	0.017962	0.151921	0.012744	-0.042460	-0.000450	0.049654	-0.035927	0.122969	0.009241	0.055475
branded_clothing	0.050980	0.023870	-0.167171	0.037356	0.102311	-0.072160	0.102639	-0.022128	-0.023504	0.058755	0.168443	-0.071428	0.002216	-0.054733	0.085430	0.046082	-0.077261	0.131949	-0.065133	-0.049483	-0.018372	-0.048418	-0.025456	-0.085911	-0.009778	0.011235
entertainment_spending	0.077017	0.040465	-0.149184	0.158651	-0.012159	-0.025171	0.025752	-0.037931	-0.076307	0.084439	0.156742	0.093928	-0.056976	-0.132646	-0.013114	0.060572	0.036816	0.075846	-0.003484	-0.102696	0.040151	0.012592	0.018294	-0.054288	-0.064669	-0.010455
spending_on_looks	-0.055802	0.001717	-0.224454	0.088474	0.087763	-0.060706	0.107111	0.007669	-0.034538	0.015058	0.114955	-0.006375	0.029099	-0.068871	0.009486	0.023977	-0.011072	0.167343	0.012914	-0.070139	-0.051148	-0.042134	0.041929	0.059541	-0.038214	-0.082515
spending_on_gadgets	0.101900	0.055546	-0.115360	0.046882	0.144027	0.033998	0.072243	0.057927	0.008825	0.065274	0.094811	-0.004151	0.082603	-0.183676	-0.021004	0.021398	0.033326	0.087038	-0.007399	-0.002742	0.033250	0.065626	-0.094706	-0.114980	0.013666	-0.122094
spending_on_healthy_eating	-0.019620	0.101095	-0.067341	-0.003088	0.030177	-0.041579	0.056091	0.146906	-0.109677	0.077139	0.103585	0.015484	0.019457	-0.092563	0.027300	0.001969	-0.057742	0.011242	-0.157231	-0.056992	-0.058219	0.093353	-0.022837	0.046833	0.210975	-0.163543
age	0.014257	0.073462	0.027129	-0.087414	0.054243	-0.165090	-0.177390	-0.067802	-0.097847	-0.149945	-0.066363	0.005597	-0.214226	-0.192610	-0.082757	-0.013675	0.134014	0.067128	0.079114	0.028383	0.027025	0.010428	-0.093110	0.008513	0.199966	-0.043595
height	0.202388	0.042468	0.008923	-0.036246	0.098996	-0.017777	-0.028748	-0.065092	-0.039843	0.041926	0.054900	0.035312	-0.023341	-0.091973	0.101339	0.022355	0.140314	-0.041062	-0.067272	-0.021022	-0.025791	-0.053657	-0.047408	0.061138	0.040682	-0.072562
weight	0.185076	0.057012	0.019143	-0.032910	0.105939	-0.018868	-0.032832	-0.085437	-0.047018	-0.028510	0.009172	0.024402	-0.025782	-0.151870	0.123971	0.026560	0.135933	-0.022147	0.043005	-0.044908	-0.043868	-0.042475	-0.089327	0.102651	0.050357	-0.098623
number_of_siblings	-0.008826	0.046878	0.018067	-0.026192	-0.002494	0.024864	-0.059993	-0.213643	0.015988	0.069661	0.039639	0.055545	-0.060988	0.099011	-0.137062	-0.206557	0.066736	0.146140	0.031972	0.055681	0.161151	0.120666	0.194598	-0.115677	0.023433	-0.062071
gender	0.246452	0.059884	0.018638	-0.057673	0.111474	0.000317	-0.042277	-0.095104	-0.021150	0.048414	0.067304	0.018335	0.002599	-0.034832	0.091548	0.006295	0.062655	-0.006104	-0.012162	-0.015493	-0.047300	-0.057658	-0.020490	0.079074	-0.013403	-0.011872
left_right_handed	0.000262	-0.022776	-0.010819	0.042825	-0.026399	0.026879	-0.033841	0.038329	-0.009732	0.010193	0.010454	0.111765	-0.001687	0.005688	-0.048538	0.091380	-0.079049	0.035836	-0.004340	0.066464	-0.026960	-0.081674	-0.193906	-0.110399	0.162530	0.183025
education	-0.008662	0.076290	0.018732	-0.049004	0.025402	-0.158966	-0.150693	-0.091784	-0.076057	-0.145296	0.012853	-0.000475	-0.179442	-0.177896	-0.081236	0.029223	0.064694	0.079353	0.111319	0.003673	-0.032577	0.043356	-0.069641	-0.003449	0.227758	0.005562
only_child	0.003235	-0.011714	-0.032285	0.035190	-0.015611	-0.036197	0.084600	0.126879	0.020687	-0.076076	0.005570	-0.085630	0.126860	-0.071333	0.061377	0.195940	-0.108041	-0.167021	-0.029624	-0.096777	-0.058270	-0.146206	-0.252946	0.103619	-0.114297	0.012413
village_town	-0.023184	0.008442	0.022041	-0.054650	-0.004329	0.108822	-0.015766	-0.200693	-0.079070	0.096661	-0.085243	-0.000530	0.053468	0.202991	0.152397	0.216037	0.088037	0.158134	0.011192	-0.050556	0.286365	0.039635	-0.118518	0.043189	0.057346	0.055013
house_block_of_flats	0.025404	-0.012947	-0.001839	0.038915	0.002587	-0.094321	-0.000475	0.211134	0.099709	-0.084540	0.053462	0.078336	-0.067014	-0.130270	-0.171438	-0.229704	-0.012618	-0.172858	-0.031293	0.043306	-0.263602	-0.107757	0.151872	-0.079285	-0.030856	-0.004563

Valores Singulares

Veamos primero un poco de como quedo nuestro modelo de componentes principales.

plot(pca$x[, 1], pca$x[, 2], main = "PCA", xlab = "PC1", ylab = "PC2")

Ahora veamos la descompisición en valores singulares de nuestros datos:

svd <- svd(scale(datos))
summary(svd)

##   Length Class  Mode   
## d    150 -none- numeric
## u 101100 -none- numeric
## v  22500 -none- numeric

Ahora, ¿por qué escalamos nuestros datos? Porque aplicar PCA es lo mismo que aplicar SVD a los datos escalados. Esto es que las columnas de la matriz U en la descomposición corresponden a los componentes principales en nuestro PCA. Aquí podemos ver que la dispersión de los datos es la misma.

plot(svd$u[, 1], svd$u[, 2], main = "SVD", xlab = "U1", ylab = "U2")

Y veamos la diferencia entre nuestros componentes principales y nuestras columnas en la matriz U.

dif <- svd$v[,1:26] - pca$rotation[,1:26]
summary(dif)

##       PC1         PC2         PC3         PC4         PC5         PC6   
##  Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0  
##  1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0  
##  Median :0   Median :0   Median :0   Median :0   Median :0   Median :0  
##  Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0  
##  3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0  
##  Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0  
##       PC7         PC8         PC9         PC10        PC11        PC12  
##  Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0  
##  1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0  
##  Median :0   Median :0   Median :0   Median :0   Median :0   Median :0  
##  Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0  
##  3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0  
##  Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0  
##       PC13        PC14        PC15        PC16        PC17        PC18  
##  Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0  
##  1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0  
##  Median :0   Median :0   Median :0   Median :0   Median :0   Median :0  
##  Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0  
##  3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0  
##  Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0  
##       PC19        PC20        PC21        PC22        PC23        PC24  
##  Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0   Min.   :0  
##  1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0   1st Qu.:0  
##  Median :0   Median :0   Median :0   Median :0   Median :0   Median :0  
##  Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0   Mean   :0  
##  3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0  
##  Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0   Max.   :0  
##       PC25        PC26  
##  Min.   :0   Min.   :0  
##  1st Qu.:0   1st Qu.:0  
##  Median :0   Median :0  
##  Mean   :0   Mean   :0  
##  3rd Qu.:0   3rd Qu.:0  
##  Max.   :0   Max.   :0

Esto nos lleva a concluir que al menos en este punto no hay diferencias entre estos métodos.

Las diferencias llegarían a ocurrir cuando realizamos rotaciones sobre nuestros componentes principales ya que nuestros vectores se moveran pero la descompisición de valores singulares serán las mismas, es decir podemos mejorar solo el modelo de PCA ya que si podemos rotar los componentes de nuestro modelo.

Reducción de Dimensiones

Luis Alberto Abaunza Guevara

02/12/2020

PCA

Datos

Componentes Principales

Valores Singulares