Aplicaciones de Cadenas de Markov

Google Page Rank

library(igraph)
sites_edges <- 
  c("A","B",
  "B","A",
  "B","C",
  "C","A",
  "C","B",
  "C","E",
  "D","A",
  "E","D",
  "E","C",
  "E","B")
net_sites <- graph(sites_edges)
plot(net_sites, layout=layout.circle)

	A	B	C	D	E
A	0	1	0	0	0
B	1	0	1	0	0
C	1	1	0	0	1
D	1	0	0	0	0
E	0	1	1	1	0

m<-
c(0,1,0,0,0,
  1,0,1,0,0,
  1,1,0,0,1,
  1,0,0,0,0,
  0,1,1,1,0)
m <- matrix(m,ncol = 5,byrow = TRUE)
colnames(m)<-c("A","B","C","D","E")
rownames(m)<-c("A","B","C","D","E")
print(m)

  A B C D E
A 0 1 0 0 0
B 1 0 1 0 0
C 1 1 0 0 1
D 1 0 0 0 0
E 0 1 1 1 0

m<-
m/rowSums(m)
print(m)

          A         B         C         D         E
A 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000
B 0.5000000 0.0000000 0.5000000 0.0000000 0.0000000
C 0.3333333 0.3333333 0.0000000 0.0000000 0.3333333
D 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000
E 0.0000000 0.3333333 0.3333333 0.3333333 0.0000000

p<-m
for(i in 1:1000){
  p<-m%*%p
}
print(p)

          A         B         C          D          E
A 0.2926829 0.3902439 0.2195122 0.02439024 0.07317073
B 0.2926829 0.3902439 0.2195122 0.02439024 0.07317073
C 0.2926829 0.3902439 0.2195122 0.02439024 0.07317073
D 0.2926829 0.3902439 0.2195122 0.02439024 0.07317073
E 0.2926829 0.3902439 0.2195122 0.02439024 0.07317073

B, A, C, E, D

EL Quijote

library(tm)
library(dplyr)
library(tidyr)
library(igraph)

Cargar el libro

libro <- file("borges1.txt")
#libro2 <- file("biblia.txt")
libro_lines <- readLines(libro)
#libro_lines2 <- readLines(libro2)
libro_words <- paste(libro_lines,collapse = " ")
libro_words <- strsplit(libro_words, split = " ") %>% unlist()
#libro_words_2 <- paste(libro_lines2,collapse = " ")
#libro_words_2 <- strsplit(libro_words_2, split = " ") %>% unlist()
#libro_words <- c(libro_words,libro_words_2)
str(libro_words)

 chr [1:3581] "CENTENARIO" "DE" "BORGES" "" "" "\"Mi" "entraÒable" "seÒor" ...

palabras unicas

length(unique(libro_words))

[1] 1133

table(libro_words) %>% as.data.frame()

Filtros

libro_words <- sapply(libro_words,"removePunctuation",USE.NAMES = FALSE)
libro_words <- sapply(libro_words,"tolower",USE.NAMES = FALSE)
libro_words <- sapply(libro_words,"stripWhitespace",USE.NAMES = FALSE)
libro_words <- sapply(libro_words,"removeNumbers",USE.NAMES = FALSE)
# libro_words <- sapply(libro_words,"removeWords",words=stopwords('spanish'), USE.NAMES = FALSE)
libro_words <- libro_words[libro_words!=""]
libro_words <- libro_words[libro_words!=" "]

bigramas

bigrams<-
lapply(ngrams(libro_words,2), paste, collapse=" ") %>% unlist()
bigrams<-
table(bigrams) %>% as.data.frame()
bigrams <- bigrams %>% separate(bigrams,into=c("word1","word2"),sep=" ") 

muestra_words <- bigrams %>% filter(Freq>10)
libro_vertices<-
paste(muestra_words$word1,muestra_words$word2) %>% strsplit(" ") %>% unlist()
g1<-
graph(libro_vertices)
plot(g1,edge.arrow.size = 0.3,
     arrow.width = 0.1,
     vertex.size = 5,
     vertex.label.cex = 0.8)

next_word <- function(palabra){
  top_words<-
  bigrams %>% 
    filter(word1 == palabra) %>% 
    arrange(desc(Freq)) %>% 
    select(word2,Freq) 
  total <- sum(top_words$Freq)
  top_words$Freq<- top_words$Freq/total
  sample(top_words$word2,size = 1,prob = top_words$Freq) %>% return()
}
next_word("dulcinea")

[1] "del"

sentence <- function(seed="don",n=10){
  oracion <- seed
  for(i in 1:n){
    oracion <- c( oracion,next_word(oracion[i]) )
  }
  paste(oracion,collapse = " ") %>% return()
}
sentence("cervantes",n = 25)

[1] "cervantes lo amo a travès de don quijote creo que los repitiera profusamente entonces tambièn debe haber pensado en el prìncipe hamlet la noche scherezade empieza"

Tarea

1. Armar la cadena de markov para el Quijote.