SVD in una matrice termine documento non danno me valori che voglio

Question

Sto cercando di replicare un esempio, in un articolo intitolato "Introduzione alla LSA": An introduction to LSA

Nell'esempio che hanno il seguente termine-documento matrix:

e poi si applicano SVD e ottenere il seguente:

Cercando di replicare questo, ho scritto il seguente codice R:

library(lsa); library(tm) 

d1 = "Human machine interface for ABC computer applications" 
d2 = "A survey of user opinion of computer system response time" 
d3 = "The EPS user interface management system" 
d4 = "System and human system engineering testing of EPS" 
d5 <- "Relation of user perceived response time to error measurement" 
d6 <- "The generation of random, binary, ordered trees" 
d7 <- "The intersection graph of paths in trees" 
d8 <- "Graph minors IV: Widths of trees and well-quasi-ordering" 
d9 <- "Graph minors: A survey" 

# Words that appear in at least two of the titles 
D <- c(d1, d2, d3, d4, d5, d6, d7, d8, d9) 

corpus <- Corpus(VectorSource(D)) 

# Remove Punctuation 
corpus <- tm_map(corpus, removePunctuation) 

# tolower 
corpus <- tm_map(corpus, content_transformer(tolower)) 

# Stopword Removal 
corpus <- tm_map(corpus, function(x) removeWords(x, stopwords("english"))) 

# term document Matrix 
myMatrix <- TermDocumentMatrix(corpus) 

# Delete terms that only appear in a document 
rowTotals <- apply(myMatrix, 1, sum) 
myMatrix.new <- myMatrix[rowTotals > 1, ] 

# Correlation Matrix of terms 
cor(t(as.matrix(myMatrix.new))) 

# lsaSpace <- lsa(myMatrix.new) 
# myMatrix.reduced <- lsaSpace$tk %*% diag(lsaSpace$sk) %*% t(lsaSpace$dk) 

mySVD <- svd(myMatrix.new) 

ho ottenuto lo stesso termine matrice-documenti, e in realtà ottenuto lo stesso correlazioni:

> inspect(myMatrix.new) 
<<TermDocumentMatrix (terms: 12, documents: 9)>> 
Non-/sparse entries: 28/80 
Sparsity   : 74% 
Maximal term length: 9 
Weighting   : term frequency (tf) 

      Docs 
Terms  1 2 3 4 5 6 7 8 9 
    computer 1 1 0 0 0 0 0 0 0 
    eps  0 0 1 1 0 0 0 0 0 
    graph  0 0 0 0 0 0 1 1 1 
    human  1 0 0 1 0 0 0 0 0 
    interface 1 0 1 0 0 0 0 0 0 
    minors 0 0 0 0 0 0 0 1 1 
    response 0 1 0 0 1 0 0 0 0 
    survey 0 1 0 0 0 0 0 0 1 
    system 0 1 1 2 0 0 0 0 0 
    time  0 1 0 0 1 0 0 0 0 
    trees  0 0 0 0 0 1 1 1 0 
    user  0 1 1 0 1 0 0 0 0 
> cor(as.matrix(t(myMatrix.new))) 
      computer  eps  graph  human interface  minors 
computer 1.0000000 -0.2857143 -0.3779645 0.3571429 0.3571429 -0.2857143 
eps  -0.2857143 1.0000000 -0.3779645 0.3571429 0.3571429 -0.2857143 
graph  -0.3779645 -0.3779645 1.0000000 -0.3779645 -0.3779645 0.7559289 
human  0.3571429 0.3571429 -0.3779645 1.0000000 0.3571429 -0.2857143 
interface 0.3571429 0.3571429 -0.3779645 0.3571429 1.0000000 -0.2857143 
minors -0.2857143 -0.2857143 0.7559289 -0.2857143 -0.2857143 1.0000000 
response 0.3571429 -0.2857143 -0.3779645 -0.2857143 -0.2857143 -0.2857143 
survey  0.3571429 -0.2857143 0.1889822 -0.2857143 -0.2857143 0.3571429 
system  0.0433555 0.8237545 -0.4588315 0.4335550 0.0433555 -0.3468440 
time  0.3571429 -0.2857143 -0.3779645 -0.2857143 -0.2857143 -0.2857143 
trees  -0.3779645 -0.3779645 0.5000000 -0.3779645 -0.3779645 0.1889822 
user  0.1889822 0.1889822 -0.5000000 -0.3779645 0.1889822 -0.3779645 
      response  survey  system  time  trees  user 
computer 0.3571429 0.3571429 0.0433555 0.3571429 -0.3779645 0.1889822 
eps  -0.2857143 -0.2857143 0.8237545 -0.2857143 -0.3779645 0.1889822 
graph  -0.3779645 0.1889822 -0.4588315 -0.3779645 0.5000000 -0.5000000 
human  -0.2857143 -0.2857143 0.4335550 -0.2857143 -0.3779645 -0.3779645 
interface -0.2857143 -0.2857143 0.0433555 -0.2857143 -0.3779645 0.1889822 
minors -0.2857143 0.3571429 -0.3468440 -0.2857143 0.1889822 -0.3779645 
response 1.0000000 0.3571429 0.0433555 1.0000000 -0.3779645 0.7559289 
survey  0.3571429 1.0000000 0.0433555 0.3571429 -0.3779645 0.1889822 
system  0.0433555 0.0433555 1.0000000 0.0433555 -0.4588315 0.2294157 
time  1.0000000 0.3571429 0.0433555 1.0000000 -0.3779645 0.7559289 
trees  -0.3779645 -0.3779645 -0.4588315 -0.3779645 1.0000000 -0.5000000 
user  0.7559289 0.1889822 0.2294157 0.7559289 -0.5000000 1.0000000 

Tuttavia ho cercato di applicare SVD alla matrice, e gli unici valori uguali sono gli autovalori, non riesco a ottenere ciò che hanno ottenuto sulla carta.

> mySVD 
$d 
[1] 3.3408838 2.5417010 2.3539435 1.6445323 1.5048316 1.3063820 0.8459031 
[8] 0.5601344 0.3636768 

$u 
      [,1]  [,2]  [,3]   [,4]  [,5]  [,6] 
[1,] -0.24047023 -0.04315195 0.1644291 0.5949618181 -0.10675529 -0.25495513 
[2,] -0.30082816 0.14127047 -0.3303084 -0.1880919179 0.11478462 0.27215528 
[3,] -0.03613585 -0.62278523 -0.2230864 -0.0007000721 -0.06825294 0.11490895 
[4,] -0.22135078 0.11317962 -0.2889582 0.4147507404 -0.10627512 -0.34098332 
[5,] -0.19764540 0.07208778 -0.1350396 0.5522395837 0.28176894 0.49587801 
[6,] -0.03175633 -0.45050892 -0.1411152 0.0087294706 -0.30049511 0.27734340 
[7,] -0.26503747 -0.10715957 0.4259985 -0.0738121922 0.08031938 -0.16967639 
[8,] -0.20591786 -0.27364743 0.1775970 0.0323519366 -0.53715000 0.08094398 
[9,] -0.64448115 0.16730121 -0.3611482 -0.3334616013 -0.15895498 -0.20652259 
[10,] -0.26503747 -0.10715957 0.4259985 -0.0738121922 0.08031938 -0.16967639 
[11,] -0.01274618 -0.49016179 -0.2311202 -0.0248019985 0.59416952 -0.39212506 
[12,] -0.40359886 -0.05707026 0.3378035 -0.0991137295 0.33173372 0.38483192 
       [,7]   [,8]  [,9] 
[1,] -0.302240236 0.0623280150 -0.49244436 
[2,] 0.032994110 -0.0189980144 0.16533917 
[3,] 0.159575477 -0.6811254380 -0.23196123 
[4,] 0.522657771 -0.0604501376 0.40667751 
[5,] -0.070423441 -0.0099400372 0.10893027 
[6,] 0.339495286 0.6784178789 -0.18253498 
[7,] 0.282915727 -0.0161465472 0.05387469 
[8,] -0.466897525 -0.0362988295 0.57942611 
[9,] -0.165828575 0.0342720233 -0.27069629 
[10,] 0.282915727 -0.0161465472 0.05387469 
[11,] -0.288317461 0.2545679452 0.22542407 
[12,] 0.002872175 -0.0003905042 -0.

$v 
       [,1]  [,2]  [,3]  [,4]  [,5]   [,6] 
[1,] -0.197392802 0.05591352 -0.11026973 0.94978502 0.04567856 -7.659356e-02 
[2,] -0.605990269 -0.16559288 0.49732649 0.02864890 -0.20632728 -2.564752e-01 
[3,] -0.462917508 0.12731206 -0.20760595 -0.04160920 0.37833623 7.243996e-01 
[4,] -0.542114417 0.23175523 -0.56992145 -0.26771404 -0.20560471 -3.688609e-01 
[5,] -0.279469108 -0.10677472 0.50544991 -0.15003543 0.32719441 3.481305e-02 
[6,] -0.003815213 -0.19284794 -0.09818424 -0.01508149 0.39484121 -3.001611e-01 
[7,] -0.014631468 -0.43787488 -0.19295557 -0.01550719 0.34948535 -2.122014e-01 
[8,] -0.024136835 -0.61512190 -0.25290398 -0.01019901 0.14979847 9.743417e-05 
[9,] -0.081957368 -0.52993707 -0.07927315 0.02455491 -0.60199299 3.622190e-01 
      [,7]   [,8]  [,9] 
[1,] 0.17731830 -0.014393259 0.06369229 
[2,] -0.43298424 0.049305326 -0.24278290 
[3,] -0.23688970 0.008825502 -0.02407687 
[4,] 0.26479952 -0.019466944 0.08420690 
[5,] 0.67230353 -0.058349563 0.26237588 
[6,] -0.34083983 0.454476523 0.61984719 
[7,] -0.15219472 -0.761527011 -0.01797518 
[8,] 0.24914592 0.449642757 -0.51989050 
[9,] 0.03803419 -0.069637550 0.45350675 

Mi manca qualcosa?

migliori saluti

EDIT:

Si suppone nell'esempio, che la dimensione è ridotta e hanno eliminato i meno autovalori. Il mio problema è che le correlazioni ricevo dopo SVD sono diverso da quello dell'esempio:

Answer 1

sono riuscito a trovare il mio errore. Quando stavo ricostruendo la matrice, la trasposizione di M = U D V 'non era stata calcolata correttamente. Ora funziona, mi dispiace, è stato un mio errore ... Inoltre, stavo calcolando il cor tra i documenti, quando quello che volevo era tra i termini.

ho aggiunto le seguenti righe:

mySVD <- svd(myMatrix.new) 

Mp <- mySVD$u[, c(1,2)] %*% diag(mySVD$d)[c(1, 2), c(1, 2)] %*% t(mySVD$v[, c(1, 2)]) 

rownames(Mp) <- rownames(myMatrix.new) 
cor(t(Mp)) 

Answer 2

Proprio per il protocollo, installando sul vostro matrice myMatrix ho potuto pressi esattamente ricostruire l'esempio. L'unica differenza (possibile spiegabile?) È in alcuni segni opposti nella Figura 2 (ad esempio u[1,1] è -0.22 anziché 0.22 come in W[1,1] Figura 2). La matrice di correlazione è identica.

Si deve tuttavia ricordare che, contrariamente a quanto affermato nel documento (pagina 13), viene utilizzata la correlazione di Spearman, il risultato esatto è ottenuto utilizzando il metodo di correlazione (predefinito) Pearson.

Ecco il codice:

> # term document Matrix 
> myMatrix <- TermDocumentMatrix(corpus) 
> 
> ## reorder rows 
> myMatrix <- mm[match(c("human","interface","computer","user","system","response","time","eps","survey","trees","graph","minors"), rownames(mm)), ] 
> 
> # Delete terms that only appear in a document 
> rowTotals <- apply(myMatrix, 1, sum) 
> myMatrix.new <- myMatrix[rowTotals > 1, ] 
> 
> mySVD <- svd(myMatrix.new) 
> 
> ## Figure 1 
> myMatrix.new 
      Docs 
Terms  1 2 3 4 5 6 7 8 9 
    human  1 0 0 1 0 0 0 0 0 
    interface 1 0 1 0 0 0 0 0 0 
    computer 1 1 0 0 0 0 0 0 0 
    user  0 1 1 0 1 0 0 0 0 
    system 0 1 1 2 0 0 0 0 0 
    response 0 1 0 0 1 0 0 0 0 
    time  0 1 0 0 1 0 0 0 0 
    eps  0 0 1 1 0 0 0 0 0 
    survey 0 1 0 0 0 0 0 0 1 
    trees  0 0 0 0 0 1 1 1 0 
    graph  0 0 0 0 0 0 1 1 1 
    minors 0 0 0 0 0 0 0 1 1 
> 
> ## mySVD Figure 2 
> lapply(mySVD,round,2) 
$d 
[1] 3.34 2.54 2.35 1.64 1.50 1.31 0.85 0.56 0.36 

$u 
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] 
[1,] -0.22 -0.11 0.29 -0.41 -0.11 -0.34 -0.52 0.06 0.41 
[2,] -0.20 -0.07 0.14 -0.55 0.28 0.50 0.07 0.01 0.11 
[3,] -0.24 0.04 -0.16 -0.59 -0.11 -0.25 0.30 -0.06 -0.49 
[4,] -0.40 0.06 -0.34 0.10 0.33 0.38 0.00 0.00 -0.01 
[5,] -0.64 -0.17 0.36 0.33 -0.16 -0.21 0.17 -0.03 -0.27 
[6,] -0.27 0.11 -0.43 0.07 0.08 -0.17 -0.28 0.02 0.05 
[7,] -0.27 0.11 -0.43 0.07 0.08 -0.17 -0.28 0.02 0.05 
[8,] -0.30 -0.14 0.33 0.19 0.11 0.27 -0.03 0.02 0.17 
[9,] -0.21 0.27 -0.18 -0.03 -0.54 0.08 0.47 0.04 0.58 
[10,] -0.01 0.49 0.23 0.02 0.59 -0.39 0.29 -0.25 0.23 
[11,] -0.04 0.62 0.22 0.00 -0.07 0.11 -0.16 0.68 -0.23 
[12,] -0.03 0.45 0.14 -0.01 -0.30 0.28 -0.34 -0.68 -0.18 

$v 
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] 
[1,] -0.20 -0.06 0.11 -0.95 0.05 -0.08 -0.18 0.01 0.06 
[2,] -0.61 0.17 -0.50 -0.03 -0.21 -0.26 0.43 -0.05 -0.24 
[3,] -0.46 -0.13 0.21 0.04 0.38 0.72 0.24 -0.01 -0.02 
[4,] -0.54 -0.23 0.57 0.27 -0.21 -0.37 -0.26 0.02 0.08 
[5,] -0.28 0.11 -0.51 0.15 0.33 0.03 -0.67 0.06 0.26 
[6,] 0.00 0.19 0.10 0.02 0.39 -0.30 0.34 -0.45 0.62 
[7,] -0.01 0.44 0.19 0.02 0.35 -0.21 0.15 0.76 -0.02 
[8,] -0.02 0.62 0.25 0.01 0.15 0.00 -0.25 -0.45 -0.52 
[9,] -0.08 0.53 0.08 -0.02 -0.60 0.36 -0.04 0.07 0.45 

> 
> Mp <- mySVD$u[, c(1,2)] %*% diag(mySVD$d)[c(1, 2), c(1, 2)] %*% t(mySVD$v[, c(1, 2)]) 
> rownames(Mp) <- rownames(myMatrix.new) 
> 
> ## Figure 3 
> round(Mp,2) 
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] 
human  0.16 0.40 0.38 0.47 0.18 -0.05 -0.12 -0.16 -0.09 
interface 0.14 0.37 0.33 0.40 0.16 -0.03 -0.07 -0.10 -0.04 
computer 0.15 0.51 0.36 0.41 0.24 0.02 0.06 0.09 0.12 
user  0.26 0.84 0.61 0.70 0.39 0.03 0.08 0.12 0.19 
system  0.45 1.23 1.05 1.27 0.56 -0.07 -0.15 -0.21 -0.05 
response 0.16 0.58 0.38 0.42 0.28 0.06 0.13 0.19 0.22 
time  0.16 0.58 0.38 0.42 0.28 0.06 0.13 0.19 0.22 
eps  0.22 0.55 0.51 0.63 0.24 -0.07 -0.14 -0.20 -0.11 
survey  0.10 0.53 0.23 0.21 0.27 0.14 0.31 0.44 0.42 
trees  -0.06 0.23 -0.14 -0.27 0.14 0.24 0.55 0.77 0.66 
graph  -0.06 0.34 -0.15 -0.30 0.20 0.31 0.69 0.98 0.85 
minors -0.04 0.25 -0.10 -0.21 0.15 0.22 0.50 0.71 0.62 
> 
> cor(Mp["human",],Mp["minors",]) 
[1] -0.83 
> 
> cor(Mp["human",],Mp["user",]) 
[1] 0.94 
> 
> ## Figure 4 
> corMo <- cor(myMatrix.new) 
> corMo[upper.tri(corMo,diag=TRUE)] <- 0 
> corMo 
     1  2  3  4  5  6 7 8 9 
1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 
2 -0.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 
3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 
4 0.00 0.00 0.47 0.00 0.00 0.00 0.00 0.00 0 
5 -0.33 0.58 0.00 -0.31 0.00 0.00 0.00 0.00 0 
6 -0.17 -0.30 -0.21 -0.16 -0.17 0.00 0.00 0.00 0 
7 -0.26 -0.45 -0.32 -0.24 -0.26 0.67 0.00 0.00 0 
8 -0.33 -0.58 -0.41 -0.31 -0.33 0.52 0.77 0.00 0 
9 -0.33 -0.19 -0.41 -0.31 -0.33 -0.17 0.26 0.56 0 
> 
> corMp <- cor(Mp) 
> corMp[upper.tri(corMp,diag=TRUE)] <- 0 
> corMp 
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] 
[1,] 0.00 0.00 0.00 0.00 0.00 0 0 0 0 
[2,] 0.91 0.00 0.00 0.00 0.00 0 0 0 0 
[3,] 1.00 0.91 0.00 0.00 0.00 0 0 0 0 
[4,] 1.00 0.88 1.00 0.00 0.00 0 0 0 0 
[5,] 0.84 0.99 0.84 0.81 0.00 0 0 0 0 
[6,] -0.86 -0.57 -0.86 -0.89 -0.44 0 0 0 0 
[7,] -0.85 -0.56 -0.85 -0.88 -0.44 1 0 0 0 
[8,] -0.85 -0.56 -0.85 -0.88 -0.43 1 1 0 0 
[9,] -0.81 -0.50 -0.81 -0.84 -0.37 1 1 1 0 
>