SVD in einem Begriff Dokument-Matrix geben Sie nicht mir Werte I

Question

möchte ich versuche, ein Beispiel in einem Papier zu replizieren namens „Eine Einführung in die LSA“: An introduction to LSA

Im Beispiel von ihnen folgende Begriff-Dokument haben Matrix:

und dann gelten sie SVD und erhalten folgendes:

dies zu replizieren Der Versuch, schrieb ich die folgende R-Code:

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) 

ich den gleichen Begriff-Dokument-Matrix bekam, und tatsächlich erhalten die gleichen Korrelationen:

> 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 

Allerdings habe ich versucht, SVD anzuwenden zu der Matrix, und die einzigen Werte, die gleich sind, sind die Eigenwerte, ich kann nicht bekommen, was sie in der Zeitung bekommen haben.

> 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 

Fehle ich etwas?

Mit freundlichen Grüßen

EDIT:

Es soll in diesem Beispiel, dass die Dimension reduziert wird und sie löschte die weniger Eigenwerte. Mein Problem ist, dass die Korrelationen ich nach SVD erhalten sind anders als die des Beispiels:

Answer 1

ich es geschafft, meinen Fehler zu finden. Als ich die Matrix rekonstruierte, wurde die Transponierte des M = U D V 'nicht korrekt berechnet. Jetzt funktioniert es, Entschuldigung, es war mein Fehler ... Außerdem war ich Computer Cor zwischen Dokumenten, als ich zwischen Begriffen wollte.

Ich habe die folgenden Zeilen:

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

Just for Protokoll, auf dem Matrix Einrichten myMatrix ich in der Nähe war in der Lage genau das Beispiel zu rekonstruieren. Der einzige Unterschied (möglicherweise erklärbar?) Besteht in einigen entgegengesetzten Zeichen in der 2 (z. B. ist -0.22 anstelle von 0.22 wie in der W[1,1] 2). Die Korrelationsmatrix ist identisch.

Es sollte jedoch erwähnt werden, dass entgegen der Behauptung in dem Papier (S. 13), dass die Spearman-Korrelation verwendet wird, das genaue Ergebnis unter Verwendung der (Standard) Pearson-Korrelationsmethode erhalten wird.

Hier den Code:

> # 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 
>