SVD देना नहीं है मुझे महत्व देता है मैं चाहता हूँ

Question

मैं एक कागज "एलएसए के लिए एक परिचय" कहा जाता है में एक उदाहरण को दोहराने के लिए कोशिश कर रहा हूँ: An introduction to LSA

उदाहरण वे निम्नलिखित अवधि-दस्तावेज़ में मैट्रिक्स:

और फिर वे SVD लागू करते हैं और निम्नलिखित मिलती है:

इस दोहराने के लिए कोशिश कर रहा है, मैं निम्नलिखित आर कोड लिखा है:

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) 

मैं एक ही अवधि-दस्तावेज़ मैट्रिक्स हो गया, और वास्तव में एक ही सहसंबंध प्राप्त:

> 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 

हालांकि मैं SVD लागू करने की कोशिश मैट्रिक्स के लिए, और एकमात्र मूल्य जो बराबर हैं, वे हैं Iigenvalues, मैं कागज में जो मिला वह प्राप्त नहीं कर सकता।

> 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 

क्या मुझे कुछ याद आ रही है?

बेस्ट सादर

संपादित करें:

यह, उदाहरण में माना जाता है कि आयाम कम हो जाता है और वे कम eigenvalues ​​नष्ट कर दिया। मेरे समस्या यह है कि सह-संबंध रहा SVD के बाद मिलता है उदाहरण की तुलना में अलग हैं:

Answer 1

मैं अपनी गलती खोजने के लिए कामयाब रहे। जब मैं मैट्रिक्स का पुनर्निर्माण कर रहा था, तो एम = यू डी वी का स्थानांतरण सही ढंग से गणना नहीं किया गया था। अब यह काम करता है, क्षमा करें, यह मेरी गलती थी ... इसके अलावा, मैं दस्तावेजों के बीच कोर की गणना कर रहा था, जब मैं चाहता था कि शर्तों के बीच था। बस प्रोटोकॉल के लिए

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

, अपने मैट्रिक्स myMatrix पर स्थापित करने मैं पास करने में सक्षम बिल्कुल उदाहरण फिर से संगठित किया गया था:

मैं निम्नलिखित लाइनों गयी। केवल अंतर (संभव व्याख्यात्मक?) चित्रा 2 में कुछ विपरीत संकेतों में है (उदा। u[1,1]0.22 के बजाय चित्रा 2 में -0.22 है)। सहसंबंध मैट्रिक्स समान है।

हालांकि इसका उल्लेख किया जाना चाहिए कि पेपर (पी। 13) में दावा के विपरीत कि स्पीरमैन सहसंबंध का उपयोग किया जाता है, सटीक परिणाम (डिफ़ॉल्ट) पियरसन सहसंबंध विधि का उपयोग करके प्राप्त किया जाता है।

यहाँ कोड:

> # 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 
>