Chapter 5 Representation

5.1 Corpus-data.frame

library(stringr)
text <- c("我家狗兒最愛睡覺", 
          "我家貓兒最愛睡覺", 
          "所有貓兒天生就會跑", 
          "所有狗兒天生就會跑", 
          "所有鳥兒天生就會飛", 
          "我家狗兒老是汪汪叫", 
          "我家貓兒老是喵喵叫", 
          "我家鳥兒老是啾啾叫")

corpus.df <- data.frame(text) %>%
    mutate(doc_id = paste0("doc", 1:n()))

library(jiebaR)
# Sys.setlocale(category = "LC_ALL", locale = "zh_TW.UTF-8")
cutter <- worker()
segment_not <- c("喵喵", "啾啾", "汪汪", "老是", "就會")
new_user_word(cutter, segment_not)

## [1] TRUE

5.2 Doc-Term-Pair (unnested)

unnested.df <- corpus.df %>%
    mutate(word = purrr::map(text, function(x)segment(x, cutter))) %>%
    unnest(word)
unnested.df

## # A tibble: 38 × 3
##    text               doc_id word 
##    <chr>              <chr>  <chr>
##  1 我家狗兒最愛睡覺   doc1   我家 
##  2 我家狗兒最愛睡覺   doc1   狗兒 
##  3 我家狗兒最愛睡覺   doc1   最愛 
##  4 我家狗兒最愛睡覺   doc1   睡覺 
##  5 我家貓兒最愛睡覺   doc2   我家 
##  6 我家貓兒最愛睡覺   doc2   貓兒 
##  7 我家貓兒最愛睡覺   doc2   最愛 
##  8 我家貓兒最愛睡覺   doc2   睡覺 
##  9 所有貓兒天生就會跑 doc3   所有 
## 10 所有貓兒天生就會跑 doc3   貓兒 
## # … with 28 more rows

5.3 Doc-Term-Count (Term-Doc)

dtcount <- unnested.df %>%
    count(doc_id, word, sort = T)
dtcount

## # A tibble: 38 × 3
##    doc_id word      n
##    <chr>  <chr> <int>
##  1 doc1   狗兒      1
##  2 doc1   睡覺      1
##  3 doc1   我家      1
##  4 doc1   最愛      1
##  5 doc2   貓兒      1
##  6 doc2   睡覺      1
##  7 doc2   我家      1
##  8 doc2   最愛      1
##  9 doc3   就會      1
## 10 doc3   貓兒      1
## # … with 28 more rows

5.4 Doc-Doc-Count

ddcount <- unnested.df %>%
    widyr::pairwise_count(doc_id, word)
ddcount

## # A tibble: 36 × 3
##    item1 item2     n
##    <chr> <chr> <dbl>
##  1 doc2  doc1      3
##  2 doc4  doc1      1
##  3 doc6  doc1      2
##  4 doc7  doc1      1
##  5 doc8  doc1      1
##  6 doc1  doc2      3
##  7 doc3  doc2      1
##  8 doc6  doc2      1
##  9 doc7  doc2      2
## 10 doc8  doc2      1
## # … with 26 more rows

5.5 Term-Term-Count

5.5.1 Term-Term-Count-by-Collocation

library(widyr)
ttcount_collocate <- unnested.df %>%
    widyr::pairwise_count(word, doc_id)
ttcount_collocate

## # A tibble: 104 × 3
##    item1 item2     n
##    <chr> <chr> <dbl>
##  1 狗兒  我家      2
##  2 最愛  我家      2
##  3 睡覺  我家      2
##  4 貓兒  我家      2
##  5 鳥兒  我家      1
##  6 老是  我家      3
##  7 汪汪  我家      1
##  8 叫    我家      3
##  9 喵喵  我家      1
## 10 啾啾  我家      1
## # … with 94 more rows

5.5.2 Term-Term-Count-by-bigram

ttcount_bigram <- unnested.df %>%
  group_by(doc_id) %>%
  mutate(w2 = lead(word, 1)) %>%
  drop_na(w2) %>%
  ungroup() %>%
  rename(w1 = word) %>%
    bind_rows(data.frame(w1 = .$w2, w2 = .$w1)) %>%
  count(w1, w2)

ttcount_bigram

## # A tibble: 48 × 3
##    w1    w2        n
##    <chr> <chr> <int>
##  1 飛    就會      1
##  2 狗兒  老是      1
##  3 狗兒  所有      1
##  4 狗兒  天生      1
##  5 狗兒  我家      2
##  6 狗兒  最愛      1
##  7 叫    啾啾      1
##  8 叫    喵喵      1
##  9 叫    汪汪      1
## 10 啾啾  叫        1
## # … with 38 more rows

5.6 Pivot-wide-to-matrix

5.6.1 Doc-Term-Matrix-tidy

dtm_tidy <- unnested.df %>%
    count(doc_id, word, sort = T) %>%
    pivot_wider(names_from = word, values_from = n, values_fill=0) %>%
  as.data.frame() %>%
    `rownames<-`(.$doc_id) %>%
    select(-doc_id)

dtm_tidy

##      狗兒 睡覺 我家 最愛 貓兒 就會 跑 所有 天生 飛 鳥兒 叫 老是 汪汪 喵喵 啾啾
## doc1    1    1    1    1    0    0  0    0    0  0    0  0    0    0    0    0
## doc2    0    1    1    1    1    0  0    0    0  0    0  0    0    0    0    0
## doc3    0    0    0    0    1    1  1    1    1  0    0  0    0    0    0    0
## doc4    1    0    0    0    0    1  1    1    1  0    0  0    0    0    0    0
## doc5    0    0    0    0    0    1  0    1    1  1    1  0    0    0    0    0
## doc6    1    0    1    0    0    0  0    0    0  0    0  1    1    1    0    0
## doc7    0    0    1    0    1    0  0    0    0  0    0  1    1    0    1    0
## doc8    0    0    1    0    0    0  0    0    0  0    1  1    1    0    0    1

5.6.2 Term-Document-Matrix-tidy

tdm_tidy <- unnested.df %>%
    count(doc_id, word, sort = T) %>%
    pivot_wider(names_from = doc_id, values_from = n, values_fill=0) %>%
  as.data.frame() %>%
    `rownames<-`(.$word) %>%
    select(-word)

tdm_tidy

##      doc1 doc2 doc3 doc4 doc5 doc6 doc7 doc8
## 狗兒    1    0    0    1    0    1    0    0
## 睡覺    1    1    0    0    0    0    0    0
## 我家    1    1    0    0    0    1    1    1
## 最愛    1    1    0    0    0    0    0    0
## 貓兒    0    1    1    0    0    0    1    0
## 就會    0    0    1    1    1    0    0    0
## 跑      0    0    1    1    0    0    0    0
## 所有    0    0    1    1    1    0    0    0
## 天生    0    0    1    1    1    0    0    0
## 飛      0    0    0    0    1    0    0    0
## 鳥兒    0    0    0    0    1    0    0    1
## 叫      0    0    0    0    0    1    1    1
## 老是    0    0    0    0    0    1    1    1
## 汪汪    0    0    0    0    0    1    0    0
## 喵喵    0    0    0    0    0    0    1    0
## 啾啾    0    0    0    0    0    0    0    1

5.6.3 Term-Term-Matrix

affmatrix <- ttcount_bigram %>% 
  pivot_wider(names_from = w2, values_from = n, values_fill = 0) %>%
  as.data.frame() %>%
    `rownames<-`(.$w1) %>%
    select(-w1)

5.7 tidytext-to-matrix

5.7.1 sparse(ttm)

library(tidytext)

sparse_ttm <- ttcount_bigram %>% tidytext::cast_sparse(w1, w2, n)
sparse_ttm

## 16 x 16 sparse Matrix of class "dgCMatrix"
##                                     
## 飛   1 . . . . . . . . . . . . . . .
## 狗兒 . 1 1 1 2 1 . . . . . . . . . .
## 叫   . . . . . . 1 1 1 . . . . . . .
## 啾啾 . 1 . . . . . . . 1 . . . . . .
## 就會 . . . 3 . . . . . . 1 2 . . . .
## 老是 . . . . . . 1 1 1 . . . 1 1 1 .
## 貓兒 . 1 1 1 2 1 . . . . . . . . . .
## 喵喵 . 1 . . . . . . . 1 . . . . . .
## 鳥兒 . 1 1 1 1 . . . . . . . . . . .
## 跑   2 . . . . . . . . . . . . . . .
## 睡覺 . . . . . 2 . . . . . . . . . .
## 所有 . . . . . . . . . . . . 1 1 1 .
## 天生 3 . . . . . . . . . . . 1 1 1 .
## 汪汪 . 1 . . . . . . . 1 . . . . . .
## 我家 . . . . . . . . . . . . 2 2 1 .
## 最愛 . . . . . . . . . . . . 1 1 . 2

5.7.2 dfm

dfm <- dtcount %>% tidytext::cast_dfm(doc_id, word, n)
dfm

## Document-feature matrix of: 8 documents, 16 features (70.31% sparse) and 0 docvars.
##       features
## docs   狗兒 睡覺 我家 最愛 貓兒 就會 跑 所有 天生 飛
##   doc1    1    1    1    1    0    0  0    0    0  0
##   doc2    0    1    1    1    1    0  0    0    0  0
##   doc3    0    0    0    0    1    1  1    1    1  0
##   doc4    1    0    0    0    0    1  1    1    1  0
##   doc5    0    0    0    0    0    1  0    1    1  1
##   doc6    1    0    1    0    0    0  0    0    0  0
## [ reached max_ndoc ... 2 more documents, reached max_nfeat ... 6 more features ]

5.7.3 dtm

dtm <- dtcount %>% tidytext::cast_dtm(doc_id, word, n)
dtm

## <<DocumentTermMatrix (documents: 8, terms: 16)>>
## Non-/sparse entries: 38/90
## Sparsity           : 70%
## Maximal term length: 2
## Weighting          : term frequency (tf)

5.7.4 tdm

tdm <- dtcount %>% tidytext::cast_tdm(word, doc_id, n)
tdm

## <<TermDocumentMatrix (terms: 16, documents: 8)>>
## Non-/sparse entries: 38/90
## Sparsity           : 70%
## Maximal term length: 2
## Weighting          : term frequency (tf)

5.8 Dimension Reduction

5.8.1 t-SNE on tt affmatrix

library(tsne)
tsne.affmatrix <- tsne(affmatrix, initial_config = NULL, k = 2, initial_dims = 30, 
                perplexity = 30, max_iter = 100, min_cost = 0, 
                epoch_callback = NULL, whiten = TRUE, epoch=20)

tsne.affmatrix

##              [,1]         [,2]
##  [1,]  4044.60338 -1120.773071
##  [2,]  -417.11626    -2.205613
##  [3,]    68.37004  -162.536259
##  [4,]  -876.07763  -303.809531
##  [5,]   816.12469    80.945270
##  [6,]   179.72277 -1106.291095
##  [7,]    71.41320   113.856501
##  [8,]   459.65619   324.122512
##  [9,]  -185.79564   132.369942
## [10,]  -302.27383   323.814001
## [11,]   700.29004   430.481347
## [12,]  -155.88574   -96.485588
## [13,] -1307.67910   388.136321
## [14,] -1807.92033   916.104862
## [15,]  -564.02625   709.178072
## [16,]  -723.40554  -626.907671

th <- theme_minimal() + 
  theme(title = element_text(family = "Heiti TC Light"),
        text = element_text(family = "Heiti TC Light"))

as.data.frame(tsne.affmatrix) %>%
  bind_cols(data.frame(name = rownames(affmatrix))) %>%
  ggplot(aes(V1, V2, label = name)) +
  geom_jitter(alpha = 0.1, color = "blue") + 
  geom_text(aes(label = name, family = "Heiti TC Light"), hjust=0, vjust=0, size = 4, alpha = 0.5) + theme_minimal()

5.8.2 t-SNE on tdm-tidy

tsne.tdmtidy <- tsne(tdm_tidy, initial_config = NULL, k = 2, initial_dims = 30, 
                perplexity = 30, max_iter = 100, min_cost = 0, 
                epoch_callback = NULL, whiten = TRUE, epoch=20)

tsne.tdmtidy

##              [,1]        [,2]
##  [1,]  -825.62567 -1977.96920
##  [2,]  -346.67123   -58.96477
##  [3,]   379.01044  1031.72957
##  [4,]    68.29747    29.63452
##  [5,]  -157.22440   -24.72322
##  [6,]   -74.76254   120.51638
##  [7,]   -82.71670    38.15536
##  [8,]   -63.88097   290.88904
##  [9,] -1729.13674  -278.05684
## [10,]    11.19381   105.77365
## [11,]   183.48526   -57.28247
## [12,]   458.67312  -150.99357
## [13,]  2801.05086   209.39330
## [14,]   -32.68982   204.01391
## [15,]  -441.31498   347.92807
## [16,]  -147.68791   169.95625

as.data.frame(tsne.tdmtidy) %>%
  bind_cols(data.frame(name = rownames(tdm_tidy))) %>%
  ggplot(aes(V1, V2, label = name)) +
  geom_jitter(alpha = 0.1, color = "blue") + 
  geom_text(aes(label = name, family = "Heiti TC Light"), hjust=0, vjust=0, size = 4, alpha = 0.5) + theme_minimal()

5.8.3 SVD on affmatrix

m.svd <- svd(affmatrix)
# D <- diag(m.svd$d)
# m.svd$u %*% D %*% t(m.svd$v)    # X = U D V'

ds <- diag(1/m.svd$d[1:3])
u <- m.svd$u
v <- m.svd$v
us <- as.matrix(u[, 1:3])
vs <- as.matrix(v[, 1:3])

(m.ginv <- vs %*% ds %*% t(us))

##                [,1]         [,2]         [,3]          [,4]         [,5]
##  [1,]  0.0676430449  0.022609643 -0.020210631  0.0096326720 -0.064754623
##  [2,]  0.0071266593  0.043274547 -0.003180411  0.0075898145  0.028138277
##  [3,]  0.0046206466  0.036227350 -0.002062054  0.0062118429  0.025546618
##  [4,] -0.0122257597  0.063880346  0.005455984  0.0088035014  0.075189764
##  [5,]  0.0085420267  0.063341786 -0.003812046  0.0109099739  0.043981949
##  [6,]  0.0060040433  0.033308572 -0.002679422  0.0058966366  0.020890809
##  [7,] -0.0067368770 -0.003363332  0.004769961 -0.0014329227  0.009632672
##  [8,] -0.0067368770 -0.003363332  0.004769961 -0.0014329227  0.009632672
##  [9,] -0.0067368770 -0.003363332  0.004769961 -0.0014329227  0.009632672
## [10,]  0.0025060127  0.007047196 -0.001118357  0.0013779716  0.002591659
## [11,] -0.0056154688  0.009217665  0.002506013  0.0008638862  0.016547715
## [12,] -0.0112309375  0.018435331  0.005012025  0.0017277724  0.033095431
## [13,] -0.0086227159 -0.007894355  0.015008815 -0.0033633317  0.022609643
## [14,] -0.0086227159 -0.007894355  0.015008815 -0.0033633317  0.022609643
## [15,]  0.0007486387 -0.002815467  0.007380592 -0.0011995090  0.008063573
## [16,] -0.0082473702 -0.004192728  0.006026211 -0.0017862811  0.012008087
##               [,6]         [,7]          [,8]         [,9]        [,10]
##  [1,] -0.036707424  0.022609643  0.0096326720  0.008063573  0.135286090
##  [2,] -0.009044530  0.043274547  0.0075898145  0.028973997  0.014253319
##  [3,] -0.005864119  0.036227350  0.0062118429  0.024432861  0.009241293
##  [4,]  0.015515859  0.063880346  0.0088035014  0.045766724 -0.024451519
##  [5,] -0.010840789  0.063341786  0.0109099739  0.042658690  0.017084053
##  [6,] -0.007619804  0.033308572  0.0058966366  0.022233069  0.012008087
##  [7,]  0.017236035 -0.003363332 -0.0014329227 -0.001199509 -0.013473754
##  [8,]  0.017236035 -0.003363332 -0.0014329227 -0.001199509 -0.013473754
##  [9,]  0.017236035 -0.003363332 -0.0014329227 -0.001199509 -0.013473754
## [10,] -0.003180411  0.007047196  0.0013779716  0.004541136  0.005012025
## [11,]  0.007126659  0.009217665  0.0008638862  0.007111287 -0.011230938
## [12,]  0.014253319  0.018435331  0.0017277724  0.014222575 -0.022461875
## [13,]  0.065915990 -0.007894355 -0.0033633317 -0.002815467 -0.017245432
## [14,]  0.065915990 -0.007894355 -0.0033633317 -0.002815467 -0.017245432
## [15,]  0.037048911 -0.002815467 -0.0011995090 -0.001004117  0.001497277
## [16,]  0.022020491 -0.004192728 -0.0017862811 -0.001495308 -0.016494740
##              [,11]        [,12]        [,13]         [,14]        [,15]
##  [1,]  0.012008087 -0.016496793  0.186432342  0.0096326720 -0.033742225
##  [2,]  0.009995515 -0.005864119  0.015515859  0.0075898145 -0.010840789
##  [3,]  0.008197756 -0.003802065  0.010059875  0.0062118429 -0.007028743
##  [4,]  0.011880974  0.010059875 -0.026617404  0.0088035014  0.018597337
##  [5,]  0.014391892 -0.007028743  0.018597337  0.0109099739 -0.012993790
##  [6,]  0.007759114 -0.004940382  0.013071748  0.0058966366 -0.009133111
##  [7,] -0.001786281  0.012466074 -0.007744557 -0.0014329227  0.022471951
##  [8,] -0.001786281  0.012466074 -0.007744557 -0.0014329227  0.022471951
##  [9,] -0.001786281  0.012466074 -0.007744557 -0.0014329227  0.022471951
## [10,]  0.001797758 -0.002062054  0.005455984  0.0013779716 -0.003812046
## [11,]  0.001227739  0.004620647 -0.012225760  0.0008638862  0.008542027
## [12,]  0.002455478  0.009241293 -0.024451519  0.0017277724  0.017084053
## [13,] -0.004192728  0.050907175  0.025039027 -0.0033633317  0.090479861
## [14,] -0.004192728  0.050907175  0.025039027 -0.0033633317  0.090479861
## [15,] -0.001495308  0.029668319  0.031914235 -0.0011995090  0.052337297
## [16,] -0.002226778  0.015994280 -0.008747831 -0.0017862811  0.028805050
##              [,16]
##  [1,] -0.033740172
##  [2,] -0.007619804
##  [3,] -0.004940382
##  [4,]  0.013071748
##  [5,] -0.009133111
##  [6,] -0.006419506
##  [7,]  0.014023351
##  [8,]  0.014023351
##  [9,]  0.014023351
## [10,] -0.002679422
## [11,]  0.006004043
## [12,]  0.012008087
## [13,]  0.052383457
## [14,]  0.052383457
## [15,]  0.029035995
## [16,]  0.017889874

plot(m.svd$v, type="n")
text(m.svd$v[,1], m.svd$v[,2], labels=rownames(affmatrix), cex= 1.5, family="Heiti TC Light")

plot(m.ginv, type="n")
text(m.ginv[,1], m.ginv[,2], labels=rownames(affmatrix), cex= 1.5, family="Heiti TC Light")

5.8.4 SVD on sparse_ttm

m.svd <- svd(sparse_ttm)
D <- diag(m.svd$d)
m.svd$u %*% D %*% t(m.svd$v)    # X = U D V'

##                              [,1]                      [,2]
##  [1,]  0.999999999999999555910790  0.0000000000000002092989
##  [2,] -0.000000000000000006640738  1.0000000000000000000000
##  [3,]  0.000000000000000480465887 -0.0000000000000001559769
##  [4,] -0.000000000000000082592489  1.0000000000000006661338
##  [5,]  0.000000000000000529764898  0.0000000000000001179612
##  [6,]  0.000000000000001069733367 -0.0000000000000005041938
##  [7,] -0.000000000000000211554949  1.0000000000000004440892
##  [8,] -0.000000000000000041433464  1.0000000000000002220446
##  [9,]  0.000000000000000008727827  0.9999999999999993338662
## [10,]  1.999999999999999111821580  0.0000000000000005801119
## [11,] -0.000000000000000032038174  0.0000000000000003191891
## [12,]  0.000000000000000346299256 -0.0000000000000003973161
## [13,]  2.999999999999999111821580  0.0000000000000004094447
## [14,] -0.000000000000000041009947  1.0000000000000006661338
## [15,]  0.000000000000000634788514 -0.0000000000000007834445
## [16,]  0.000000000000000553963042  0.0000000000000000756231
##                             [,3]                       [,4]
##  [1,]  0.00000000000000005006675 -0.00000000000000026950293
##  [2,]  0.99999999999999922284388  1.00000000000000022204460
##  [3,] -0.00000000000000072148103 -0.00000000000000016944767
##  [4,] -0.00000000000000007230008  0.00000000000000084751778
##  [5,]  0.00000000000000002775558  3.00000000000000177635684
##  [6,] -0.00000000000000022589483 -0.00000000000000022737033
##  [7,]  0.99999999999999988897770  1.00000000000000044408921
##  [8,] -0.00000000000000011663425 -0.00000000000000007572407
##  [9,]  1.00000000000000044408921  1.00000000000000044408921
## [10,]  0.00000000000000012356633 -0.00000000000000002187772
## [11,] -0.00000000000000018041124 -0.00000000000000026714742
## [12,] -0.00000000000000028761292 -0.00000000000000055333830
## [13,]  0.00000000000000014303587 -0.00000000000000020374695
## [14,] -0.00000000000000030372714 -0.00000000000000017504883
## [15,] -0.00000000000000032829642  0.00000000000000027636313
## [16,]  0.00000000000000012007539 -0.00000000000000003459960
##                             [,5]                       [,6]
##  [1,]  0.00000000000000032200805 -0.00000000000000005891284
##  [2,]  1.99999999999999866773237  1.00000000000000044408921
##  [3,] -0.00000000000000025673907 -0.00000000000000031078655
##  [4,]  0.00000000000000038857806  0.00000000000000083201675
##  [5,] -0.00000000000000089858676  0.00000000000000015742616
##  [6,] -0.00000000000000015373987  0.00000000000000015924219
##  [7,]  1.99999999999999933386619  1.00000000000000111022302
##  [8,] -0.00000000000000010061396  0.00000000000000045883436
##  [9,]  1.00000000000000000000000  0.00000000000000139124823
## [10,] -0.00000000000000001669671  0.00000000000000043164799
## [11,] -0.00000000000000013877788  2.00000000000000044408921
## [12,] -0.00000000000000048745730 -0.00000000000000014219311
## [13,]  0.00000000000000033686161  0.00000000000000009049022
## [14,] -0.00000000000000022898350  0.00000000000000050328665
## [15,] -0.00000000000000057809660 -0.00000000000000030991919
## [16,]  0.00000000000000024313234 -0.00000000000000009893345
##                              [,7]                        [,8]
##  [1,]  0.000000000000000063874677  0.000000000000000105251203
##  [2,] -0.000000000000000458766335 -0.000000000000000171887894
##  [3,]  1.000000000000000666133815  1.000000000000000666133815
##  [4,]  0.000000000000000137101866  0.000000000000000354348143
##  [5,]  0.000000000000000696233978 -0.000000000000000422103623
##  [6,]  1.000000000000000444089210  1.000000000000000444089210
##  [7,] -0.000000000000000244880874 -0.000000000000000183405158
##  [8,] -0.000000000000000204046989  0.000000000000000178916221
##  [9,]  0.000000000000000007914676 -0.000000000000000001301043
## [10,]  0.000000000000000143292727  0.000000000000000232328321
## [11,] -0.000000000000000065770414  0.000000000000000250369387
## [12,] -0.000000000000000250180984 -0.000000000000000193279067
## [13,] -0.000000000000000122217938 -0.000000000000000114554162
## [14,]  0.000000000000000036424831  0.000000000000000035623292
## [15,] -0.000000000000000432902022 -0.000000000000000430913612
## [16,] -0.000000000000000101851794 -0.000000000000000104700737
##                             [,9]                       [,10]
##  [1,]  0.00000000000000011659400 -0.000000000000000024117152
##  [2,] -0.00000000000000001863379  0.000000000000000236513962
##  [3,]  1.00000000000000066613381 -0.000000000000000116808346
##  [4,]  0.00000000000000012097853  0.999999999999999888977698
##  [5,] -0.00000000000000051730674 -0.000000000000000324393290
##  [6,]  1.00000000000000044408921 -0.000000000000000069782848
##  [7,] -0.00000000000000004134969  0.000000000000000311658656
##  [8,] -0.00000000000000004738542  0.999999999999999666933093
##  [9,] -0.00000000000000005274644 -0.000000000000001165734176
## [10,]  0.00000000000000017252934  0.000000000000000183925351
## [11,] -0.00000000000000005622944  0.000000000000000499600361
## [12,] -0.00000000000000020524945 -0.000000000000000077564477
## [13,] -0.00000000000000010784220 -0.000000000000000009157259
## [14,] -0.00000000000000012919913  1.000000000000000000000000
## [15,] -0.00000000000000049166874  0.000000000000000053776428
## [16,] -0.00000000000000009885272  0.000000000000000047325425
##                             [,11]                      [,12]
##  [1,] -0.000000000000000075668047 -0.00000000000000015101083
##  [2,] -0.000000000000000092184878 -0.00000000000000016355308
##  [3,]  0.000000000000000086706612  0.00000000000000017384690
##  [4,]  0.000000000000000314442152  0.00000000000000058725094
##  [5,]  1.000000000000000222044605  2.00000000000000000000000
##  [6,]  0.000000000000000076032134  0.00000000000000015098007
##  [7,] -0.000000000000000171493090 -0.00000000000000032216950
##  [8,] -0.000000000000000084843291 -0.00000000000000021825884
##  [9,] -0.000000000000000166533454 -0.00000000000000026367797
## [10,] -0.000000000000000044764346 -0.00000000000000008866133
## [11,]  0.000000000000000138777878  0.00000000000000011102230
## [12,] -0.000000000000000162349841 -0.00000000000000032621757
## [13,] -0.000000000000000161124334 -0.00000000000000032246551
## [14,]  0.000000000000000007190893 -0.00000000000000002725158
## [15,]  0.000000000000000193313247  0.00000000000000038510861
## [16,] -0.000000000000000081518451 -0.00000000000000015870009
##                             [,13]                       [,14]
##  [1,] -0.000000000000000076598883 -0.000000000000000076598883
##  [2,] -0.000000000000000122298005 -0.000000000000000122298005
##  [3,] -0.000000000000000372763953 -0.000000000000000372763953
##  [4,] -0.000000000000000193868901 -0.000000000000000193868901
##  [5,] -0.000000000000000073319172 -0.000000000000000073319172
##  [6,]  0.999999999999999666933093  0.999999999999999666933093
##  [7,] -0.000000000000000005637851 -0.000000000000000005637851
##  [8,] -0.000000000000000164812283 -0.000000000000000164812283
##  [9,] -0.000000000000000081315163 -0.000000000000000081315163
## [10,] -0.000000000000000151185217 -0.000000000000000151185217
## [11,]  0.000000000000000013335687  0.000000000000000013335687
## [12,]  0.999999999999999888977698  0.999999999999999888977698
## [13,]  0.999999999999999444888488  0.999999999999999444888488
## [14,] -0.000000000000000166275956 -0.000000000000000166275956
## [15,]  1.999999999999999777955395  1.999999999999999777955395
## [16,]  0.999999999999999666933093  0.999999999999999666933093
##                            [,15]                      [,16]
##  [1,] -0.00000000000000006555696  0.00000000000000015492910
##  [2,] -0.00000000000000031268391 -0.00000000000000020762472
##  [3,]  0.00000000000000004751516  0.00000000000000105667191
##  [4,] -0.00000000000000026096746 -0.00000000000000028721871
##  [5,] -0.00000000000000011053441 -0.00000000000000047723869
##  [6,]  1.00000000000000066613381  0.00000000000000014451060
##  [7,] -0.00000000000000027018318 -0.00000000000000002461139
##  [8,] -0.00000000000000026893635 -0.00000000000000009070706
##  [9,] -0.00000000000000034867942 -0.00000000000000047574791
## [10,] -0.00000000000000012317553  0.00000000000000021057578
## [11,]  0.00000000000000005399327 -0.00000000000000007795414
## [12,]  1.00000000000000022204460 -0.00000000000000021078584
## [13,]  0.99999999999999966693309 -0.00000000000000007719604
## [14,] -0.00000000000000026579216 -0.00000000000000009845911
## [15,]  0.99999999999999977795540 -0.00000000000000109902186
## [16,] -0.00000000000000041053569  2.00000000000000088817842

plot(m.svd$v, type="n")
text(m.svd$v[,1], m.svd$v[,2], labels=rownames(affmatrix), cex= 1.5, family="Heiti TC Light")

5.8.5 SVD on tdm

m.svd <- svd(tdm)
D <- diag(m.svd$d)
m.svd$u %*% D %*% t(m.svd$v)    # X = U D V'

##                             [,1]                        [,2]
##  [1,]  1.00000000000000000000000  0.000000000000000592819477
##  [2,]  1.00000000000000000000000  1.000000000000001776356839
##  [3,]  1.00000000000000000000000  1.000000000000000444089210
##  [4,]  1.00000000000000022204460  1.000000000000001776356839
##  [5,] -0.00000000000000032914151  1.000000000000000666133815
##  [6,]  0.00000000000000029028033  0.000000000000000212355793
##  [7,]  0.00000000000000014990836  0.000000000000000371376041
##  [8,]  0.00000000000000015774063  0.000000000000000071784974
##  [9,]  0.00000000000000016088481  0.000000000000000074929160
## [10,]  0.00000000000000015134590 -0.000000000000000163488965
## [11,]  0.00000000000000019775104 -0.000000000000000751344666
## [12,] -0.00000000000000015410978 -0.000000000000001068633099
## [13,] -0.00000000000000015410978 -0.000000000000001068633099
## [14,]  0.00000000000000005382522 -0.000000000000000359136552
## [15,] -0.00000000000000039026399  0.000000000000000001685931
## [16,]  0.00000000000000005974082 -0.000000000000000630464846
##                            [,3]                      [,4]
##  [1,] -0.0000000000000010785420  0.9999999999999970023978
##  [2,]  0.0000000000000021728830  0.0000000000000002635362
##  [3,]  0.0000000000000006571139  0.0000000000000008460240
##  [4,]  0.0000000000000022448286  0.0000000000000004188393
##  [5,]  0.9999999999999995559108 -0.0000000000000008504705
##  [6,]  0.9999999999999998889777  0.9999999999999988897770
##  [7,]  0.9999999999999984456878  0.9999999999999972244424
##  [8,]  0.9999999999999998889777  0.9999999999999986677324
##  [9,]  0.9999999999999998889777  0.9999999999999988897770
## [10,]  0.0000000000000015437513  0.0000000000000017591622
## [11,]  0.0000000000000019909183  0.0000000000000032826411
## [12,] -0.0000000000000018686443  0.0000000000000001714342
## [13,] -0.0000000000000018686443  0.0000000000000001714342
## [14,] -0.0000000000000015837537 -0.0000000000000006922035
## [15,] -0.0000000000000007510865 -0.0000000000000008587369
## [16,]  0.0000000000000004090031  0.0000000000000015061316
##                            [,5]                       [,6]
##  [1,]  0.0000000000000029369591  1.00000000000000066613381
##  [2,] -0.0000000000000024598379 -0.00000000000000247536622
##  [3,] -0.0000000000000009801188  0.99999999999999922284388
##  [4,] -0.0000000000000023019781 -0.00000000000000262018853
##  [5,]  0.0000000000000007718797  0.00000000000000045796700
##  [6,]  0.9999999999999993338662  0.00000000000000015041248
##  [7,]  0.0000000000000029976022  0.00000000000000162627674
##  [8,]  0.9999999999999993338662 -0.00000000000000005267170
##  [9,]  0.9999999999999993338662 -0.00000000000000003879391
## [10,]  0.9999999999999964472863 -0.00000000000000160746590
## [11,]  0.9999999999999938937734 -0.00000000000000242782146
## [12,]  0.0000000000000008521829  1.00000000000000177635684
## [13,]  0.0000000000000008521829  1.00000000000000177635684
## [14,]  0.0000000000000022742225  1.00000000000000177635684
## [15,]  0.0000000000000010564466  0.00000000000000044408921
## [16,] -0.0000000000000024424907 -0.00000000000000076831385
##                             [,7]                      [,8]
##  [1,]  0.00000000000000283106871 -0.0000000000000038932126
##  [2,]  0.00000000000000000858944  0.0000000000000022412627
##  [3,]  0.99999999999999988897770  1.0000000000000011102230
##  [4,] -0.00000000000000027853439  0.0000000000000021736085
##  [5,]  1.00000000000000044408921 -0.0000000000000018105582
##  [6,] -0.00000000000000019551529 -0.0000000000000001110223
##  [7,]  0.00000000000000192643694 -0.0000000000000032196468
##  [8,] -0.00000000000000006875894  0.0000000000000001457168
##  [9,] -0.00000000000000005488115  0.0000000000000001040834
## [10,] -0.00000000000000219504795  0.0000000000000034972025
## [11,] -0.00000000000000413637218  1.0000000000000062172489
## [12,]  0.99999999999999922284388  0.9999999999999987787547
## [13,]  0.99999999999999922284388  0.9999999999999987787547
## [14,]  0.00000000000000049960036 -0.0000000000000024633073
## [15,]  1.00000000000000066613381 -0.0000000000000015612511
## [16,] -0.00000000000000200724371  1.0000000000000026645353

plot(m.svd$v, type="n")
text(m.svd$v[,1], m.svd$v[,2], labels=rownames(tdm), cex= 1.5, family="Heiti TC Light")

5.8.6 SVD on dtm

m.svd <- svd(dtm)
D <- diag(m.svd$d)
m.svd$u %*% D %*% t(m.svd$v)    # X = U D V'

##                           [,1]                      [,2]
## [1,]  0.9999999999999991118216  0.9999999999999991118216
## [2,] -0.0000000000000017195258  0.9999999999999997779554
## [3,] -0.0000000000000005147980  0.0000000000000009124790
## [4,]  1.0000000000000002220446  0.0000000000000004232581
## [5,]  0.0000000000000002692221 -0.0000000000000011136925
## [6,]  1.0000000000000002220446 -0.0000000000000012727898
## [7,] -0.0000000000000001110223 -0.0000000000000010916383
## [8,] -0.0000000000000017932708  0.0000000000000017815610
##                            [,3]                      [,4]
## [1,] 0.999999999999998778754673  0.9999999999999991118216
## [2,] 0.999999999999999555910790  0.9999999999999992228439
## [3,] 0.000000000000000796602672 -0.0000000000000001446946
## [4,] 0.000000000000000005706935 -0.0000000000000007244019
## [5,] 0.000000000000000562050406  0.0000000000000012403273
## [6,] 0.999999999999999222843883 -0.0000000000000002914234
## [7,] 0.999999999999999444888488  0.0000000000000002168302
## [8,] 0.999999999999999222843883 -0.0000000000000004059253
##                            [,5]                        [,6]
## [1,] -0.00000000000000005683104  0.000000000000000003059455
## [2,]  1.00000000000000044408921 -0.000000000000000078953607
## [3,]  1.00000000000000000000000  0.999999999999999111821580
## [4,] -0.00000000000000088685853  1.000000000000000000000000
## [5,]  0.00000000000000154529868  0.999999999999999444888488
## [6,] -0.00000000000000065225603 -0.000000000000000143104620
## [7,]  1.00000000000000088817842  0.000000000000000306168627
## [8,] -0.00000000000000060758652  0.000000000000000312250226
##                             [,7]                       [,8]
## [1,] -0.000000000000000004991662 -0.00000000000000007513064
## [2,] -0.000000000000000533639978 -0.00000000000000016382752
## [3,]  0.999999999999999777955395  0.99999999999999922284388
## [4,]  1.000000000000000666133815  0.99999999999999966693309
## [5,] -0.000000000000000555111512  0.99999999999999944488849
## [6,] -0.000000000000000272189271 -0.00000000000000034562538
## [7,]  0.000000000000000299944847  0.00000000000000020337806
## [8,]  0.000000000000000277555756  0.00000000000000050653925
##                            [,9]                      [,10]
## [1,] -0.00000000000000008651476 -0.00000000000000003464917
## [2,] -0.00000000000000016827275  0.00000000000000038072651
## [3,]  0.99999999999999911182158 -0.00000000000000051235395
## [4,]  0.99999999999999955591079 -0.00000000000000051460235
## [5,]  0.99999999999999955591079  1.00000000000000044408921
## [6,] -0.00000000000000037338096 -0.00000000000000009568422
## [7,]  0.00000000000000023807253 -0.00000000000000007084923
## [8,]  0.00000000000000035388359  0.00000000000000005551115
##                          [,11]                      [,12]
## [1,] -0.0000000000000001435317 -0.00000000000000023427092
## [2,]  0.0000000000000005508665 -0.00000000000000002294249
## [3,] -0.0000000000000005479873  0.00000000000000064738155
## [4,] -0.0000000000000007877497  0.00000000000000029934379
## [5,]  1.0000000000000006661338 -0.00000000000000062840358
## [6,] -0.0000000000000002713383  0.99999999999999966693309
## [7,] -0.0000000000000002525482  0.99999999999999900079928
## [8,]  0.9999999999999996669331  0.99999999999999933386619
##                           [,13]                      [,14]
## [1,] -0.00000000000000023427092  0.00000000000000004181150
## [2,] -0.00000000000000002294249 -0.00000000000000018058938
## [3,]  0.00000000000000064738155  0.00000000000000006956708
## [4,]  0.00000000000000029934379  0.00000000000000015247753
## [5,] -0.00000000000000062840358 -0.00000000000000043021142
## [6,]  0.99999999999999966693309  1.00000000000000000000000
## [7,]  0.99999999999999900079928 -0.00000000000000049960036
## [8,]  0.99999999999999933386619  0.00000000000000021163626
##                           [,15]                      [,16]
## [1,] -0.00000000000000026349983 -0.00000000000000016385158
## [2,] -0.00000000000000006956708  0.00000000000000018380090
## [3,]  0.00000000000000048590071 -0.00000000000000003216395
## [4,]  0.00000000000000034676656 -0.00000000000000030090296
## [5,] -0.00000000000000043021142  0.00000000000000027755576
## [6,] -0.00000000000000038857806 -0.00000000000000010973454
## [7,]  0.99999999999999977795540 -0.00000000000000016782121
## [8,] -0.00000000000000051694760  0.99999999999999977795540

plot(m.svd$v, type="n")
text(m.svd$v[,1], m.svd$v[,2], labels=rownames(dtm), cex= 1.5, family="Heiti TC Light")

5.8.7 Viz Dim Reduction

affmatrix %>%
  rownames_to_column(var = "w1") %>%
  pivot_longer(names_to = "w2", values_to = "n", -w1) %>%
  ggplot() + aes(w1, w2, fill=n) +
  geom_tile() + th

m.svd <- svd(affmatrix)
ds <- diag(1/m.svd$d[1:3])
u <- m.svd$u
v <- m.svd$v
us <- as.matrix(u[, 1:3])
vs <- as.matrix(v[, 1:3])

(m.ginv <- vs %*% ds %*% t(us))

##                [,1]         [,2]         [,3]          [,4]         [,5]
##  [1,]  0.0676430449  0.022609643 -0.020210631  0.0096326720 -0.064754623
##  [2,]  0.0071266593  0.043274547 -0.003180411  0.0075898145  0.028138277
##  [3,]  0.0046206466  0.036227350 -0.002062054  0.0062118429  0.025546618
##  [4,] -0.0122257597  0.063880346  0.005455984  0.0088035014  0.075189764
##  [5,]  0.0085420267  0.063341786 -0.003812046  0.0109099739  0.043981949
##  [6,]  0.0060040433  0.033308572 -0.002679422  0.0058966366  0.020890809
##  [7,] -0.0067368770 -0.003363332  0.004769961 -0.0014329227  0.009632672
##  [8,] -0.0067368770 -0.003363332  0.004769961 -0.0014329227  0.009632672
##  [9,] -0.0067368770 -0.003363332  0.004769961 -0.0014329227  0.009632672
## [10,]  0.0025060127  0.007047196 -0.001118357  0.0013779716  0.002591659
## [11,] -0.0056154688  0.009217665  0.002506013  0.0008638862  0.016547715
## [12,] -0.0112309375  0.018435331  0.005012025  0.0017277724  0.033095431
## [13,] -0.0086227159 -0.007894355  0.015008815 -0.0033633317  0.022609643
## [14,] -0.0086227159 -0.007894355  0.015008815 -0.0033633317  0.022609643
## [15,]  0.0007486387 -0.002815467  0.007380592 -0.0011995090  0.008063573
## [16,] -0.0082473702 -0.004192728  0.006026211 -0.0017862811  0.012008087
##               [,6]         [,7]          [,8]         [,9]        [,10]
##  [1,] -0.036707424  0.022609643  0.0096326720  0.008063573  0.135286090
##  [2,] -0.009044530  0.043274547  0.0075898145  0.028973997  0.014253319
##  [3,] -0.005864119  0.036227350  0.0062118429  0.024432861  0.009241293
##  [4,]  0.015515859  0.063880346  0.0088035014  0.045766724 -0.024451519
##  [5,] -0.010840789  0.063341786  0.0109099739  0.042658690  0.017084053
##  [6,] -0.007619804  0.033308572  0.0058966366  0.022233069  0.012008087
##  [7,]  0.017236035 -0.003363332 -0.0014329227 -0.001199509 -0.013473754
##  [8,]  0.017236035 -0.003363332 -0.0014329227 -0.001199509 -0.013473754
##  [9,]  0.017236035 -0.003363332 -0.0014329227 -0.001199509 -0.013473754
## [10,] -0.003180411  0.007047196  0.0013779716  0.004541136  0.005012025
## [11,]  0.007126659  0.009217665  0.0008638862  0.007111287 -0.011230938
## [12,]  0.014253319  0.018435331  0.0017277724  0.014222575 -0.022461875
## [13,]  0.065915990 -0.007894355 -0.0033633317 -0.002815467 -0.017245432
## [14,]  0.065915990 -0.007894355 -0.0033633317 -0.002815467 -0.017245432
## [15,]  0.037048911 -0.002815467 -0.0011995090 -0.001004117  0.001497277
## [16,]  0.022020491 -0.004192728 -0.0017862811 -0.001495308 -0.016494740
##              [,11]        [,12]        [,13]         [,14]        [,15]
##  [1,]  0.012008087 -0.016496793  0.186432342  0.0096326720 -0.033742225
##  [2,]  0.009995515 -0.005864119  0.015515859  0.0075898145 -0.010840789
##  [3,]  0.008197756 -0.003802065  0.010059875  0.0062118429 -0.007028743
##  [4,]  0.011880974  0.010059875 -0.026617404  0.0088035014  0.018597337
##  [5,]  0.014391892 -0.007028743  0.018597337  0.0109099739 -0.012993790
##  [6,]  0.007759114 -0.004940382  0.013071748  0.0058966366 -0.009133111
##  [7,] -0.001786281  0.012466074 -0.007744557 -0.0014329227  0.022471951
##  [8,] -0.001786281  0.012466074 -0.007744557 -0.0014329227  0.022471951
##  [9,] -0.001786281  0.012466074 -0.007744557 -0.0014329227  0.022471951
## [10,]  0.001797758 -0.002062054  0.005455984  0.0013779716 -0.003812046
## [11,]  0.001227739  0.004620647 -0.012225760  0.0008638862  0.008542027
## [12,]  0.002455478  0.009241293 -0.024451519  0.0017277724  0.017084053
## [13,] -0.004192728  0.050907175  0.025039027 -0.0033633317  0.090479861
## [14,] -0.004192728  0.050907175  0.025039027 -0.0033633317  0.090479861
## [15,] -0.001495308  0.029668319  0.031914235 -0.0011995090  0.052337297
## [16,] -0.002226778  0.015994280 -0.008747831 -0.0017862811  0.028805050
##              [,16]
##  [1,] -0.033740172
##  [2,] -0.007619804
##  [3,] -0.004940382
##  [4,]  0.013071748
##  [5,] -0.009133111
##  [6,] -0.006419506
##  [7,]  0.014023351
##  [8,]  0.014023351
##  [9,]  0.014023351
## [10,] -0.002679422
## [11,]  0.006004043
## [12,]  0.012008087
## [13,]  0.052383457
## [14,]  0.052383457
## [15,]  0.029035995
## [16,]  0.017889874

m.ginv %>% as_tibble() %>%
  mutate(w1 = row.names(affmatrix)) %>%
  pivot_longer(names_to = "w2", values_to = "n", -w1) %>%
  ggplot() + aes(w2, w1, fill=n) +
  geom_tile() + th + 
  scale_fill_gradient2(low = "blue", high = "blue")