ノート/R/画像ノイズ除去をしてみる

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メニュー編集

画像ノイズ除去をしてみる（2010-09-17） †

背景：　岸本プロジェクトで、フローサイトメトリデータをクラスタ化。その時の雑音データを取り除く。

↑

Rでの行列操作によるノイズデータの除去 †

Mclustをそのまま使うには、入力データ（＝点のX-Y値の列挙）を行列（ベクトル）で与えることになる。

(FSC-H)  (SSC-H)
  253      327
  310      332
  289      132

そのデータは、読み込んだままでは雑音（X-Yに描画した時の孤立点）があって不可なので、雑音データを除去したい。

上記のデータから、雑音と判定された「行」を除きたいのだが、全部コピーすることは実行効率上したくない。配列の指定した行を除去するにはどうするか？　　参考　⇒　　（"-"は除外を意味する、を使う）

> x <- cbind(c(1,3,5,7), c(2,4,6,8), c(3,5,7,9))
> x
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    3    4    5
[3,]    5    6    7
[4,]    7    8    9
> x[-2,]
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    5    6    7
[3,]    7    8    9
> x[c(-2,-4),]
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    5    6    7

のように、指定した行（複数もできる）を除去することができる。

これを使えば、もし消したい行（行番号）のリストが与えられれば、それらの行を全て消す、という操作ができる。

↑

孤立点を判定する †

点の落ちる場所（X-Y座標）ごとに、点を順番にカウントするのもよいが、そうでない方法を考える。

まず、XとYでソートする。ソートした結果が、N行目≠N+1行目であれば、N行目は孤立と言えるだろう。但し両端（N=1とN=max）は片側だけでいい。ソートしたものを２つコピーして、１行ずらして（N行目とN+1行目を）横に並べる。

XとYでソートするには、うまい関数が見つからないので（ありそうなのだが）、 Xの値の範囲が0～1023のはずなので、(x[,1]*10000) + x[,2]を値としてソートする。その結果の順で、xを並べなおす（表示しなおす）と

> x <- cbind(c(1,3,1,5,7,9,11), c(2,4,1,6,8,10,12))
> x
     [,1] [,2]
[1,]    1    2
[2,]    3    4
[3,]    1    1
[4,]    5    6
[5,]    7    8
[6,]    9   10
[7,]   11   12
 
> y <- x[order(x[,1]*10000+x[,2]), ]
> y
     [,1] [,2]
[1,]    1    1
[2,]    1    2
[3,]    3    4
[4,]    5    6
[5,]    7    8
[6,]    9   10
[7,]   11   12

次に３つずつコピーして並べるところは、

> l <- length(y[,1])
> z <- cbind(y[1:(l-1),], y[2:l,])
> z
      [,1] [,2] [,3] [,4]
[1,]    1    1    1    2
[2,]    1    2    3    4
[3,]    3    4    5    6
[4,]    5    6    7    8
[5,]    7    8    9   10

で作ることができる。

重複のある例でやってみると、

> x <- cbind(c(1,3,1,5,7,9,1,11), c(2,4,1,6,8,10,2,12))
> x
     [,1] [,2]
[1,]    1    2
[2,]    3    4
[3,]    1    1
[4,]    5    6
[5,]    7    8
[6,]    9   10
[7,]    1    2      <-- 重複あり
[8,]   11   12
> y <- x[order(x[,1]*10000+x[,2]), ]
> l <- length(y[,1])
> z <- cbind(y[1:(l-1),], y[2:l,])
> z
     [,1] [,2] [,3] [,4]
[1,]    1    1    1    2
[2,]    1    2    1    2   <-- 重複ありの情報
[3,]    1    2    3    4
[4,]    3    4    5    6
[5,]    5    6    7    8
[6,]    7    8    9   10
[7,]    9   10   11   12

ここで、重複ありの行を抽出するためには

> t <- (z[,1]==z[,3]) & (z[,2]==z[,4])
> t <- c(FALSE, t)    <-- 1行減らした分を先頭に補う。2行目==3行目だと3がTRUEになる。

なお、&は１つだけ（vectorized）である。

しかし、重複がXの値がまったく同値、かつ、Yの値がまったく同値、としてしまうと、少し細かすぎるので、ここは、

> t <- (abs(z[,1]-z[,3])<=N) & (abs(z[,2]-z[,4])<=N)
> t <- c(FALSE, t)    <-- 1行減らした分を先頭に補う。2行目==3行目だと3がTRUEに

のようにしたほうがよさそうである。（結果を見ると）

↑

孤立点の除去 †

このtを使って、行列yから、tが値TRUEの行のみ（つまり近隣に落ちるデータが無い）取り出す操作は、

> y[t,]

と書ける。

尚、余分なこととして、

> s <- cbind(c(1;length(t)), t)
> s
       t
[1,] 1 0
[2,] 2 0
[3,] 3 1    <-- （ソート後）データyの3行目が（2行目と）重複
[4,] 4 0
[5,] 5 0
[6,] 6 0
[7,] 7 0
[8,] 8 0

もできるが、yから行を抜き取る操作は上記の方が簡単である。

全体をまとめると、

> y <- x[order(x[,1]*10000*x[,2]), ]
> l <- length(y[,1])
> z <- cbind(y[1:(l-1),], y[2:l,])
> t <- (abs(z[,1]-z[,3])<=N) & (abs(z[,2]-z[,4])<=N)
> t <- c(FALSE, t)    <-- 1行減らした分を先頭に補う。2行目==3行目だと3がTRUEになる。
> m <- y[t,]

と書ける。

↑

フローサイトメトリデータ処理への応用 †

これを使って、フローサイトメトリデータを処理してみると、次のようになる

# Need to "download" the library "mclust" beforehand.
#
# First, filter the data (1) remove x=0 data, (2) remove isolated data.
# Then, apply Mclust, and display.
#
install.packages("mclust")
library(mclust)

memory.limit(3071)  # Temporary
datalimit <- 10000
N <- 4
# Read the data
f <- file("37C/100124 37-2_limit.csv", "r")

readLines(f, n=3)  ## Read 3 lines to ignore them.
#u <- matrix(scan(f, sep=","), ncol=8, byrow=TRUE)
u <- matrix(scan(f, sep=","), ncol=8, byrow=TRUE)
  # ncol should be 8 because lines end with comma (with one more hidden column.)
close(f)
u <- u[,1:2]   # erase the hidden=empty column
# Reduce to "datalimit" samples, two dimensions(FSC vs SSC).
if (length(u[,1])>datalimit) u <- u[1:datalimit,]

print(length(u[,1]))

y <- u[order(u[,1]*10000+u[,2]), ]
l <- length(y[,1])
z <- cbind(y[1:(l-1),], y[2:l,])
#s <- (z[,1]==z[,3]) & (z[,2]==z[,4])
s <- ((abs(z[,1]-z[,3])<=N) & (abs(z[,2]-z[,4])<=N)) | (z[,1]<N) | (z[,2]<N)
s <- c(FALSE, s)
u <- y[s,]
print(length(u[,1]))

# Now calculate Mclust
#x <- Mclust(u, G=3, modelNames="VII")
  # modelNames may be either "EII", "VII", "EEI", "VEI".
  # This calculation takes a long time, possibly due to the data size(1987440 items).
# Instead, calculate BIC
#BIC <- mclustBIC(u)

x <- Mclust(u, G=5, modeNames="VEV")
mclust2Dplot(data=u, what="classification", identify=TRUE, parameters=x$parameters, z=x$z, scale=TRUE)

↑

<<37編>> †

↑

処理結果　37C/100124 37-2_limit.csv †

Read 147648 items
[1] 10000
[1] 5928
$Vinv
NULL
$pro
[1] 0.008365081 0.139807240 0.119567031 0.196275078 0.217181430 0.076706666
[7] 0.116521647 0.125575827
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
[1,] 276.4347 426.9785 572.0128 486.4956 479.0643 529.0192 537.5909 566.7286
[2,] 384.2431 476.0807 526.4424 511.7898 475.8735 522.8688 490.9496 533.1137
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 8
$variance$sigma
, , 1
          [,1]      [,2]
[1,] 17628.748 -5867.392
[2,] -5867.392  8566.723
, , 2
          [,1]     [,2]
[1,] 4181.9544 159.9707
[2,]  159.9707 214.7473
, , 3
         [,1]     [,2]
[1,] 5361.645 3208.185
[2,] 3208.185 2535.281
, , 4
          [,1]     [,2]
[1,] 1465.4985 175.4553
[2,]  175.4553 251.2087
, , 5
           [,1]      [,2]
[1,] 1304.28096  97.71196
[2,]   97.71196 175.27455
, , 6
          [,1]      [,2]
[1,]  654.6105 -137.2886
[2,] -137.2886  114.2930
, , 7
         [,1]     [,2]
[1,] 556.6931 131.3741
[2,] 131.3741 180.0008
, , 8
          [,1]      [,2]
[1,] 711.91442  13.11913
[2,]  13.11913 108.89344
$variance$cholsigma
, , 1
          [,1]      [,2]
[1,] -132.7733  44.19105
[2,]    0.0000 -81.32572
, , 2
          [,1]       [,2]
[1,] -64.66803  -2.473722
[2,]   0.00000 -14.443961
, , 3
          [,1]      [,2]
[1,] -73.22325 -43.81374
[2,]   0.00000 -24.81204
, , 4
          [,1]      [,2]
[1,] -38.28183 -4.583252
[2,]   0.00000 15.172426
, , 5
          [,1]       [,2]
[1,] -36.11483  -2.705591
[2,]   0.00000 -12.959719
, , 6
          [,1]     [,2]
[1,] -25.58536 5.365904
[2,]   0.00000 9.246622
, , 7
          [,1]       [,2]
[1,] -23.59434  -5.568035
[2,]   0.00000 -12.206465
, , 8
          [,1]       [,2]
[1,] -26.68172 -0.4916899
[2,]   0.00000 10.4236115

↑

処理結果　37C/100207 37-2_limit.csv †

Read 133800 items
[1] 10000
[1] 4353
$Vinv
NULL
$pro
[1] 0.04699748 0.14027222 0.09260779 0.23007086 0.26211838 0.09559291
[7] 0.09629144 0.03604891
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
[1,] 306.0208 418.6529 439.8381 493.5509 572.6118 497.0098 537.7538 643.8109
[2,] 361.4996 492.4958 455.9503 493.0856 528.3183 526.6853 511.7776 593.3946
$variance
$variance$modelName
[1] "VEV"
$variance$d
[1] 2
$variance$G
[1] 8
$variance$sigma
, , 1
         [,1]      [,2]
[1,] 11693.40 -5307.200
[2,] -5307.20  8209.293
, , 2
          [,1]     [,2]
[1,] 1941.3360 216.0946
[2,]  216.0946 588.6128
, , 3
         [,1]     [,2]
[1,] 2416.137 1433.995
[2,] 1433.995 2722.357
, , 4
           [,1]       [,2]
[1,] 922.159679   8.647484
[2,]   8.647484 259.248368
, , 5
         [,1]     [,2]
[1,] 591.2982 261.6259
[2,] 261.6259 400.7722
, , 6
         [,1]     [,2]
[1,] 666.6134 128.2134
[2,] 128.2134 232.1553
, , 7
          [,1]      [,2]
[1,]  220.1749 -147.9005
[2,] -147.9005  372.9192
, , 8
          [,1]     [,2]
[1,] 1607.0957 568.3284
[2,]  568.3284 837.9530
$variance$scale
[1] 8235.7848 1046.8994 2126.3222  488.8697  410.5213  371.9128  245.4239
[8] 1011.7675
$variance$shape
[1] 1.8865403 0.5300708
$variance$orientation
, , 1
           [,1]      [,2]
[1,] -0.8098987 0.5865698
[2,]  0.5865698 0.8098987
, , 2
           [,1]       [,2]
[1,] -0.9880697 -0.1540073
[2,] -0.1540073  0.9880697
, , 3
           [,1]       [,2]
[1,] -0.6685177 -0.7436962
[2,] -0.7436962  0.6685177
, , 4
            [,1]        [,2]
[1,] -0.99991496 -0.01304138
[2,] -0.01304138  0.99991496
, , 5
           [,1]       [,2]
[1,] -0.8191897  0.5735226
[2,] -0.5735226 -0.8191897
, , 6
           [,1]       [,2]
[1,] -0.9646724 -0.2634525
[2,] -0.2634525  0.9646724
, , 7
           [,1]      [,2]
[1,] -0.5201847 0.8540538
[2,]  0.8540538 0.5201847
, , 8
           [,1]       [,2]
[1,] -0.8832959 -0.4688159
[2,] -0.4688159  0.8832959

↑

処理結果　37C/100222 37-2_limit.csv †

Read 128200 items
[1] 10000
[1] 4356
$Vinv
NULL
$pro
[1] 0.0862894 0.2481755 0.1795777 0.2320187 0.2539387
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 362.0790 483.1855 545.4415 535.3017 584.2430
[2,] 340.3189 505.1435 534.5480 534.8650 533.5848
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 5
$variance$sigma
, , 1
          [,1]      [,2]
[1,] 9147.5254 -677.4772
[2,] -677.4772 7311.8394
, , 2
           [,1]      [,2]
[1,] 2051.84683  62.33014
[2,]   62.33014 398.44143
, , 3
         [,1]     [,2]
[1,] 5608.921 3480.902
[2,] 3480.902 2932.788
, , 4
          [,1]     [,2]
[1,] 1070.4228 188.3379
[2,]  188.3379 257.9111
, , 5
         [,1]     [,2]
[1,] 672.1205 423.0666
[2,] 423.0666 512.7710
$variance$cholsigma
, , 1
         [,1]       [,2]
[1,] -95.6427   7.083418
[2,]   0.0000 -85.215401
, , 2
          [,1]      [,2]
[1,] -45.29732 -1.376023
[2,]   0.00000 19.913513
, , 3
          [,1]      [,2]
[1,] -74.89273 -46.47850
[2,]   0.00000  27.79455
, , 4
          [,1]     [,2]
[1,] -32.71732 -5.75652
[2,]   0.00000 14.99245
, , 5
          [,1]      [,2]
[1,] -25.92529 -16.31868
[2,]   0.00000 -15.69941

37-0124	37-0207	37-0222

↑

<<40編>> †

↑

処理結果　40C/100130 40C_limit.csv †

Read 132728 items
[1] 10000
[1] 2717
$Vinv
NULL
$pro
[1] 0.08627891 0.08369000 0.17293510 0.21230533 0.08960009 0.13767879
[7] 0.21751179
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
[1,] 272.4490 331.3218 473.3830 590.2983 657.1372 641.3339 725.5653
[2,] 256.1549 398.3479 520.5002 549.8457 628.3205 657.4361 668.5336
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 7
$variance$sigma
, , 1
           [,1]      [,2]
[1,] 10986.1228  -78.7728
[2,]   -78.7728 1656.4718
, , 2
         [,1]     [,2]
[1,] 6806.218 1196.392
[2,] 1196.392 6875.475
, , 3
         [,1]     [,2]
[1,] 3287.212 1666.060
[2,] 1666.060 2221.489
, , 4
          [,1]     [,2]
[1,] 1528.4977 969.9005
[2,]  969.9005 913.7396
, , 5
          [,1]     [,2]
[1,] 1045.9485 299.5733
[2,]  299.5733 232.4328
, , 6
         [,1]     [,2]
[1,] 5096.412 1882.042
[2,] 1882.042 1830.718
, , 7
         [,1]     [,2]
[1,] 2025.672 1938.037
[2,] 1938.037 2024.082
$variance$cholsigma
, , 1
          [,1]        [,2]
[1,] -104.8147   0.7515434
[2,]    0.0000 -40.6928372
, , 2
         [,1]      [,2]
[1,] -82.4998 -14.50175
[2,]   0.0000  81.64052
, , 3
          [,1]      [,2]
[1,] -57.33422 -29.05873
[2,]   0.00000  37.10901
, , 4
          [,1]      [,2]
[1,] -39.09601 -24.80817
[2,]   0.00000 -17.27119
, , 5
          [,1]      [,2]
[1,] -32.34113 -9.262922
[2,]   0.00000 12.109134
, , 6
          [,1]      [,2]
[1,] -71.38916 -26.36313
[2,]   0.00000  33.70020
, , 7
          [,1]      [,2]
[1,] -45.00746 -43.06035
[2,]   0.00000 -13.03414

↑

処理結果　40C/100131 40C-2_limit.csv †

Read 138504 items
[1] 10000
[1] 3867
$Vinv
NULL
$pro
[1] 0.0708716 0.1769284 0.1491971 0.2780176 0.1609299 0.1640554
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
[1,] 301.0512 479.3534 481.4737 553.1853 643.9201 646.4777
[2,] 325.0113 481.0801 519.9109 521.1925 589.2686 628.2585
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 6
$variance$sigma
, , 1
         [,1]     [,2]
[1,] 7845.995 1967.291
[2,] 1967.291 9829.285
, , 2
          [,1]     [,2]
[1,] 1857.7216 330.3594
[2,]  330.3594 234.9704
, , 3
          [,1]     [,2]
[1,] 2692.0382 659.3057
[2,]  659.3057 341.5811
, , 4
          [,1]     [,2]
[1,] 1110.8005 450.6766
[2,]  450.6766 363.0634
, , 5
         [,1]     [,2]
[1,] 3622.571 3387.179
[2,] 3387.179 3288.265
, , 6
         [,1]     [,2]
[1,] 3976.527 1861.752
[2,] 1861.752 1388.307
$variance$cholsigma
, , 1
          [,1]      [,2]
[1,] -88.57762 -22.20979
[2,]   0.00000  96.62303
, , 2
          [,1]       [,2]
[1,] -43.10129  -7.664721
[2,]   0.00000 -13.274880
, , 3
          [,1]      [,2]
[1,] -51.88486 -12.70709
[2,]   0.00000 -13.42054
, , 4
          [,1]      [,2]
[1,] -33.32867 -13.52219
[2,]   0.00000 -13.42438
, , 5
         [,1]      [,2]
[1,] -60.1878 -56.27684
[2,]   0.0000 -11.00825
, , 6
          [,1]      [,2]
[1,] -63.05971 -29.52363
[2,]   0.00000  22.73021

↑

処理結果　40C/100202 40C-2_limit.csv †

Read 127000 items
[1] 10000
[1] 2987
$Vinv
NULL
$pro
[1] 0.08337143 0.05570773 0.17876734 0.12477475 0.23229551 0.20140907
[7] 0.12367416
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
[1,] 349.9035 374.7882 611.4276 499.6387 607.7975 662.6251 762.0650
[2,] 411.9781 256.9926 617.4432 494.8893 562.5699 610.3566 691.4602
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 7
$variance$sigma
, , 1
          [,1]      [,2]
[1,] 16072.626  9225.822
[2,]  9225.822 11034.045
, , 2
           [,1]       [,2]
[1,] 2712.66456   25.34234
[2,]   25.34234 1722.33045
, , 3
          [,1]     [,2]
[1,] 10771.492 7047.211
[2,]  7047.211 5343.205
, , 4
         [,1]     [,2]
[1,] 5213.002 3713.708
[2,] 3713.708 3662.314
, , 5
         [,1]     [,2]
[1,] 925.7252 539.2082
[2,] 539.2082 749.8059
, , 6
         [,1]     [,2]
[1,] 738.1418 429.2458
[2,] 429.2458 414.4744
, , 7
         [,1]     [,2]
[1,] 1607.196 1552.762
[2,] 1552.762 1790.061
$variance$cholsigma
, , 1
          [,1]      [,2]
[1,] -126.7779 -72.77156
[2,]    0.0000  75.75187
, , 2
          [,1]        [,2]
[1,] -52.08325  -0.4865736
[2,]   0.00000 -41.4981168
, , 3
          [,1]      [,2]
[1,] -103.7858 -67.90149
[2,]    0.0000  27.06644
, , 4
          [,1]      [,2]
[1,] -72.20112 -51.43560
[2,]   0.00000 -31.88562
, , 5
          [,1]      [,2]
[1,] -30.42573 -17.72211
[2,]   0.00000 -20.87421
, , 6
          [,1]      [,2]
[1,] -27.16877 -15.79924
[2,]   0.00000 -12.83972
, , 7
          [,1]      [,2]
[1,] -40.08985 -38.73204
[2,]   0.00000 -17.02617

↑

処理結果　40C/100206 40C-2_limit.csv †

Read 143512 items
[1] 10000
[1] 4352
$Vinv
NULL
$pro
[1] 0.02547121 0.29099435 0.07388858 0.22176791 0.07915986 0.18513305
[7] 0.12358504
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
[1,] 326.5259 488.1971 535.3663 566.5123 595.7151 650.5835 683.7027
[2,] 368.9300 504.8604 595.9315 528.9039 606.3186 612.4143 650.6195
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 7
$variance$sigma
 , , 1
          [,1]      [,2]
[1,] 12142.045 -2211.784
[2,] -2211.784 10760.556
, , 2
          [,1]     [,2]
[1,] 2265.2013 604.6191
[2,]  604.6191 578.4554
, , 3
          [,1]     [,2]
[1,] 13499.441 6467.233
[2,]  6467.233 3768.151
, , 4
          [,1]     [,2]
[1,] 1198.8135 690.9153
[2,]  690.9153 781.3351
, , 5
           [,1]      [,2]
[1,] 1101.48659 -84.76034
[2,]  -84.76034 288.74142
, , 6
         [,1]     [,2]
[1,] 530.4911 217.3745
[2,] 217.3745 246.5619
, , 7
          [,1]     [,2]
[1,] 1186.0582 433.9824
[2,]  433.9824 426.4151
$variance$cholsigma
, , 1
          [,1]       [,2]
[1,] -110.1909   20.07229
[2,]    0.0000 -101.77259
, , 2
          [,1]      [,2]
[1,] -47.59413 -12.70365
[2,]   0.00000 -20.42236
, , 3
          [,1]      [,2]
[1,] -116.1871 -55.66223
[2,]    0.0000 -25.88178
, , 4
          [,1]      [,2]
[1,] -34.62389 -19.95488
[2,]   0.00000 -19.57391
, , 5
          [,1]      [,2]
[1,] -33.18865  2.553895
[2,]   0.00000 16.799376
, , 6
          [,1]      [,2]
[1,] -23.03239 -9.437774
[2,]   0.00000 12.549514
, , 7
          [,1]      [,2]
[1,] -34.43920 -12.60141
[2,]   0.00000  16.35908

↑

処理結果　40C/100213 40C-2_limit.csv †

Read 139224 items
[1] 10000
[1] 4111
$Vinv
NULL
$pro
[1] 0.03772979 0.19006704 0.31427003 0.16695336 0.10767037 0.18330941
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
[1,] 348.4743 479.9382 563.7061 644.9337 625.0681 691.0621
[2,] 359.8323 494.3479 524.7628 606.8775 625.2827 625.0112
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 6
$variance$sigma
, , 1
           [,1]      [,2]
 [1,] 10240.881  1626.031
 [2,]  1626.031 10977.447
, , 2
          [,1]     [,2]
[1,] 2768.2229 609.9427
[2,]  609.9427 678.0838
, , 3
          [,1]     [,2]
[1,] 1340.6985 585.8402
[2,]  585.8402 639.4631
, , 4
         [,1]     [,2]
[1,] 800.3198 371.3095
[2,] 371.3095 465.1034
, , 5
         [,1]     [,2]
[1,] 6596.206 3492.190
[2,] 3492.190 2381.841
, , 6
         [,1]     [,2]
[1,] 1799.778 1543.032
[2,] 1543.032 1528.821
$variance$cholsigma
, , 1
          [,1]       [,2]
[1,] -101.1972  -16.06794
[2,]    0.0000 -103.53390
, , 2
         [,1]      [,2]
[1,] -52.6139 -11.59280
[2,]   0.0000 -23.31718
, , 3
          [,1]      [,2]
[1,] -36.61555 -15.99977
[2,]   0.00000 -19.58241
, , 4
          [,1]      [,2]
[1,] -28.28992 -13.12515
[2,]   0.00000  17.11239
, , 5
          [,1]      [,2]
[1,] -81.21703 -42.99825
[2,]   0.00000 -23.08661
, , 6
          [,1]      [,2]
[1,] -42.42379 -36.37184
[2,]   0.00000 -14.34956

↑

処理結果　40C/100222 40C-2_limit.csv †

Read 134408 items
[1] 10000
[1] 3969
$Vinv
NULL
$pro
[1] 0.06542553 0.16157240 0.14877678 0.18182725 0.17895889 0.26343916
$mean
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
[1,] 361.0161 523.3542 559.6788 649.4959 608.7483 725.5666
[2,] 302.7612 513.4298 542.3724 609.8812 558.8478 664.8292
$variance
$variance$modelName
[1] "VVV"
$variance$d
[1] 2
$variance$G
[1] 6
$variance$sigma
, , 1
          [,1]      [,2]
[1,] 9309.3649  342.6209
[2,]  342.6209 7529.9921
, , 2
         [,1]     [,2]
[1,] 3453.989 1547.289
[2,] 1547.289 1698.183
, , 3
          [,1]     [,2]
[1,] 1230.5867 142.9697
[2,]  142.9697 247.2928
, , 4
          [,1]     [,2]
[1,] 1336.2549 703.8288
[2,]  703.8288 909.8132
, , 5
         [,1]     [,2]
[1,] 558.7936 200.6191
[2,] 200.6191 282.5990
, , 6
         [,1]     [,2]
[1,] 2480.592 1970.225
[2,] 1970.225 2072.693
$variance$cholsigma
, , 1
          [,1]      [,2]
[1,] -96.48505 -3.551026
[2,]   0.00000 86.702839
, , 2
          [,1]      [,2]
[1,] -58.77065 -26.32758
[2,]   0.00000  31.70239
, , 3
          [,1]      [,2]
[1,] -35.07972 -4.075564
[2,]   0.00000 15.188238
, , 4
          [,1]      [,2]
[1,] -36.55482 -19.25406
[2,]   0.00000  23.21840
, , 5
          [,1]     [,2]
[1,] -23.63881 -8.48685
[2,]   0.00000 14.51111
, , 6
          [,1]      [,2]
[1,] -49.80554 -39.55836
[2,]   0.00000 -22.53507

40-0130	40-0131	40-0202

40-0206	40-0213	40-0222

最新の5件

画像ノイズ除去をしてみる（2010-09-17） †

Rでの行列操作によるノイズデータの除去 †

孤立点を判定する †

孤立点の除去 †

フローサイトメトリデータ処理への応用 †

<<37編>> †

処理結果 37C/100124 37-2_limit.csv †

処理結果 37C/100207 37-2_limit.csv †

処理結果 37C/100222 37-2_limit.csv †

<<40編>> †

処理結果 40C/100130 40C_limit.csv †

処理結果 40C/100131 40C-2_limit.csv †

処理結果 40C/100202 40C-2_limit.csv †

処理結果 40C/100206 40C-2_limit.csv †

処理結果 40C/100213 40C-2_limit.csv †

処理結果 40C/100222 40C-2_limit.csv †