622: hw4_final

Jie Zou

2022-12-14

Objectives

In the final project, I am going to try to do email classification. The dataset is coming from Kaggle. The technologies for classification that I will used according to the requirement are SVM, XGBoost and NN.

The data has been pre-processed a little which means that the non alphabet letters/words have been excluded from the data, as well as that the text has been stored as features, and rows are the frequency of the corresponding words. Therefore, the dataset only contains three parts: name of email, extracted text and target variable.

Read Data

As we see from the first input, the dataset contains 5172 rows and 3002 features, so that there are 3000 words extracted from 5172 emails. Since the records only contains the frequencies, and it contains too many features which exceed the print limit in R, I did not show the summary of the data set, but the top few rows are showing just to see how the table will be like. In addition, there is no missing values found on the data.

## [1] 5172 3002
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## [1] 0

Basic Cleaning

As we see from the table above, the first column does not seem to provide any useful information for either analysis or model learning, so it is dropped from the table. Since all features are lower case words and only the name of target variable is capital in initial, it might be confuse when only of feature names is the same as target variable, therefore, I change the name of target variable into target_class, also convert it into factor type.

Secondly, if we pay more attention on the name of features, there is . comes with words. As a result, I remove all dots and spaces(in case there is spaces as well) from column names. Meanwhile, the small table shows that target class is imbalanced class. It is normal in email classification because spam email is always less than non-spam email.

## 
##    0    1 
## 3672 1500

Visualization

The plot shows the top 500 words with the most frequency. The larger text, the more frequently appear in an email, and the bolder, the more frequent.

Curse of Dimension

Sentiment

I figure that there are some single letters appears so many time, it could be some non-alphabet letters with them before. A single letter does not sound like a pretty good predictor, besides, there are too many features in the dataset, it will increase the computational complexity. So, first of all, remove single lower case letters, stopwords, extra spaces caused by removing and near zero variables. Then create a new subset of data based on the cleaned text, which reduce the dimension from 3000+ features to 300+. Note: I did not convert text into its root form, because I tried multiple times, the function will break some words, for example, ability -> abil which makes no sense.

## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(plain_words)` instead of `plain_words` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.
## [1] 5172  325

PCA

Even though the dimension has been tremendous decreased, I would like to see if PCA can help do some feature extraction so that there is still a chance to reduce a little more uninformative features.

From summary of PCA, PC70 is the limit of eigenvalue to be 1 and achieve 74.6% accumulative proportion of variance. That is already not bad. But from contribution plot, it is very hard to pick out individual features. So, I am going to leave 300+ feature as they are.

## Importance of components:
##                           PC1     PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     8.7113 3.67354 3.20616 2.63467 2.60260 2.52940 2.22242
## Proportion of Variance 0.2342 0.04165 0.03173 0.02142 0.02091 0.01975 0.01524
## Cumulative Proportion  0.2342 0.27587 0.30760 0.32902 0.34993 0.36967 0.38492
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     2.09590 2.04070 1.95654 1.89025 1.80597 1.79298 1.75726
## Proportion of Variance 0.01356 0.01285 0.01181 0.01103 0.01007 0.00992 0.00953
## Cumulative Proportion  0.39848 0.41133 0.42315 0.43417 0.44424 0.45416 0.46369
##                           PC15    PC16    PC17    PC18    PC19    PC20    PC21
## Standard deviation     1.72114 1.69945 1.67000 1.63640 1.60734 1.58073 1.54663
## Proportion of Variance 0.00914 0.00891 0.00861 0.00826 0.00797 0.00771 0.00738
## Cumulative Proportion  0.47284 0.48175 0.49036 0.49862 0.50660 0.51431 0.52169
##                           PC22   PC23    PC24   PC25    PC26    PC27    PC28
## Standard deviation     1.52175 1.4951 1.46915 1.4512 1.44330 1.43054 1.41506
## Proportion of Variance 0.00715 0.0069 0.00666 0.0065 0.00643 0.00632 0.00618
## Cumulative Proportion  0.52884 0.5357 0.54240 0.5489 0.55533 0.56165 0.56783
##                           PC29    PC30    PC31   PC32    PC33   PC34    PC35
## Standard deviation     1.40858 1.38904 1.36937 1.3593 1.34221 1.3102 1.29495
## Proportion of Variance 0.00612 0.00596 0.00579 0.0057 0.00556 0.0053 0.00518
## Cumulative Proportion  0.57395 0.57990 0.58569 0.5914 0.59695 0.6022 0.60743
##                           PC36    PC37    PC38    PC39    PC40    PC41    PC42
## Standard deviation     1.28009 1.27091 1.26467 1.24863 1.23550 1.23475 1.22383
## Proportion of Variance 0.00506 0.00499 0.00494 0.00481 0.00471 0.00471 0.00462
## Cumulative Proportion  0.61249 0.61747 0.62241 0.62722 0.63193 0.63664 0.64126
##                           PC43   PC44    PC45    PC46    PC47    PC48    PC49
## Standard deviation     1.20447 1.1937 1.18929 1.18360 1.17728 1.16500 1.15447
## Proportion of Variance 0.00448 0.0044 0.00437 0.00432 0.00428 0.00419 0.00411
## Cumulative Proportion  0.64574 0.6501 0.65450 0.65882 0.66310 0.66729 0.67140
##                           PC50    PC51    PC52    PC53   PC54    PC55    PC56
## Standard deviation     1.14921 1.14284 1.12611 1.11954 1.1092 1.10624 1.09726
## Proportion of Variance 0.00408 0.00403 0.00391 0.00387 0.0038 0.00378 0.00372
## Cumulative Proportion  0.67548 0.67951 0.68343 0.68729 0.6911 0.69487 0.69858
##                           PC57    PC58    PC59    PC60    PC61    PC62    PC63
## Standard deviation     1.09114 1.07909 1.07489 1.07380 1.06020 1.05306 1.04556
## Proportion of Variance 0.00367 0.00359 0.00357 0.00356 0.00347 0.00342 0.00337
## Cumulative Proportion  0.70226 0.70585 0.70942 0.71298 0.71645 0.71987 0.72324
##                           PC64   PC65    PC66    PC67    PC68    PC69   PC70
## Standard deviation     1.03725 1.0348 1.03056 1.02657 1.01074 1.00559 1.0015
## Proportion of Variance 0.00332 0.0033 0.00328 0.00325 0.00315 0.00312 0.0031
## Cumulative Proportion  0.72656 0.7299 0.73315 0.73640 0.73955 0.74267 0.7458
##                           PC71    PC72    PC73    PC74    PC75    PC76    PC77
## Standard deviation     0.99196 0.99140 0.98449 0.97882 0.97365 0.96717 0.96260
## Proportion of Variance 0.00304 0.00303 0.00299 0.00296 0.00293 0.00289 0.00286
## Cumulative Proportion  0.74881 0.75184 0.75483 0.75779 0.76071 0.76360 0.76646
##                           PC78   PC79    PC80    PC81    PC82    PC83    PC84
## Standard deviation     0.96023 0.9524 0.95017 0.93864 0.93766 0.93210 0.92411
## Proportion of Variance 0.00285 0.0028 0.00279 0.00272 0.00271 0.00268 0.00264
## Cumulative Proportion  0.76931 0.7721 0.77489 0.77761 0.78033 0.78301 0.78564
##                           PC85   PC86    PC87    PC88    PC89    PC90    PC91
## Standard deviation     0.92219 0.9173 0.91541 0.90965 0.90814 0.89532 0.89522
## Proportion of Variance 0.00262 0.0026 0.00259 0.00255 0.00255 0.00247 0.00247
## Cumulative Proportion  0.78827 0.7909 0.79345 0.79601 0.79855 0.80102 0.80350
##                           PC92    PC93    PC94    PC95    PC96    PC97    PC98
## Standard deviation     0.89122 0.88735 0.88472 0.87889 0.87686 0.86989 0.86468
## Proportion of Variance 0.00245 0.00243 0.00242 0.00238 0.00237 0.00234 0.00231
## Cumulative Proportion  0.80595 0.80838 0.81080 0.81318 0.81555 0.81789 0.82020
##                           PC99   PC100   PC101   PC102   PC103   PC104   PC105
## Standard deviation     0.86026 0.85571 0.85002 0.84688 0.84161 0.84076 0.83295
## Proportion of Variance 0.00228 0.00226 0.00223 0.00221 0.00219 0.00218 0.00214
## Cumulative Proportion  0.82248 0.82474 0.82697 0.82918 0.83137 0.83355 0.83569
##                          PC106   PC107   PC108   PC109   PC110  PC111   PC112
## Standard deviation     0.82668 0.82259 0.81866 0.81517 0.81223 0.8056 0.80296
## Proportion of Variance 0.00211 0.00209 0.00207 0.00205 0.00204 0.0020 0.00199
## Cumulative Proportion  0.83780 0.83989 0.84196 0.84401 0.84605 0.8480 0.85004
##                          PC113   PC114   PC115   PC116   PC117   PC118   PC119
## Standard deviation     0.79752 0.79367 0.79169 0.78619 0.78269 0.77718 0.77614
## Proportion of Variance 0.00196 0.00194 0.00193 0.00191 0.00189 0.00186 0.00186
## Cumulative Proportion  0.85200 0.85395 0.85588 0.85779 0.85968 0.86154 0.86340
##                          PC120   PC121   PC122   PC123   PC124   PC125   PC126
## Standard deviation     0.77146 0.77138 0.76697 0.76525 0.75852 0.75692 0.75228
## Proportion of Variance 0.00184 0.00184 0.00182 0.00181 0.00178 0.00177 0.00175
## Cumulative Proportion  0.86524 0.86708 0.86889 0.87070 0.87247 0.87424 0.87599
##                          PC127  PC128   PC129   PC130   PC131   PC132   PC133
## Standard deviation     0.74855 0.7415 0.73867 0.73748 0.73176 0.72686 0.72564
## Proportion of Variance 0.00173 0.0017 0.00168 0.00168 0.00165 0.00163 0.00163
## Cumulative Proportion  0.87772 0.8794 0.88110 0.88278 0.88443 0.88606 0.88769
##                         PC134   PC135   PC136   PC137   PC138   PC139   PC140
## Standard deviation     0.7204 0.71451 0.71236 0.70545 0.70220 0.69879 0.69582
## Proportion of Variance 0.0016 0.00158 0.00157 0.00154 0.00152 0.00151 0.00149
## Cumulative Proportion  0.8893 0.89087 0.89243 0.89397 0.89549 0.89700 0.89849
##                          PC141   PC142   PC143   PC144   PC145  PC146   PC147
## Standard deviation     0.69351 0.69175 0.68588 0.68365 0.67712 0.6743 0.67205
## Proportion of Variance 0.00148 0.00148 0.00145 0.00144 0.00142 0.0014 0.00139
## Cumulative Proportion  0.89998 0.90145 0.90290 0.90435 0.90576 0.9072 0.90856
##                          PC148   PC149   PC150   PC151   PC152  PC153   PC154
## Standard deviation     0.66965 0.66408 0.66025 0.65656 0.65221 0.6491 0.64379
## Proportion of Variance 0.00138 0.00136 0.00135 0.00133 0.00131 0.0013 0.00128
## Cumulative Proportion  0.90994 0.91130 0.91265 0.91398 0.91529 0.9166 0.91787
##                          PC155   PC156   PC157   PC158   PC159   PC160   PC161
## Standard deviation     0.64043 0.63826 0.63059 0.62918 0.62555 0.61867 0.61690
## Proportion of Variance 0.00127 0.00126 0.00123 0.00122 0.00121 0.00118 0.00117
## Cumulative Proportion  0.91914 0.92040 0.92162 0.92284 0.92405 0.92523 0.92641
##                          PC162   PC163   PC164   PC165   PC166   PC167  PC168
## Standard deviation     0.61320 0.61168 0.60938 0.60571 0.60244 0.59883 0.5971
## Proportion of Variance 0.00116 0.00115 0.00115 0.00113 0.00112 0.00111 0.0011
## Cumulative Proportion  0.92757 0.92872 0.92987 0.93100 0.93212 0.93323 0.9343
##                          PC169   PC170   PC171   PC172   PC173   PC174  PC175
## Standard deviation     0.59044 0.58714 0.58492 0.58123 0.57983 0.57212 0.5683
## Proportion of Variance 0.00108 0.00106 0.00106 0.00104 0.00104 0.00101 0.0010
## Cumulative Proportion  0.93541 0.93647 0.93753 0.93857 0.93961 0.94062 0.9416
##                          PC176   PC177   PC178   PC179   PC180   PC181   PC182
## Standard deviation     0.56438 0.56051 0.55718 0.55583 0.55366 0.54788 0.54460
## Proportion of Variance 0.00098 0.00097 0.00096 0.00095 0.00095 0.00093 0.00092
## Cumulative Proportion  0.94260 0.94357 0.94452 0.94548 0.94642 0.94735 0.94827
##                         PC183  PC184   PC185   PC186   PC187   PC188   PC189
## Standard deviation     0.5402 0.5391 0.53814 0.53600 0.52863 0.52557 0.52459
## Proportion of Variance 0.0009 0.0009 0.00089 0.00089 0.00086 0.00085 0.00085
## Cumulative Proportion  0.9492 0.9501 0.95096 0.95184 0.95271 0.95356 0.95441
##                          PC190   PC191   PC192   PC193   PC194   PC195   PC196
## Standard deviation     0.51887 0.51860 0.51630 0.51215 0.51071 0.50074 0.50018
## Proportion of Variance 0.00083 0.00083 0.00082 0.00081 0.00081 0.00077 0.00077
## Cumulative Proportion  0.95524 0.95607 0.95689 0.95770 0.95851 0.95928 0.96005
##                          PC197   PC198   PC199   PC200   PC201   PC202   PC203
## Standard deviation     0.49473 0.49052 0.48912 0.48630 0.48453 0.48363 0.48076
## Proportion of Variance 0.00076 0.00074 0.00074 0.00073 0.00072 0.00072 0.00071
## Cumulative Proportion  0.96081 0.96155 0.96229 0.96302 0.96374 0.96447 0.96518
##                         PC204   PC205   PC206   PC207   PC208   PC209   PC210
## Standard deviation     0.4771 0.47267 0.46974 0.46494 0.46267 0.45908 0.45843
## Proportion of Variance 0.0007 0.00069 0.00068 0.00067 0.00066 0.00065 0.00065
## Cumulative Proportion  0.9659 0.96657 0.96725 0.96792 0.96858 0.96923 0.96988
##                          PC211   PC212  PC213  PC214   PC215   PC216   PC217
## Standard deviation     0.45315 0.44318 0.4420 0.4401 0.43475 0.43259 0.43173
## Proportion of Variance 0.00063 0.00061 0.0006 0.0006 0.00058 0.00058 0.00058
## Cumulative Proportion  0.97051 0.97112 0.9717 0.9723 0.97290 0.97348 0.97406
##                          PC218   PC219   PC220   PC221   PC222   PC223   PC224
## Standard deviation     0.42791 0.42639 0.42256 0.42088 0.41903 0.41362 0.40997
## Proportion of Variance 0.00057 0.00056 0.00055 0.00055 0.00054 0.00053 0.00052
## Cumulative Proportion  0.97462 0.97518 0.97573 0.97628 0.97682 0.97735 0.97787
##                          PC225   PC226   PC227   PC228   PC229   PC230   PC231
## Standard deviation     0.40855 0.40643 0.39998 0.39496 0.39314 0.39000 0.38469
## Proportion of Variance 0.00052 0.00051 0.00049 0.00048 0.00048 0.00047 0.00046
## Cumulative Proportion  0.97838 0.97889 0.97939 0.97987 0.98035 0.98082 0.98127
##                          PC232   PC233   PC234   PC235   PC236   PC237   PC238
## Standard deviation     0.38301 0.38098 0.37204 0.36932 0.36689 0.36512 0.36342
## Proportion of Variance 0.00045 0.00045 0.00043 0.00042 0.00042 0.00041 0.00041
## Cumulative Proportion  0.98172 0.98217 0.98260 0.98302 0.98344 0.98385 0.98426
##                         PC239   PC240   PC241   PC242   PC243   PC244   PC245
## Standard deviation     0.3595 0.35616 0.35492 0.34933 0.34671 0.34288 0.34124
## Proportion of Variance 0.0004 0.00039 0.00039 0.00038 0.00037 0.00036 0.00036
## Cumulative Proportion  0.9847 0.98505 0.98543 0.98581 0.98618 0.98655 0.98690
##                          PC246   PC247   PC248   PC249   PC250   PC251   PC252
## Standard deviation     0.33664 0.33371 0.33186 0.32937 0.32538 0.32297 0.32047
## Proportion of Variance 0.00035 0.00034 0.00034 0.00033 0.00033 0.00032 0.00032
## Cumulative Proportion  0.98725 0.98760 0.98794 0.98827 0.98860 0.98892 0.98924
##                          PC253  PC254  PC255   PC256   PC257   PC258   PC259
## Standard deviation     0.31471 0.3110 0.3094 0.30656 0.30132 0.29812 0.29495
## Proportion of Variance 0.00031 0.0003 0.0003 0.00029 0.00028 0.00027 0.00027
## Cumulative Proportion  0.98954 0.9898 0.9901 0.99043 0.99071 0.99098 0.99125
##                          PC260   PC261   PC262   PC263   PC264   PC265   PC266
## Standard deviation     0.29258 0.28905 0.28736 0.28428 0.28313 0.27932 0.27807
## Proportion of Variance 0.00026 0.00026 0.00025 0.00025 0.00025 0.00024 0.00024
## Cumulative Proportion  0.99152 0.99177 0.99203 0.99228 0.99252 0.99277 0.99300
##                          PC267   PC268   PC269   PC270   PC271   PC272   PC273
## Standard deviation     0.27369 0.27165 0.26956 0.26721 0.26365 0.26110 0.26077
## Proportion of Variance 0.00023 0.00023 0.00022 0.00022 0.00021 0.00021 0.00021
## Cumulative Proportion  0.99324 0.99346 0.99369 0.99391 0.99412 0.99433 0.99454
##                         PC274  PC275   PC276   PC277   PC278   PC279   PC280
## Standard deviation     0.2572 0.2528 0.25131 0.24760 0.24555 0.24261 0.24077
## Proportion of Variance 0.0002 0.0002 0.00019 0.00019 0.00019 0.00018 0.00018
## Cumulative Proportion  0.9948 0.9949 0.99514 0.99533 0.99551 0.99570 0.99588
##                          PC281   PC282   PC283   PC284   PC285   PC286   PC287
## Standard deviation     0.23710 0.23352 0.23153 0.22946 0.22379 0.22237 0.21808
## Proportion of Variance 0.00017 0.00017 0.00017 0.00016 0.00015 0.00015 0.00015
## Cumulative Proportion  0.99605 0.99622 0.99638 0.99654 0.99670 0.99685 0.99700
##                          PC288   PC289   PC290   PC291   PC292   PC293   PC294
## Standard deviation     0.21632 0.21553 0.20890 0.20756 0.20213 0.20104 0.19728
## Proportion of Variance 0.00014 0.00014 0.00013 0.00013 0.00013 0.00012 0.00012
## Cumulative Proportion  0.99714 0.99729 0.99742 0.99755 0.99768 0.99781 0.99793
##                          PC295   PC296   PC297   PC298  PC299  PC300  PC301
## Standard deviation     0.19549 0.19296 0.19149 0.18722 0.1833 0.1810 0.1776
## Proportion of Variance 0.00012 0.00011 0.00011 0.00011 0.0001 0.0001 0.0001
## Cumulative Proportion  0.99804 0.99816 0.99827 0.99838 0.9985 0.9986 0.9987
##                         PC302   PC303   PC304   PC305   PC306   PC307   PC308
## Standard deviation     0.1756 0.17315 0.16989 0.16576 0.16310 0.15987 0.15848
## Proportion of Variance 0.0001 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008
## Cumulative Proportion  0.9988 0.99887 0.99896 0.99904 0.99913 0.99920 0.99928
##                          PC309   PC310   PC311   PC312   PC313   PC314   PC315
## Standard deviation     0.15525 0.15414 0.14837 0.14473 0.14157 0.13075 0.12869
## Proportion of Variance 0.00007 0.00007 0.00007 0.00006 0.00006 0.00005 0.00005
## Cumulative Proportion  0.99936 0.99943 0.99950 0.99956 0.99962 0.99968 0.99973
##                          PC316   PC317   PC318   PC319   PC320   PC321   PC322
## Standard deviation     0.12331 0.12129 0.11874 0.11555 0.10493 0.09531 0.07607
## Proportion of Variance 0.00005 0.00005 0.00004 0.00004 0.00003 0.00003 0.00002
## Cumulative Proportion  0.99977 0.99982 0.99986 0.99990 0.99994 0.99997 0.99998
##                          PC323   PC324
## Standard deviation     0.06521 0.02664
## Proportion of Variance 0.00001 0.00000
## Cumulative Proportion  1.00000 1.00000

Correlation

as I left texts as they are, different tense of a words are metaphors of their root. So human will diagnose them the same, but to machine, it is two different words. From intuition, a word with its metaphor should have strong relationship in appearance. Therefore, I can reduce dimension by removing those highly correlated words as well. Now it has less than 300 features. Until now, I could not think of other methods to reduce the dimension on the top of my head, so let’s stay with it then.

## [1] 5172  283

Data Preparation

Preprocessing

standardize data point to decrease intense computation.

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-0.3110182 -0.5533387 -0.4322405 -0.290913 0.0547681 -0.3281881 -0.250174 0.5705392 -0.2282083 0.3060112 1.7799028 -0.1561671 0.2290698 -0.2123344 -0.4077790 -0.3871189 -0.2893234 -0.2320977 -0.2329628 -0.2739720 -0.1176470 0.8985229 0.6910512 -0.4054030 -0.2850929 -0.2238634 -0.5052932 0.2623791 -0.258585 -0.2196776 -0.2254011 -0.3171963 -0.2570206 -0.2328978 -0.2364422 -0.2656516 -0.2731103 -0.2161784 -0.2324949 -0.5816848 -0.3694938 -0.2955737 -0.4731070 -0.2985460 -0.3803985 -0.281825 -0.2981742 -0.2563642 0.6235816 -0.3219623 -0.210072 1.6676695 -0.2913541 -0.2225708 -0.3466158 0.7725676 1.4497730 -0.3466040 0.4043616 0.9370237 -0.2869891 -0.2417602 0.0213215 0.0047381 -0.0008674 -0.2033319 0.471173 -0.2240416 -0.3675837 2.0293765 -0.2921473 -0.1643309 -0.2148726 0.4180828 -0.1840168 0.8055766 2.1005660 0.2362856 0.9845269 -0.247425 -0.3290167 -0.2769094 -0.2165714 -0.2113297 -0.2032312 -0.2964961 -0.2723046 -0.2880967 -0.3889671 -0.3619845 -0.254554 -0.2234391 -0.2886389 -0.2423834 -0.4803733 -0.2116685 -0.3347133 -0.3767636 -0.2587587 0.2092882 -0.2301763 0.4452830 -0.2489132 -0.2125338 -0.27502 -0.1802970 -0.2082801 -0.2029419 1.2111770 -0.2905277 -0.4386438 -0.2627247 -0.1373812 0.1141919 -0.3699553 1.2114244 3.1078204 -0.3033004 -0.2679259 -0.4979340 -0.2493229 -0.2918325 -0.3210115 1.4113472 -0.3153851 -0.4607352 -0.2427205 -0.1877792 -0.2385517 0.9090513 1.0498784 1.4344455 -0.3754101 -0.3095768 -0.2531406 -0.1273378 -0.2273583 0.2958757 -0.1112706 -0.2454933 -0.237769 -0.2556597 -0.2558859 0.3065804 -0.3306073 0.2901556 -0.0704575 -0.1815231 -0.2815015 0.2148108 -0.1980432 -0.3741470 -0.2238381 -0.2200684 -0.3044181 -0.4636598 -0.0225969 -0.2527857 -0.2765858 -0.2022504 0.3061468 0.1553040 -0.2467981 1.7876762 -0.3199346 -0.2517382 -0.3355190 -0.2687588 -0.3523645 -0.3854322 -0.0833513 0.4240799 -0.2112762 -0.4250954 -0.1944808 -0.2110278 -0.5096671 -0.2534893 1.7783263 -0.2202784 -0.3097150 -0.3707219 -0.2305037 3.0706800 0.3605266 -0.1766781 0.9888489 -0.4280871 -0.2805776 -0.2083507 -0.1995629 -0.1828675 -0.37513 -0.3070740 -0.2163227 -0.2593466 -0.5551719 -0.3574879 -0.1534382 -0.2106675 -0.291384 0.3899663 -0.2436797 1.118433 0.5571836 -0.2221599 -0.2092243 -0.3427394 -0.2092828 -0.3907582 -0.4662025 1.4978619 -0.2363724 -0.2785179 0.9537283 0.7563712 1.6167038 -0.2916884 1.0882777 -0.5022962 0.0885393 -0.1761571 -0.2128057 -0.2649194 -0.2035329 -0.4348948 -0.2434664 -0.3186232 -0.1912958 -0.2638317 -0.247463 -0.2263396 1.1942357 -0.2873062 -0.2072372 -0.2135705 -0.2478094 -0.1952744 -0.4402687 -0.199335 1.8525353 -0.2342667 -0.2899096 0.3305516 -0.2551209 -0.2236754 -0.5089003 -0.2903215 -0.2575475 0.9250798 -0.1779382 -0.279416 -0.2988328 -0.1886804 0.6019445 -0.2500655 -0.2296109 0.3049080 -0.2202604 0.2032304 0.3749096 0.5332462 0.1443078 -0.0440354 -0.2277324 -0.3116438 -0.2012385 -0.2063031 -0.1970754 -0.3085002 -0.2159384 -0.3386373 -0.2366115 -0.2241185 -0.2646904 -0.1817069 -0.1102017 -0.4119245 -0.2831531 -0.3002747 -0.2631077 -0.1533210 1

Spliting

split data by 7:3, so 70% to training, 30% to test set. Therefore, training has 3621 records and 283 features. Now we still face on imbalanced class issue. I am going to use up-Sampling technique to get more sample in training and counter imbalance problem. (Deep down, I am not sure if decreasing features is a good idea because email classification is based on the analysis of email content, which is based on words. That is why I use up-Sampling to get more sample, at least it will potentially increase some accuracy)

## [1] 3621  283
## 
##    0    1 
## 2571 1050
## [1] 5142  283
## 
##    0    1 
## 2571 2571

Modeling

  • SVM
  • XGBoost
  • Neural Network

SVM

## 
## Call:
## svm.default(x = train.x, y = train.y)
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  radial 
##        cost:  1 
## 
## Number of Support Vectors:  1714
## 
##  ( 811 903 )
## 
## 
## Number of Classes:  2 
## 
## Levels: 
##  0 1

XGBoost

I’d run xgb directly, but instead of 10 iterations, I ran 30-50 iteration with the same parameters, the training accuracy was close to 0.98. However, I was skeptical about over-fitting. Therefore, I use cross validation technique to verify, it turns out that 10 iterations achieve roughly 98% accuracy and the accuracy of test set is roughly the same. So 10 iteration does not cause over-fitting.

## [1]  train-rmse:0.435379+0.000644    train-auc:0.831287+0.001557 test-rmse:0.435406+0.003412 test-auc:0.831384+0.014235 
## [2]  train-rmse:0.391378+0.000750    train-auc:0.897325+0.001090 test-rmse:0.391455+0.004456 test-auc:0.897360+0.009974 
## [3]  train-rmse:0.357934+0.000777    train-auc:0.942635+0.001695 test-rmse:0.358006+0.005402 test-auc:0.942323+0.007246 
## [4]  train-rmse:0.335086+0.000721    train-auc:0.957638+0.003213 test-rmse:0.335276+0.005875 test-auc:0.957666+0.007358 
## [5]  train-rmse:0.318852+0.001893    train-auc:0.958345+0.001906 test-rmse:0.319719+0.006737 test-auc:0.957473+0.005542 
## [6]  train-rmse:0.301760+0.001680    train-auc:0.963843+0.002668 test-rmse:0.303865+0.008830 test-auc:0.961979+0.007178 
## [7]  train-rmse:0.290199+0.001326    train-auc:0.967369+0.002179 test-rmse:0.292449+0.008155 test-auc:0.964990+0.005603 
## [8]  train-rmse:0.278997+0.001499    train-auc:0.971643+0.000562 test-rmse:0.281107+0.008285 test-auc:0.969354+0.004683 
## [9]  train-rmse:0.269254+0.002209    train-auc:0.975635+0.001221 test-rmse:0.271293+0.008287 test-auc:0.974302+0.002915 
## [10] train-rmse:0.260518+0.002076    train-auc:0.978173+0.001536 test-rmse:0.263489+0.008894 test-auc:0.975462+0.003155
## [1]  train-logloss:0.569878 
## [2]  train-logloss:0.489885 
## [3]  train-logloss:0.430045 
## [4]  train-logloss:0.388704 
## [5]  train-logloss:0.358802 
## [6]  train-logloss:0.328089 
## [7]  train-logloss:0.305985 
## [8]  train-logloss:0.286733 
## [9]  train-logloss:0.269471 
## [10] train-logloss:0.251683

Neural Network

For NN, there is going to be 2 neurons, and train 1 times. It took me too long to compute 10 time, so I decide to keep it as default. (Note: you don’t want to see the output of nn in detail because it involves everything shown below, and R will print a whole page or two to show)

Performance

  • SVM
  • XGBoost
  • Neural Network

SVM

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 998 103
##          1  35 415
##                                           
##                Accuracy : 0.911           
##                  95% CI : (0.8957, 0.9247)
##     No Information Rate : 0.666           
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.7932          
##                                           
##  Mcnemar's Test P-Value : 1.174e-08       
##                                           
##             Sensitivity : 0.9661          
##             Specificity : 0.8012          
##          Pos Pred Value : 0.9064          
##          Neg Pred Value : 0.9222          
##              Prevalence : 0.6660          
##          Detection Rate : 0.6435          
##    Detection Prevalence : 0.7099          
##       Balanced Accuracy : 0.8836          
##                                           
##        'Positive' Class : 0               
##

XBGoost

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 934 167
##          1   4 446
##                                           
##                Accuracy : 0.8897          
##                  95% CI : (0.8731, 0.9049)
##     No Information Rate : 0.6048          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.7582          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
##                                           
##             Sensitivity : 0.9957          
##             Specificity : 0.7276          
##          Pos Pred Value : 0.8483          
##          Neg Pred Value : 0.9911          
##              Prevalence : 0.6048          
##          Detection Rate : 0.6022          
##    Detection Prevalence : 0.7099          
##       Balanced Accuracy : 0.8617          
##                                           
##        'Positive' Class : 0               
##

NN

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    0    1
##          0 1008   93
##          1   19  431
##                                           
##                Accuracy : 0.9278          
##                  95% CI : (0.9138, 0.9402)
##     No Information Rate : 0.6622          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.8328          
##                                           
##  Mcnemar's Test P-Value : 5.279e-12       
##                                           
##             Sensitivity : 0.9815          
##             Specificity : 0.8225          
##          Pos Pred Value : 0.9155          
##          Neg Pred Value : 0.9578          
##              Prevalence : 0.6622          
##          Detection Rate : 0.6499          
##    Detection Prevalence : 0.7099          
##       Balanced Accuracy : 0.9020          
##                                           
##        'Positive' Class : 0               
##

Conclusion

Based on the table shown below, it looks like Neural Network works best, and XGBoost works the worst. that is not what I expected. I thought that these three modeling techniques should perform similarly because they are powerful than others. If ordering is required between the three, me personally would do NN > XGBoost > SVM.

##     model accuracy sensitivity specificity precision recall
## 1     SVM    0.911      0.9661      0.8012    0.9064 0.9661
## 2 XGBoost   0.8897      0.9957      0.7276    0.8483 0.9957
## 3      NN   0.9278      0.9815      0.8225    0.9155 0.9815

Concern

Like I mention before, spam email classification is based on the content of email. Analyzing sentence and words to judge if an email is spam or not. So that, does it mean the more sentence, the better spam detection? if so, do you think my dimension reduction here is necessary? if not, how are you going to do analysis and modeling with 3000+ features?

check repo with code