IBM-Summit

Introduction

We had discussed HPC race previously. See: https://rpubs.com/alex-lev/696179, https://rpubs.com/alex-lev/694840, https://rpubs.com/alex-lev/693131, https://rpubs.com/alex-lev/553777

TOP500 data

Data for November 2020 can be downloaded here: https://www.top500.org/lists/top500/2020/11/

Filtering Data

Note: the original names of variables were changed (truncated, concatenated and simplified) for the purpose of data exploration and visualization as much as possible. 

library(readxl)
library(tidyverse)
library(tidyquant)
library(broom)
library(DT)
library(knitr)
library(popbio)
library(pscl)
library(caTools)



TOP500_202011 <- read_excel("top500/TOP500_202011.xlsx")
names(TOP500_202011)
##  [1] "Rank"                        "PreviousRank"               
##  [3] "FirstAppearance"             "FirstRank"                  
##  [5] "Name"                        "Computer"                   
##  [7] "Site"                        "Manufacturer"               
##  [9] "Country"                     "Year"                       
## [11] "Segment"                     "TotalCores"                 
## [13] "AcceleratorCoProcessorCores" "Rmax"                       
## [15] "Rpeak"                       "Nmax"                       
## [17] "Nhalf"                       "HPCG"                       
## [19] "Power"                       "PowerSource"                
## [21] "PowerEfficiency"             "Architecture"               
## [23] "Processor"                   "ProcessorTechnology"        
## [25] "ProcessorSpeed"              "OperatingSystem"            
## [27] "OSFamily"                    "AcceleratorCoProcessor"     
## [29] "CoresperSocket"              "ProcessorGeneration"        
## [31] "SystemModel"                 "SystemFamily"               
## [33] "InterconnectFamily"          "Interconnect"               
## [35] "Continent"                   "SiteID"                     
## [37] "SystemID"

Problem

We want to classify HPC mainframes of China and USA, applying General Linear Model with logistic regression.

TOP500_USCH <- as_tibble(TOP500_202011) %>% filter(Country %in% c("United States","China")) %>% select(Country,  Year, TotalCores, Rmax, Rpeak, Nmax, Power, PowerEfficiency, ProcessorSpeed, CoresperSocket) %>%mutate (Country=as.factor(Country)) %>% drop_na()

TOP500_USCH  %>% datatable() #kable(align = "r",caption = "TOP500: China - USA")

This dataset above contains 98 individuals (mainframes) and 10 variables.

Logistic regression model

set.seed(12345)
MisClassError <- c()
for (i in 1:3000) {
train <- sample_frac(TOP500_USCH,0.5,replace = F)
test <-TOP500_USCH %>% setdiff(train)
fit.glm <- glm(Country ~.,data = train,family = binomial(link = "logit"))
res_test <- predict.glm(fit.glm,test,type="response")

fitted.results <- ifelse(res_test > 0.5,1,0)
MisClassError[i] <- round(mean(fitted.results != ifelse(test$Country=="China",0,1)),3)

}

summary(1-MisClassError)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.6420  0.8840  0.9160  0.9079  0.9370  0.9790
quantile(1-MisClassError,c(0.1,0.5,0.9))
##   10%   50%   90% 
## 0.853 0.916 0.947
print(paste('Mean Classifucation Accuracy =',round(mean(1-MisClassError),3)))
## [1] "Mean Classifucation Accuracy = 0.908"
par(mfrow=c(1,1))
hist(1-MisClassError,breaks = 20,col="blue",main = "True Classification Proportion",
     xlab = "Proportion")

summary(fit.glm)
## 
## Call:
## glm(formula = Country ~ ., family = binomial(link = "logit"), 
##     data = train)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
##   0.00    0.00    0.00    0.00    8.49  
## 
## Coefficients:
##                   Estimate Std. Error   z value Pr(>|z|)    
## (Intercept)      2.608e+16  1.355e+10   1925498   <2e-16 ***
## Year            -1.401e+13  6.708e+06  -2088551   <2e-16 ***
## TotalCores      -1.609e+09  1.425e+02 -11285719   <2e-16 ***
## Rmax             1.789e+11  2.701e+03  66240523   <2e-16 ***
## Rpeak           -1.415e+11  2.835e+03 -49911351   <2e-16 ***
## Nmax             1.822e+08  6.895e+00  26421993   <2e-16 ***
## Power            3.534e+11  5.741e+03  61548681   <2e-16 ***
## PowerEfficiency  3.490e+13  4.708e+06   7413749   <2e-16 ***
## ProcessorSpeed   4.108e+10  3.844e+04   1068658   <2e-16 ***
## CoresperSocket   4.920e+13  1.019e+06  48267957   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance:  65.438  on 48  degrees of freedom
## Residual deviance: 360.437  on 39  degrees of freedom
## AIC: 380.44
## 
## Number of Fisher Scoring iterations: 14

Classification by specifications

Here we generate classification charts by specifications (variables), applied in glm model above.

fun1 <- function(x, column, model){
  logi.hist.plot(x[[column]],ifelse(x[[1]]=="China",1,0),boxp=FALSE,type="hist",col="gray",
                 xlabel = colnames(x)[[column]],
                 mainlabel = "Probability of HPC CHINA in TOP500",logi.mod = 2)
  points(x[[column]],fitted(model),pch=20)
  grid()

}

set.seed(12345)
fit.glm <- glm(Country ~.,data = TOP500_USCH,family = binomial(link = "logit"))
par(mfrow=c(3,3))
for (i in 2:length(TOP500_USCH)){
  fun1(TOP500_USCH,i,fit.glm)
}

Conclusion

  1. Logistic regression provides 90% true classification of HPC mainframes by country due to specifications.
  2. The most common way for logistic regression classification is glm(Country~Rmax/Rpeak) discussed in https://rpubs.com/alex-lev/693131.