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(MASS)
library(klaR)
library(tidyverse)
library(readxl)
library(DT)
library(knitr)
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 Linear Discriminant Analysis (LDA).

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.

Linear Discriminant Analysis

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.lda<-lda(Country~., data = train)
prd.lda<-predict(fit.lda,test)
MisClassError[i] <-sum(ifelse(prd.lda$class!=test$Country,1,0))/length(test$Country)
}

summary(1-MisClassError)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.5652  0.7826  0.8125  0.8147  0.8511  0.9792

quantile(1-MisClassError,c(0.1,0.5,0.9))

##       10%       50%       90% 
## 0.7446809 0.8125000 0.8775510

print(paste('Mean Classifucation Accuracy =',round(mean(1-MisClassError),3)))

## [1] "Mean Classifucation Accuracy = 0.815"

par(mfrow=c(1,1))
hist(1-MisClassError,breaks = 10,col="blue",main = "True Classification Proportion",
     xlab = "Proportion")

Classification by specifications

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

fit.lda<-lda(Country~., data = train)
fit.lda

## Call:
## lda(Country ~ ., data = train)
## 
## Prior probabilities of groups:
##         China United States 
##     0.6122449     0.3877551 
## 
## Group means:
##                   Year TotalCores      Rmax     Rpeak    Nmax     Power
## China         2018.333   86191.87  1845.025  5556.772 4152753  839.5687
## United States 2017.579  290629.68 15259.898 21096.322 5710221 2834.3679
##               PowerEfficiency ProcessorSpeed CoresperSocket
## China                3.620117       2344.333       14.66667
## United States        5.570498       2387.895       28.00000
## 
## Coefficients of linear discriminants:
##                           LD1
## Year            -2.309067e-01
## TotalCores       6.023370e-07
## Rmax             8.044349e-05
## Rpeak           -7.267139e-05
## Nmax             4.807595e-08
## Power            1.736957e-04
## PowerEfficiency  1.190417e-03
## ProcessorSpeed   1.501589e-03
## CoresperSocket   8.499059e-02

plot(fit.lda)

prd.lda<-predict(fit.lda,test)
cbind(prd.lda,test) %>%  kable(align = "r",caption = "TOP500: China - USA")

TOP500: China - USA
class	posterior.China	posterior.United States	LD1	Country	Year	TotalCores	Rmax	Rpeak	Nmax	Power	PowerEfficiency	ProcessorSpeed	CoresperSocket
United States	0.0325934	0.9674066	2.2677565	United States	2018	1572480	94640.00	125712.000	11902464	7438.28	12.7233715	3100	22
United States	0.0000000	1.0000000	27.2249760	China	2016	10649600	93014.59	125435.904	12288000	15371.00	6.0513040	1450	260
United States	0.0074150	0.9925850	3.0734836	China	2018	4981760	61444.50	100678.664	9773000	18482.00	3.3245590	2200	12
United States	0.0050262	0.9949738	3.2827541	United States	2016	622336	14014.70	27880.653	6984960	3939.00	3.5579335	1400	68
United States	0.2164626	0.7835374	1.1422629	United States	2016	241108	5951.55	7107.149	6500160	4407.00	1.3504765	2800	10
China	0.5566414	0.4433586	0.3324499	China	2018	163840	4325.00	6134.170	1876000	380.00	11.3815789	2000	32
United States	0.3811640	0.6188360	0.7133828	United States	2020	71424	4281.00	6628.150	5491968	960.00	4.4593750	2900	24
United States	0.3940838	0.6059162	0.6842665	United States	2015	145920	4042.46	5369.856	8338176	1800.00	2.2458111	2300	16
China	0.7798834	0.2201166	-0.2224824	United States	2014	72800	3577.00	6131.840	2336000	1498.90	2.3864167	2200	10
China	0.7038960	0.2961040	-0.0090202	United States	2016	60512	3307.00	4896.512	1419552	349.50	9.4620887	2200	20
United States	0.0898173	0.9101827	1.6929276	United States	2014	225984	3143.52	4881.254	2541684	6327.55	0.4967989	2700	12
United States	0.2119009	0.7880991	1.1567611	United States	2015	152692	3126.24	5610.481	5572800	4819.50	0.6486648	2300	18
United States	0.3918472	0.6081528	0.6892818	United States	2013	194616	2539.13	3388.032	4032000	1384.00	1.8346315	2600	8
United States	0.3716777	0.6283223	0.7350012	United States	2014	100064	2485.00	3682.355	6441408	1465.78	1.6953431	2300	16
China	0.7186991	0.2813009	-0.0475855	United States	2019	46080	2375.54	3686.400	4872960	578.10	4.1092199	2500	20
United States	0.0102314	0.9897686	2.8997476	United States	2020	19840	2356.00	2812.800	1262888	89.94	26.1952413	2250	64
China	0.9395062	0.0604938	-1.0129765	China	2019	67200	2192.00	4515.840	5097000	740.00	2.9621622	2100	16
China	0.7901082	0.2098918	-0.2548926	China	2019	40960	2109.00	3434.086	5153000	430.00	4.9046512	2600	16
China	0.9652747	0.0347253	-1.3243595	China	2019	44032	2087.00	3843.379	503000	260.00	8.0269231	2300	12
China	0.6909118	0.3090882	0.0238948	China	2014	174720	2071.39	3074.534	2366976	997.00	2.0776229	2200	12
China	0.9606012	0.0393988	-1.2542226	China	2018	121920	1979.00	4096.512	6769000	1216.00	1.6274671	2100	8
China	0.9411639	0.0588361	-1.0287814	China	2019	60800	1976.00	4085.760	4848000	660.00	2.9939394	2100	16
China	0.8569216	0.1430784	-0.5032888	China	2019	47600	1955.00	3960.320	3744000	650.00	3.0076923	2600	14
China	0.8842030	0.1157970	-0.6332138	China	2019	53280	1952.00	3921.408	3494000	570.00	3.4245614	2300	18
China	0.9455579	0.0544421	-1.0727910	China	2019	58112	1934.00	3905.126	3870000	630.00	3.0698413	2100	16
China	0.8575688	0.1424312	-0.5061177	China	2019	46200	1901.00	3843.840	3689000	630.00	3.0174603	2600	14
China	0.9419946	0.0580054	-1.0368600	China	2019	55040	1838.00	3698.688	4613000	600.00	3.0633333	2100	16
China	0.9417742	0.0582258	-1.0347059	China	2019	54240	1815.00	3644.928	4626000	600.00	3.0250000	2100	16
China	0.7993553	0.2006447	-0.2852175	China	2019	30600	1814.00	2674.100	824000	180.00	10.0777778	2500	20
China	0.9273206	0.0726794	-0.9078296	China	2018	105000	1790.00	3696.000	7657000	1100.00	1.6272727	2200	10
China	0.9278801	0.0721199	-0.9122859	China	2018	97920	1736.00	7206.912	6750000	1000.00	1.7360000	2300	12
United States	0.4429828	0.5570172	0.5766908	United States	2015	57600	1703.28	2304.000	3450432	2880.00	0.5914167	2500	12
China	0.9102326	0.0897674	-0.7849283	China	2018	97920	1683.00	3446.784	6750000	1050.00	1.6028571	2200	12
United States	0.2103187	0.7896813	1.1618427	United States	2011	31524	1653.92	2467.699	3745920	558.60	2.9608306	2100	20
China	0.5127871	0.4872129	0.4267976	United States	2015	48960	1635.02	2036.736	3950400	956.25	1.7098248	2600	12
China	0.9322958	0.0677042	-0.9486215	China	2018	92000	1562.00	3238.400	7167000	960.00	1.6270833	2200	10
China	0.7302297	0.2697703	-0.0784871	United States	2016	53352	1524.72	1792.627	4268160	603.40	2.5268810	2100	18
China	0.8107501	0.1892499	-0.3240628	United States	2019	23040	1464.00	1739.776	2582016	94.00	15.5744681	2400	20
China	0.8959148	0.1040852	-0.6972881	China	2018	26180	1432.90	2153.536	1186560	159.94	8.9589846	2400	14
China	0.8992554	0.1007446	-0.7167281	China	2018	30240	1418.00	2413.824	936000	240.00	5.9083333	2400	14
China	0.8397313	0.1602687	-0.4317595	China	2018	52080	1416.00	1999.872	4895000	560.00	2.5285714	2400	14
China	0.9280924	0.0719076	-0.9139850	China	2018	78000	1405.00	5740.800	6024000	800.00	1.7562500	2300	12
China	0.7942162	0.2057838	-0.2682392	China	2018	28000	1405.00	2329.600	3590000	350.00	4.0142857	2600	14
China	0.9024748	0.0975252	-0.7360120	China	2018	30624	1389.00	2459.002	829000	176.00	7.8920455	2400	14
China	0.9452403	0.0547597	-1.0695006	China	2019	43200	1379.00	2903.040	4086000	480.00	2.8729167	2100	16
China	0.9196537	0.0803463	-0.8497442	China	2018	78720	1345.00	2770.944	6052000	810.00	1.6604938	2200	12

  #posterior probabilities of classification  combined with initial classes (Parties)
table(prd.lda$class,test$Country)#confusion matrix

##                
##                 China United States
##   China            26             6
##   United States     2            12

partimat(Country~log(TotalCores)+log(Rpeak), data = train,method="lda")

Conclusion

Linear Discriminant Analysis provides 80% true classification of HPC mainframes by country due to specifications.
The most common way for LDA classification is Country~log(TotalCores)+log(Rpeak).

TOP500 HPC Race by LDA: China - United States

Alexander Levakov, Senior Research Fellow, Ph.D