Gait data

Descriptive analysis

Load data

cf4 <- read.csv("cf4.txt", sep="")
#cf4 = do.call(rbind.data.frame, cf4)
df <- data.frame(matrix(unlist(cf4), nrow=2789, byrow=TRUE))
colnames(df) = names(cf4)
head(df)

##    rt.uaw  rt.uax  rt.uay  rt.uaz  rt.faw  rt.fax  rt.fay  rt.faz  rt.thw
## 1 -0.7614 -0.7614 -0.7614 -0.7614 -0.7604 -0.7604 -0.7604 -0.7604 -0.7604
## 2 -0.7565 -0.7565 -0.7565 -0.7565 -0.7565 -0.7506 -0.7506 -0.7506 -0.7506
## 3 -0.7516 -0.7458 -0.7458 -0.7458 -0.7458 -0.7458 -0.7458 -0.7401 -0.7401
## 4 -0.7647 -0.7647 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646
## 5 -0.7742 -0.7742 -0.7742 -0.7658 -0.7658 -0.7658 -0.7658 -0.7658 -0.7658
## 6 -0.7565 -0.7565 -0.7565 -0.7565 -0.7565 -0.7642 -0.7642 -0.7642 -0.7642
##    rt.thx  rt.thy  rt.thz  rt.llw  rt.llx  rt.lly  rt.llz  rt.ftw  rt.ftx
## 1 -0.7604 -0.7604 -0.7604 -0.7598 -0.7598 -0.7598 -0.7598 -0.7598 -0.7598
## 2 -0.7506 -0.7506 -0.7506 -0.7506 -0.7555 -0.7555 -0.7555 -0.7555 -0.7555
## 3 -0.7401 -0.7401 -0.7401 -0.7401 -0.7401 -0.7440 -0.7440 -0.7440 -0.7440
## 4 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7601
## 5 -0.7658 -0.7609 -0.7609 -0.7609 -0.7609 -0.7609 -0.7609 -0.7609 -0.7576
## 6 -0.7642 -0.7642 -0.7648 -0.7648 -0.7648 -0.7648 -0.7648 -0.7648 -0.7648
##    rt.fty  rt.ftz  lt.uaw  lt.uax  lt.uay  lt.uaz  lt.faw  lt.fax  lt.fay
## 1 -0.7598 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7558
## 2 -0.7555 -0.7580 -0.7580 -0.7580 -0.7580 -0.7580 -0.7580 -0.7580 -0.7587
## 3 -0.7440 -0.7440 -0.7440 -0.7561 -0.7561 -0.7561 -0.7561 -0.7561 -0.7561
## 4 -0.7601 -0.7601 -0.7601 -0.7601 -0.7601 -0.7601 -0.7644 -0.7644 -0.7644
## 5 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7587 -0.7587 -0.7587
## 6 -0.7648 -0.7715 -0.7715 -0.7715 -0.7715 -0.7715 -0.7715 -0.7715 -0.7646
##    lt.faz  lt.thw  lt.thx  lt.thy  lt.thz  lt.llw  lt.llx  lt.lly  lt.llz
## 1 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558
## 2 -0.7587 -0.7587 -0.7587 -0.7587 -0.7587 -0.7587 -0.7516 -0.7516 -0.7516
## 3 -0.7561 -0.7627 -0.7627 -0.7627 -0.7627 -0.7627 -0.7627 -0.7627 -0.7647
## 4 -0.7644 -0.7644 -0.7644 -0.7735 -0.7735 -0.7735 -0.7735 -0.7735 -0.7735
## 5 -0.7587 -0.7587 -0.7587 -0.7578 -0.7578 -0.7578 -0.7578 -0.7578 -0.7578
## 6 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646 -0.7570 -0.7570 -0.7570 -0.7570
##    lt.ftw  lt.ftx  lt.fty  lt.ftz
## 1 -0.7558 -0.7558 -0.7558 -0.7565
## 2 -0.7516 -0.7516 -0.7516 -0.7516
## 3 -0.7647 -0.7647 -0.7647 -0.7647
## 4 -0.7735 -0.7742 -0.7742 -0.7742
## 5 -0.7578 -0.7565 -0.7565 -0.7565
## 6 -0.7570 -0.7570 -0.7570 -0.7570

Rescale and plots

# scale data
library("dplyr")

## Warning: package 'dplyr' was built under R version 4.0.3

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

df_scaled <- df %>%           # Applying functions of dplyr
  mutate_at(names(df), ~(scale(.) %>% as.vector))

#df_scaled = scale(df)
#par(mfrow=c(2, 2))
#for (j in seq(1,36,4)){
#  for(i in 1:4) {
#  plot(cf4[,i+j],type="l")
  #lines(lowess(cf4[,i+j],f=.01), lwd=1, col=2)   
#  }
#}

max(df[,1])

## [1] 0.9848

head(df)

##    rt.uaw  rt.uax  rt.uay  rt.uaz  rt.faw  rt.fax  rt.fay  rt.faz  rt.thw
## 1 -0.7614 -0.7614 -0.7614 -0.7614 -0.7604 -0.7604 -0.7604 -0.7604 -0.7604
## 2 -0.7565 -0.7565 -0.7565 -0.7565 -0.7565 -0.7506 -0.7506 -0.7506 -0.7506
## 3 -0.7516 -0.7458 -0.7458 -0.7458 -0.7458 -0.7458 -0.7458 -0.7401 -0.7401
## 4 -0.7647 -0.7647 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646
## 5 -0.7742 -0.7742 -0.7742 -0.7658 -0.7658 -0.7658 -0.7658 -0.7658 -0.7658
## 6 -0.7565 -0.7565 -0.7565 -0.7565 -0.7565 -0.7642 -0.7642 -0.7642 -0.7642
##    rt.thx  rt.thy  rt.thz  rt.llw  rt.llx  rt.lly  rt.llz  rt.ftw  rt.ftx
## 1 -0.7604 -0.7604 -0.7604 -0.7598 -0.7598 -0.7598 -0.7598 -0.7598 -0.7598
## 2 -0.7506 -0.7506 -0.7506 -0.7506 -0.7555 -0.7555 -0.7555 -0.7555 -0.7555
## 3 -0.7401 -0.7401 -0.7401 -0.7401 -0.7401 -0.7440 -0.7440 -0.7440 -0.7440
## 4 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7590 -0.7601
## 5 -0.7658 -0.7609 -0.7609 -0.7609 -0.7609 -0.7609 -0.7609 -0.7609 -0.7576
## 6 -0.7642 -0.7642 -0.7648 -0.7648 -0.7648 -0.7648 -0.7648 -0.7648 -0.7648
##    rt.fty  rt.ftz  lt.uaw  lt.uax  lt.uay  lt.uaz  lt.faw  lt.fax  lt.fay
## 1 -0.7598 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7558
## 2 -0.7555 -0.7580 -0.7580 -0.7580 -0.7580 -0.7580 -0.7580 -0.7580 -0.7587
## 3 -0.7440 -0.7440 -0.7440 -0.7561 -0.7561 -0.7561 -0.7561 -0.7561 -0.7561
## 4 -0.7601 -0.7601 -0.7601 -0.7601 -0.7601 -0.7601 -0.7644 -0.7644 -0.7644
## 5 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7576 -0.7587 -0.7587 -0.7587
## 6 -0.7648 -0.7715 -0.7715 -0.7715 -0.7715 -0.7715 -0.7715 -0.7715 -0.7646
##    lt.faz  lt.thw  lt.thx  lt.thy  lt.thz  lt.llw  lt.llx  lt.lly  lt.llz
## 1 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558 -0.7558
## 2 -0.7587 -0.7587 -0.7587 -0.7587 -0.7587 -0.7587 -0.7516 -0.7516 -0.7516
## 3 -0.7561 -0.7627 -0.7627 -0.7627 -0.7627 -0.7627 -0.7627 -0.7627 -0.7647
## 4 -0.7644 -0.7644 -0.7644 -0.7735 -0.7735 -0.7735 -0.7735 -0.7735 -0.7735
## 5 -0.7587 -0.7587 -0.7587 -0.7578 -0.7578 -0.7578 -0.7578 -0.7578 -0.7578
## 6 -0.7646 -0.7646 -0.7646 -0.7646 -0.7646 -0.7570 -0.7570 -0.7570 -0.7570
##    lt.ftw  lt.ftx  lt.fty  lt.ftz
## 1 -0.7558 -0.7558 -0.7558 -0.7565
## 2 -0.7516 -0.7516 -0.7516 -0.7516
## 3 -0.7647 -0.7647 -0.7647 -0.7647
## 4 -0.7735 -0.7742 -0.7742 -0.7742
## 5 -0.7578 -0.7565 -0.7565 -0.7565
## 6 -0.7570 -0.7570 -0.7570 -0.7570

Plots of differences

Correlation Analysis

Correlation coefficient for each device

## Warning: package 'psych' was built under R version 4.0.5

Correlation coefficients between different devices

Cross correlation with lag

## Warning: package 'astsa' was built under R version 4.0.5

## 
## Attaching package: 'astsa'

## The following object is masked from 'package:psych':
## 
##     scatter.hist

Correlation coefficient matrix and eigenvector, PCA

## Warning: package 'factoextra' was built under R version 4.0.5

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 4.0.3

## 
## Attaching package: 'ggplot2'

## The following objects are masked from 'package:psych':
## 
##     %+%, alpha

## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

## Warning: ggrepel: 2786 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

## Warning: ggrepel: 2786 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

Unscaled

## Warning: ggrepel: 2781 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

## Warning: ggrepel: 2779 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

## Warning: ggrepel: 29 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

Correlation plot

Overall correlation plot

A plain version
another version

Pearson v.s. Spearman

Extra plots

more customized version
A better version

Same direction

Largest correlations

Overall

Try a plot

largest correlation

# function for plot top correlations

top_cor <- function(df, n){
  
  n = 2*n
  # compute the correlation matrix and minus diagonal 
  m = cor(df,method = "spearman") - diag(dim(df)[2])
  
  # find the top correlations
  ij_pos <- which(m >= sort(m, decreasing=T)[n], arr.ind=TRUE)
  #sort(m[ij_pos])

  ij_neg <- which(-m >= sort(-m, decreasing=T)[n], arr.ind=TRUE)
  #sort(m[ij_neg])
  
  # create a zero matrix
  test = matrix(0,nrow = dim(df)[2], ncol = dim(df)[2])
  
  # pass index to zero matrix
  for (i in 1:n) {
  test[ij_pos[i,1],ij_pos[i,2]]=m[ij_pos[i,1],ij_pos[i,2]]
  test[ij_neg[i,1],ij_neg[i,2]]=m[ij_neg[i,1],ij_neg[i,2]]
  }
  
  
  # return results
  #return(test1)
  # plot 
  rownames(test) = names(df)
  colnames(test) = names(df)
  corrplot::corrplot(test)
  #return(test)
}

Top correlation overall

Each direction (make sense??)

##  [1] 0.6339022 0.6339022 0.6842742 0.6842742 0.6870818 0.6870818 0.6955016
##  [8] 0.6955016 0.7512215 0.7512215

##  [1] -0.5927696 -0.5927696 -0.5123219 -0.5123219 -0.4969329 -0.4969329
##  [7] -0.4735347 -0.4735347 -0.4240953 -0.4240953

##  [1] 0.4131197 0.4131197 0.4432934 0.4432934 0.4680090 0.4680090 0.5917081
##  [8] 0.5917081 0.6848475 0.6848475

##  [1] -0.5116982 -0.5116982 -0.4599920 -0.4599920 -0.4142687 -0.4142687
##  [7] -0.3872607 -0.3872607 -0.3631521 -0.3631521

##  [1] 0.5303046 0.5303046 0.6271936 0.6271936 0.6531508 0.6531508 0.6855158
##  [8] 0.6855158 0.7278851 0.7278851

##  [1] -0.7197638 -0.7197638 -0.6555251 -0.6555251 -0.5870003 -0.5870003
##  [7] -0.5031092 -0.5031092 -0.4891882 -0.4891882

##  [1] 0.6984086 0.6984086 0.7002466 0.7002466 0.7258311 0.7258311 0.7692318
##  [8] 0.7692318 0.7769656 0.7769656

##  [1] -0.7332564 -0.7332564 -0.7184782 -0.7184782 -0.6900608 -0.6900608
##  [7] -0.6380025 -0.6380025 -0.6034289 -0.6034289

Gait data

Ziwei Ma

6/8/2021

Descriptive analysis

Correlation Analysis

Correlation plot

Overall correlation plot

Pearson v.s. Spearman

Extra plots

Same direction

Largest correlations

Overall

Top correlation overall

Each direction (make sense??)

Each direction plot