PCA

Dataset with missing names, and you want to quickly identify the relation between variables, identify the 'Principle Components'.

>library(ggplot2)

>data(mpg)

>data <- mpg[,c("displ", "year", "cyl", "cty", "hwy")]

# get the numeric columns only for this easy demo

>prcomp(data, scale=TRUE)

Standard deviations:

  [1] 1.8758132 1.0069712 0.5971261 0.2658375 0.2002613

Rotation:

  PC1         PC2        PC3         PC4         PC5

displ  0.49818034 -0.07540283  0.4897111  0.70386376 -0.10435326

year   0.06047629 -0.98055060 -0.1846807 -0.01604536  0.02233245

cyl    0.49820578 -0.04868461  0.5028416 -0.68062021  0.18255766

cty   -0.50575849 -0.09911736  0.4348234  0.15195854  0.72264881

hwy   -0.49412379 -0.14366800  0.5330619 -0.13410105 -0.65807527

Here is how you interpret the result:

(1) The standard deviations, which is the diagonal matrix in the middle when you apply the singular value decomposition. Explains how much variance each 'Principle Component'? / layer / transparency explains in the whole variance in the matrix. For example,

70 % = 1.8758132^2 / (1.8758132^2 + 1.0069712^2 + 0.5971261^2 + 0.2658375^2 + 0.2002613^2)

Which indicates the first column itself already explains 70% of the variance in the whole matrix.

(2) Now let's look at the first column in the rotation matrix / V:

          PC1      

displ  0.49818034

year   0.06047629

cyl    0.49820578

cty   -0.50575849

hwy   -0.49412379

We can see: displ has a positive relation with cyl and negative relation with cty and hwy. And in this dominant layer, year is not that obvious.

The makes sense, the more displacement or cylinders you have in your car, it probably has a very high MPG.

Here is the plot between the variables just for you information.

pairs(data)

density

d <- density(mtcars$mpg)

 
plot(d)

# Filled Density Plot
d <- density(mtcars$mpg)
plot(d, main="Kernel Density of Miles Per Gallon")
polygon(d, col="red", border="blue")

Box New

input=mtcars[,c('mpg','cyl')]    -  notch=false is box format and true is like some different format    
print(tail(input))

boxplot(mpg ~ cyl,data=mtcars,xlab="number of cylinders",ylab="miles per gallon",main="mileage data",notch=FALSE,varwidth=TRUE,col=c("green","yellow","purple"),names=c("high","medium","low"))

BoxPlot

input=mtcars[16:20,c('mpg','cyl')]         

 boxplot(mpg ~ cyl,data=input,xlab="number of cylinders",ylab="miles per gallon",main="mileage data")

Bar Plot

h=c(7,12,28,3,41)                 

m=c("mar","apr","may","jun","jul")

barplot(h,names.arg=m,xlab="month",ylab="revenue",col="blue",main="revenue chart",border="red")

___________________________________________________

colors=c("green","orange","brown")   

months=c("mar","apr","may","jun","jul")

regions=c("east","west","north")

values=matrix(c(2,4,5,3,5,2,5,3,7,8,9,4,7),nrow=3,ncol=5,byrow=TRUE)

barplot(values,names.arg=m,xlab="month",ylab="revenue",col=colors,main="revenue chart",border="red")

legend("topleft",regions,cex=1.3,fill=colors)

PIE Plot

x=c(21,62,10,53)

labels=c("london","newyork","singapore","Dubai")

piepercent=round(100*x/sum(x),1)

pie(x,labels,col=rainbow(length(x)),radius=1.0,main="popoular cities",clockwise = FALSE)

legend("topright",c("london","newyork","singapore","mumbai"), cex=0.8, fill=rainbow(length(x)))

Pie

x=c(21,62,10,53)
labels=c("london","newyork","singapore","Dubai")
pie(x,labels)

ANN

install.packages('neuralnet')

library("neuralnet")

#Going to create a neural network to perform sqare rooting

#Type ?neuralnet for more information on the neuralnet library

#Generate 50 random numbers uniformly distributed between 0 and 100

#And store them as a dataframe

traininginput <-  as.data.frame(runif(50, min=0, max=100))

trainingoutput <- sqrt(traininginput)

#Column bind the data into one variable

trainingdata <- cbind(traininginput,trainingoutput)

colnames(trainingdata) <- c("Input","Output")

#Train the neural network

#Going to have 10 hidden layers

#Threshold is a numeric value specifying the threshold for the partial

#derivatives of the error function as stopping criteria.

net.sqrt <- neuralnet(Output~Input,trainingdata, hidden=10, threshold=0.01)

print(net.sqrt)

#Plot the neural network

plot(net.sqrt)

#Test the neural network on some training data

testdata <- as.data.frame((1:10)^2) #Generate some squared numbers

net.results <- compute(net.sqrt, testdata) #Run them through the neural network

#Lets see what properties net.sqrt has

ls(net.results)

#Lets see the results

print(net.results$net.result)

#Lets display a better version of the results

cleanoutput <- cbind(testdata,sqrt(testdata),

                         as.data.frame(net.results$net.result))

colnames(cleanoutput) <- c("Input","Expected Output","Neural Net Output")

print(cleanoutput)