In a very simple language I will explain
you what is log
or logarithmic function and what is the
significance of
it in data science and machine learning.
We'll also look at some Python code
let's get started
let's say I have five dollar and I am
putting that in a bank
which gives me five X return so if I put
five it will give me five x
if I put seven dollar it will give me
seven x return it's a magic bank you
know very customer friendly bank
after one year I will have 25 after two
year I will have 125
because every year it is being
multiplied by 5x to represent this
concept
in mathematics you use something called
exponent.
so exponent meaning 5 raised to 2 is 25
5 is to 3 is 125.
now let me ask a different question or
rather a reverse
question where I have 125 dollar
today in my bank. I know that at
some point I started with five dollar
base
investment but I don't know how many
years
it took to get to 125
so how do you find that so the question
is again simple I started with
base investment of five dollar. I know
that bank is giving me
5x return but I don't know how many
years will it take to
make that money 125 dollar. Well
that answer can be given by log function
so log to the base 5 because I started
with base investment of 5
125 is the amount I have today and
that can tell me that it takes three
years
so you see log is basically a
reverse or an inverse
of an exponent function it tells you
125 dollar is a given amount how many
years will it take
for your base amount which is 5
dollar to become 125
and the answer is 3. The popular log
is log to the base 10
and log 10 to the base 10 is 1.
in general log x to the base x is 1. You
have to remember this formula
if you have log 100 to the base 10 that
can be written as
this and then 2 comes in the front and
you
already know log 10 to the base 10 is 1
so this becomes 2.
similarly log 1000 to the base 10 is
3. Now let's see how log can be used in
the data analysis process
so here i have downloaded a company's
revenue into my pandas data frame. I have
six companies
and these are the revenues for example
amazon has 386 billion dollar a year.
Uber has 11 and so on now if I want to
compare revenues using a bar
chart you know which is what people
normally do they use
bar chart or different kind of charting
visualization
for doing data analysis. So here I am
using
you know by a bar chart for comparing
the revenues
and what I will notice is since Amazon's
bar
is so high it is almost flattening
the smaller bars so here I'm having hard
time comparing Jindal steel and Axis
bank
because the bars are almost looking same
see
you see only one big bar everything else
is kind of similar
log axis solve this comparison problem
so if you want to
do comparison of all the smaller players
in a better way
you can run the same function df dot
plot
same exactly same function but you
supply
additional argument called log y is
equal to true
and you get this as a result now you see
the bars are little comparable. Here I
can at least say
jindal stills revenues are less than Axis
bank access bank
is close to five you see this is 10
this is hundred so here Axis Bank is
close to 5.
Jindas is little less than 5.
Vedanta is more than ten so you see
Vedanta
is what 11. X is 5.6 4.7
and so on so using log axis you can do
better comparison
when you have some values which are very
high and
other values are in average scale
so you will see people using log Axis
on occasions like this a lot in the
jupiter notebook when you're performing
your data analysis
another use case of log is using log
transform in machine learning.
Here is a classical problem of
predicting if
a loan should be approved for a given
person
for a person there are different
features such as credit score
income and age and based on these three
columns you are deciding if loan will be
approved or not and this is a standard
supervised learning problem. Now if you
notice income column
here you will see that Puja's income is
very very high
550 000 a year versus all other players
are
32000, 77000 a year so
you have this one data sample which is
very high income you you might have
couple of
such samples and when you train a
machine learning models
what happens is because of the magnitude
of this
data point it will negatively influence
your model. So basically
your machine learning model will be
biased you know
so to solve this problem you can create
a new column called log income so you
see the last column here
and that will be a simple log of this
income so log to the base 10
of this column gives you this. Now here
you see puja's income is 5.7
and rest of the people are 4.8, 4.5
so log will bring all these values on
more
comparable scale so you can compare
these values in a better way
and when you train machine learning
model using these comparable values
the model will not be biased and it will
give you more accurate results.
earthquake measuring earthquake is
another classical
example of a logarithm function
here when you are comparing let's say
earthquake 5 versus
earthquake 4 you can tell one thing
immediately which is earthquake
of scale 5 is 10 times more powerful
than
scale 4 so if you're living in
California if you're going through
earthquake
and you know if it is 4 versus 5
versus 6
6 is very very high so 5 is 10
times
more powerful than four 6 is 10 times
more powerful than five okay
so I have been to an earthquake
situation in India in the state of
gujarat where the scale was like
somewhat around seven
and it was devastating and I have heard
about earthquakes
with with scale you know five and six
and I always wonder like
why you know our earthquake was seven
and others are like 4 and 5. So why
that earthquake with seven scale was
more more devastating and the reason was
it was on a logarithmic
scale. So I hope this gives you some
understanding of
log and the use of that and data
analysis and machine learning
there are many more use cases as well
such as log is used in
loss function as well but this gives
you some base understanding.
I will see you in a next video with
another interesting math and statistics
topic for
data science and machine learning if you
like this video please share it with
your friends so
they also get some understanding of
logarithm. Thank You.