Before we jump into various ML concepts and algorithms, let’s have a quick look into basic workflow when we apply Machine Learning to a problem.
A short brief about Machine Learning, it’s association with AI or Data Science world is here.
How does Machine Learning help?
Machine Learning is about having a training algorithm that helps predict an output based on the past data. This input data can keep on changing and accordingly the algorithm can fine tune to provide better output.
It has vast applications across. For example, Google is using it to predict natural disasters like floods. A very common use we hear these days in news are usage in Politics and how to attack the demography of voters.
How does Machine Learning work?
Data is the key here. More the data is, better the algorithm can learn and fine tune. For any problem output, there would be multiple factors at play. Some of them would have more affect then others. Analyzing and applying all such findings are part of a machine learning problem. Mathematically, ML converts a problem output as a function of multiple input factors.
Y = f(x)
Y = predicted output x = multiple factors as an input
How does a typical ML workflow look?
There is a structured way to apply ML on a problem. I tried to put the workflow in a pictorial view to easily visualize and understand it:
It’s goes in a cycle and once we have some insights from the published model, it goes back into the funnel as learning to make output better.
Roughly, Data scientists spend 60% of their time on cleaning and organizing data
Walk through an example?
Let’s use dataset of Titanic survivors found here and run through basic workflow to see how certain features like traveling class, sex, age and fare are helping us assess survival probability.
Load data from file
Data could be in various format. Easiest is to have it in a csv and then load it using pandas. More details around how to play with data is discussed here. .
# lets load and see the info of the dataset
titanicdf = pd.read_csv("data-files/titanic.csv")
print(titanicdf.info())
It’s not always that the data captured is the only data you need. You will have a superset of data that has additional information which are not relevant for your problem statement. This data will work as a noise and thus it’s better to clean the dataset before starting to work on them for any ML algorithm. .
# there seems to be handful of columns which
# we might not need for our analysis
# lets drop all those column that we know
# are irrelevant
titanicdf.drop(['embarked','body','boat','name',
'cabin','home.dest','ticket', 'sibsp', 'parch'],
axis='columns', inplace=True)
titanicdf.head(2)
pclass
survived
sex
age
fare
0
1
1
female
29
211.3375
1
1
1
male
0.9167
151.55
Data analysis
There could be various ways to analyze data. Based on the problem statement, we would need to know the general trend of the data in discussion. Statistics Probability Distribution knowledge help here. For gaining insights to understand more around correlations and patterns, data visualization based insights help. .
# let's see if there are any highly corelated data
# if we observe something, we will remove that
# one of the feature to avoid bias
import seaborn as sns
sns.pairplot(titanicdf)
# looking at graphs, seems we don't have
# anything right away to remove.
Data transform – Ordinal/Nominal/Datatype, etc
In order to work through data, it’s easy to interpret once they are converted into numbers (from strings) if possible. This helps them input them into various statistics formulas to get more insights. More details on how to apply numerical modifications to data is discussed here. .
# There seems to be 3 class of people,
# lets represent class as numbers
# We don't have info of relative relation of
# class so we will one-hot-encode it
titanicdf = pd.get_dummies(titanicdf,
columns=['pclass'])
# Lets Convert sex to a number
from sklearn import preprocessing
le = preprocessing.LabelEncoder()
titanicdf["sex"] = le.fit_transform(titanicdf.sex)
titanicdf.head(2)
survived
sex
age
fare
pclass_1
pclass_2
pclass_3
0
1
0
29
211.3375
1
0
0
1
1
1
0.9167
151.55
1
0
0
Data imputation: Fill the missing values
There are always some missing data or an outlier. Running algorithms with missing data could lead to inconsistent results or algorithm failure. Based on the context, we can choose to remove them or fill/replace them with an appropriate value. .
# When we saw the info, lots of age were missing
# Missing ages values filled with mean age.
titanicdf.loc[ titanicdf["age"].isnull(), "age" ] =
titanicdf["age"].mean()
# titanicdf.loc[ titanicdf["fare"].isnull(), "fare"]
# = titanicdf["fare"].mean()
# => can do but we will use another way
titanicdf.info()
# When we saw the info,
# 1 fare was missing
# Lets drop that one record
titanicdf.dropna(inplace=True)
titanicdf.info()
#<class 'pandas.core.frame.DataFrame'>
#Int64Index: 1308 entries, 0 to 1308
Normalize training data
At times, various data in context are of different scales. In such cases, if the data is not normalized, algorithm can induce bias towards the data that has higher magnitude. Eg, feature A value range is 0-10 and feature B range is 0-10000. In such case, even though a small change in magnitude of A can make a difference but if data is not normalized, feature B will influence results more (which could be not the actual case). .
X = titanicdf
y = X['survived']
X = X.drop(['survived'], axis=1)
# Scales each column to have 0 mean and 1 std.dev
from sklearn import preprocessing
X_scaled = preprocessing.scale(X)
Split data – Train/Test dataset
It’s always best to split the dataset into two unequal parts. Bigger one to train the algorithm and then then smaller one to test the trained algorithm. This way, algorithm is not biased to just the input data and results for test data can provide better picture. .
Once we have our training dataset ready as per our need, we can apply machine learning algorithms and find which model fits in best. .
# for now, picking any one of the classifier - KN
# Ignore details or syntax for now
from sklearn.neighbors import KNeighborsClassifier
dtc = KNeighborsClassifier(n_neighbors=5)
dtc.fit(X_train,y_train)
Check the accuracy of model
In order to validate the model, we use test dataset where comparing the predicted value by model to actual data helps us know about ML model accuracy. .
import sklearn.metrics as met
pred_knc = dtc.predict(X_test)
print( "Nearest neighbors: %.3f"
% (met.accuracy_score(y_test, pred_knc)))
Nearest neighbors: 0.817
Voila! With basic workflow, we have a model that can predict the survivor with more than 80% probability.
Currently, it covers examples on following datasets:
Titanic Survivors
Sci-kit Iris
Sci-kit Digits
Bread Basket Bakery
Over time, I would continue building on the same repository with more samples with different algorithms.
Closure
Believe, now it’s pretty clear on how we can attack any problem for an insight using Machine learning. Try out and see for yourself.
We can apply Machine Learning to multiple problems in multiple fields. I have shared a pictorial view of sectors in the AI section that are already leveraging it’s benefit.
Off late, Microsoft has been working on providing more and more learning materials. This is as per their Global Skills Initiative aimed at helping 25 million people worldwide acquire new digital skills.
Our goal is to ignite the passion to solve important problems relevant to their lives, families and communities.
Microsoft
Last week, they partnered with Netflix to release a new learning experience featuring a young female hero Fei Fei, who has a passion for science and explores space.
Newly launched
Microsoft has launched three new modules under Explore Space with “Over the Moon” learning path. These modules will help learn basic concepts of data science, artificial intelligence and machine learning:
Plan a Moon Mission using the Python Pandas Library
Predict Meteor Showers using Python and VC Code
Use AI to Recognize Objects in Images using Azure Custom Vision
The movie’s story takes place in a beautifully animated universe and tackles problems real-life space engineers face.
How is it?
They cover the basic workflow of a machine learning problem similar to what I shared in my previous article here.
Looking at it, seems a fun way to learn and explore the data world. Microsoft is really trying to make things simple and available to all. An effort worth to try out. Would recommend and ask to give it a shot.
Let’s walk into the Data Science world and see what it means and how does it connect with other terms that we often hear in the context – Artificial Intelligence & Machine Learning.
What is Data Science?
In a context of a particular domain, data science is gaining insights into data through statistics, computation and visualization. Below diagram represents this multi-focal field well:
For a real world problem, based on statistics, we make certain assumptions. Based on assumptions, we make a learning model using mathematics. With this model, we make software that can help validate and solve the problem. This leads to solving complex problems fast and more accurately.
How to use Data Science?
Clearly, it can be defined as a process. When followed, it would help move towards destination with proper next steps:
There are multiple iterative stages that solves specific queries. Based on answers to the queries, we might have to circle back and reassess the steps of the entire process.
Various stages involved?
Once we have a defined process, it’s easier to break it down into different functional groups. It would help us interpret how to visualize, connect them and know who can help us at each of those stage:
There is a strong correlation of business intelligence with data science here. Current advancements in algorithms and tools has helped us improve accuracy for each of the stages above.
Where does AI or ML fits in?
Data Science, Artificial Intelligence & Machine Learning are different but often used interchangeably. There are overlaps and a part covers all of them together:
On a high level, part of the data science provides processed data. AI or ML or DL helps to process the data to get the needed output.
Artificial Intelligence (AI)
It is a program that enables machine to mimic human behavior. As such, goal here is to understand human intelligence, learn to imitate and act accordingly. I came across a good AI exhibit by BCG:
Self driving cars and route change suggestion are few common AI solutions
Machine Learning (ML)
These are AI techniques that enables machines to learn from examples, without being explicitly programmed to do so. It incorporates mathematics and statistics to learn from itself and improve with experience.
Recommendation engines & Spam email classification are few common ML solutions
I will cover Machine Learning in much more detail in later posts.
Deep Learning (DL)
These are subset of ML that makes the computation of multi-layer neural network feasible. It does not require feature selection/engineering. They classify information similar to human brains. They often continue to improve as the size of your data increases.
Face detection and number recognition are few common DL solutions
Moving On …
Overall, Data Science is more about extracting insights to build a robust strategy for business solution and is different from AI or ML.
To read more around differences between the Data Science and other terms, Vincent Granville has shared in detail here.
With above, we have entered into the Data Science world. Going forward, I will concentrate more on Machine Learning aspect for now.
Open Data Science Conference (ODSC) is one of the biggest specialized data science upcoming event, scheduled on December 8-9, 2020. Read details about the event here. Theme for the year is RETHINK AI.
Virtual Conference is spread across two days: – December 8th – ODSC India – December 9th – ODSC Asia & Pacific
The Largest Applied Data Science & AI Conference Returns to India!
Learn the latest AI & data science topics, tools, and languages from some of the best and brightest minds in the field.
Event highlight shared by ODSC team
The conference promises to accelerate your knowledge on data science and related disciplines with insightful sessions, workshops and speakers from various fields. There would be speakers that include core contributors to many open source libraries and languages.
A probability distribution helps understand the likelihood of possible values that a random variable can take. It is one of the must needed statistical knowledge for any data science aspirant.
Few consider, Probability distributions are fundamental to statistics, like data structures are to computer science
In Layman terms
Let’s say, you pick any 100 employees of an organization. Measure their heights (or weights). As you measure them, create a distribution of it on a graph. Keep height on X-Axis & frequency of a particular height on Y-Axis. With this, we will get a distribution for a range of heights.
This distribution will help know which outcomes are most likely, the spread of potential values, and the likelihood of different results.
Basic terminology
Random Sample
The set of 100 people selected above in our example will be termed as random sample.
Sample Space
The range of possible heights of the 100 people is our sample space. It’s the set of all possible values in the setup.
Random Variable
The height of the 100 people measured are termed as random variable. It’s a variable that takes different values of the sample space randomly.
Mean (Expected Value)
Let’s say most of the people in those 100 are of height 5 feet, 3 inches (making it an average height of those 100). This would be termed expected value. It’s an average value of a random variable.
Standard deviation & Variance
Let’s say most of the people in those 100 are of height 5 feet, 1 inches to 5 feet, 5 inches. This is variance for us. It’s an average spread of values around the expected value. Standard Deviation is the square root of the variance.
Types of data
Ordinal – They have a meaningful order. All numerical data fall in this bucket. They can be ordered in relative numerical strength.
Nominal – They cannot be ordered. All categorical data fall in this bucket. Like, colors – Red, Blue & Green – there cannot be an order or a sequence of high or low in them by itself.
Discrete – an ordinal data that can take only certain values (like soccer match score)
Continuous – an ordinal data that can take any real or fractional value (like height & weight)
In Continuous distribution, random variables can have an infinite range of possible outcomes
Probability Distribution Flowchart
Following diagram shares few of the common distributions used:
Based on above diagram, will cover three distributions to have a broad understanding:
Uniform Distribution
It is the simplest form of distribution. Every outcome of the sample space has equal probability to happen. An example would be to roll a fair dice that would have an equal probability outcome of 1-6.
Normal (Gaussian) Distribution
The most common distribution. Few would recognize this by a ‘bell curve’. Most values are around the mean value making the distribution arrangement symmetric.
Central limit theorem suggests that sum of several independent random variables is normally distributed
The area under the distribution curve is equal to 1 (all the probabilities must sum up to 1)
A parameter Mew drives the distribution center (mean). It corresponds to the maximum height of the graph. A parameter Sigma corresponds to the range of variation (variance or standard deviation).
68–95–99.7 rule (empirical rule) – approximate percentage of the data covered by ranges defined by 1, 2, and 3 standard deviations from the mean
Exponential Distribution
It is where a few outcomes are most likely with a rapid decrease in probability to all other outcomes. An example of it would be a car battery life in months.
A parameter Beta deals with scale that defines the mean and standard deviation of the distribution. A parameter Lambda deals with rate of change in the distribution
Probability Distribution Choices
I came across an awesome representation of the probability distribution choices. It works as a cheat sheet to understand the provided data.
Though above is just an introduction, believe it should be good enough to start, correlate and understand some basics of machine learning algorithms. There would be more to it while working on algorithms and problems while analyzing data to predict trends, etc.
Recently, Google opened up its Flood Forecasting Initiative that uses Artificial Intelligence to predict when and where flood will occur for India and Bangladesh. They worked with governments to develop systems that predict flood and thus keep people safe and informed.
Google now covers 200 million people living in more than 250,000 square kilometers in India.
This topic was also touched upon in the Decode with Google event last week.
Floods are devastating natural disasters worldwide—it’s estimated that every year, 250 million people around the world are affected by floods, causing around $10 billion in damages.
The plan was to use AI and create forecasting models based on:
historical events
river level readings
terrain and elevation of an area
An inside look at the flood forecasting was published here that covers: 1. The Inundation Model 2. Real time water level measurements 3. Elevation Map creation 4. Hydraulic modeling
Recent Improvements
The new approach devised for inundation modeling is called a morphological inundation model. It combines physics-based modeling with machine learning to create more accurate and scalable inundation models in real-world settings.
This new forecasting system covers: 1. Forecasting Water Levels 2. Morphological Inundation Modeling 3. Alert targeting 4. Improved Water Levels Forecasting
Have a read of the following blog for full details.
Current State
As shared here, they partnered with Indian Central Water Commission to expand forecasting models and services. For research, they have collaborated with Yale to visit flood affected areas. This helps them to understand how to provide information and what information would people need to protect themselves.
We’re providing people with information about flood depth: when and how much flood waters are likely to rise. And in areas where we can produce depth maps throughout the floodplain, we’re sharing information about depth in the user’s village or area.
While working on a machine learning problem, Matplotlib is the most popular python library used for visualization that helps in representing & analyzing the data and work through insights.
Generally, it’s difficult to interpret much about data, just by looking at it. But, a presentation of the data in any visual form, helps a great deal to peek into it. It becomes easy to deduce correlations, identify patterns & parameters of importance.
In data science world, data visualization plays an important role around data pre-processing stage. It helps in picking appropriate features and apply appropriate machine learning algorithm. Later, it helps in representing the data in a meaningful way.
Data Insights via various plots
If needed, we will use these dataset for plot examples and discussions. Based on the need, following are the common plots that are used:
Line Chart | ax.plot(x,y)
It helps in representing series of data points against a given range of defined parameter. Real benefit is to plot multiple line charts in a single plot to compare and track changes.
Points next to each other are related that helps to identify repeated or a defined pattern
With the above, we have couple of quick assessments: Q: How a particular stock fared over last year? A: Stocks were roughly rising till Feb 2020 and then took a dip in April and then back up since then.
Q: How the three stocks behaved during the same period? A: Stock price of ADBE was more sensitive and AAPL being least sensitive to the change during the same period.
Histogram | ax.hist(data, n_bins)
It helps in showing distributions of variables where it plots quantitative data with range of the data grouped into intervals.
We can use Log scale if the data range is across several orders of magnitude.
import numpy as np
import matplotlib.pyplot as plt
mean = [0, 0]
cov = [[2,4], [5, 9]]
xn, yn = np.random.multivariate_normal(
mean, cov, 100).T
plt.hist(xn,bins=25,label="Distribution on x-axis");
plt.xlabel('x')
plt.ylabel('frequency')
plt.grid(True)
plt.legend()
Real world example
We will work with dataset of Indian Census data downloaded from here.
With the above, couple of quick assessments about population in states of India: Q: What’s the general population distribution of states in India? A: More than 50% of states have population less than 2 crores (20 million)
Q: How many states are having population more than 10 crores (100 million)? A: Only 3 states have that high a population.
Bar Chart | ax.bar(x_pos, heights)
It helps in comparing two or more variables by displaying values associated with categorical data.
Most commonly used plot in Media sharing data around surveys displaying every data sample.
With the above, couple of quick assessments about population in states of India: – Uttar Pradesh has the highest total population and Lakshadeep has lowest – Relative popluation across states with Uttar Pradesh almost double the second most populated state
Pie Chart | ax.pie(sizes, labels=[labels])
It helps in showing the percentage (or proportional) distribution of categories at a certain point of time. Usually, it works well if it’s limited to single digit categories.
A circular statistical graphic where the arc length of each slice is proportional to the quantity it represents.
import numpy as np
import matplotlib.pyplot as plt
# Slices will be ordered n plotted counter-clockwise
labels = ['Audi','BMW','LandRover','Tesla','Ferrari']
sizes = [90, 70, 35, 20, 25]
fig, ax = plt.subplots()
ax.pie(sizes,labels=labels, autopct='%1.1f%%')
ax.set_title('Car Sales')
plt.show()
Real world example
We will work with dataset of Alcohol Consumption downloaded from here.
With the above, we can have a quick assessment that alcohol consumption is distributed overall. This view helps if we have less number of slices (categories).
Scatter plot | ax.scatter(x_points, y_points)
It helps representing paired numerical data either to compare how one variable is affected by another or to see how multiple dependent variables value is spread for each value of independent variable.
Sometimes the data points in a scatter plot form distinct groups and are called as clusters.
import numpy as np
import matplotlib.pyplot as plt
# random but focused cluster data
x1 = np.random.randn(100) + 8
y1 = np.random.randn(100) + 8
x2 = np.random.randn(100) + 3
y2 = np.random.randn(100) + 3
x = np.append(x1,x2)
y = np.append(y1,y2)
plt.scatter(x,y, label="xy distribution")
plt.legend()
Real world example
We will work with dataset of Alcohol Consumption downloaded from here.
import pandas as pd
import matplotlib.pyplot as plt
drinksdf = pd.read_csv('data-files/drinks.csv',
skiprows=1,
names = ['country', 'beer', 'spirit',
'wine', 'alcohol', 'continent'])
drinksdf['total'] = drinksdf['beer']
+ drinksdf['spirit']
+ drinksdf['wine']
+ drinksdf['alcohol']
# drinksdf.corr() tells beer and alcochol
# are highly corelated
fig = plt.figure()
# Compare beet and alcohol consumption
# Use color to show a third variable.
# Can also use size (s) to show a third variable.
scat = plt.scatter(drinksdf['beer'],
drinksdf['alcohol'],
c=drinksdf['total'],
cmap=plt.cm.rainbow)
# colorbar to explain the color scheme
fig.colorbar(scat, label='Total drinks')
plt.xlabel('Beer')
plt.ylabel('Alcohol')
plt.title('Comparing beer and alcohol consumption')
plt.grid(True)
plt.show()
With the above, we can have a quick assessment that beer and alcohol consumption have strong positive correlation which would suggest a large overlap of people who drink beer and alcohol.
2. We will work with dataset of Mall Customers downloaded from here.
With the above, we can have a quick assessment that there are five clusters there and thus five segments or types of customers one can make plan for.
Box Plot | ax.boxplot([data list])
A statistical plot that helps in comparing distributions of variables because the center, spread and range are immediately visible. It only shows the summary statistics like mean, median and interquartile range.
Easy to identify if data is symmetrical, how tightly it is grouped, and if and how data is skewed
import numpy as np
import matplotlib.pyplot as plt
# some random data
data1 = np.random.normal(0, 2, 100)
data2 = np.random.normal(0, 4, 100)
data3 = np.random.normal(0, 3, 100)
data4 = np.random.normal(0, 5, 100)
data = list([data1, data2, data3, data4])
fig, ax = plt.subplots()
bx = ax.boxplot(data, patch_artist=True)
ax.set_title('Box Plot Sample')
ax.set_ylabel('Spread')
xticklabels=['category A',
'category B',
'category B',
'category D']
colors = ['pink','lightblue','lightgreen','yellow']
for patch, color in zip(bx['boxes'], colors):
patch.set_facecolor(color)
ax.set_xticklabels(xticklabels)
ax.yaxis.grid(True)
plt.show()
Real world example
We will work with dataset of Tips downloaded from here.
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
tipsdf = pd.read_csv('data-files/tips.csv')
sns.boxplot(x="time", y="tip",
hue='sex', data=tipsdf,
order=["Dinner", "Lunch"],
palette='coolwarm')
With the above, we can have a quick couple of assessments: – male gender gives more tip compared to females – tips during dinner time can vary a lot (more) by males mean tip
Violen Plot | ax.violinplot([data list])
A statistical plot that helps in comparing distributions of variables because the center, spread and range are immediately visible. It shows the full distribution of data.
A quick way to compare distributions across multiple variables
import numpy as np
import matplotlib.pyplot as plt
data = [np.random.normal(0, std, size=100)
for std in range(2, 6)]
fig, ax = plt.subplots()
bx = ax.violinplot(data)
ax.set_title('Violin Plot Sample')
ax.set_ylabel('Spread')
xticklabels=['category A',
'category B',
'category B',
'category D']
ax.set_xticks([1,2,3,4])
ax.set_xticklabels(xticklabels)
ax.yaxis.grid(True)
plt.show()
Real world example
We will work with dataset of Tips downloaded from here.
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
tipsdf = pd.read_csv('data-files/tips.csv')
sns.violinplot(x="day", y="tip",
split="True", data=tipsdf)
With the above, we can have a quick assessment that the tips on Saturday has more relaxed distribution whereas Friday has much narrow distribution in comparison.
2. We will work with dataset of Indian Census data downloaded from here.
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
populationdf = pd.read_csv(
"./data-files/census-population.csv")
mask1 = populationdf['Level']=='DISTRICT'
mask2 = populationdf['TRU']!='Total'
statesdf = populationdf[mask1 & mask2]
maskUP = statesdf['State']==9
maskM = statesdf['State']==27
data = statesdf.loc[maskUP | maskM]
sns.violinplot( x='State', y='P_06',
inner='quartile', hue='TRU',
palette={'Rural':'green','Urban':'blue'},
scale='count', split=True,
data=data, size=6)
plt.title('In districts of UP and Maharashtra')
plt.show()
With the above, we can have couple of quick assessments: – Uttar Pradesh has high volume and distribution of rural child population. – Maharashtra has almost equal spread of rural and urban child population
Heatmap
It helps in representing a 2-D matrix form of data using variation of color for different values. Variation of color maybe hue or intensity.
Generally used to visualize correlation matrix which in turn helps in features (variables) selection.
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
# create 2D array
array_2d = np.random.rand(4, 6)
sns.heatmap(array_2d, annot=True)
Real world example
We will work with dataset of Alcohol Consumption downloaded from here.
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
drinksdf = pd.read_csv('data-files/drinks.csv',
skiprows=1,
names = ['country', 'beer', 'spirit',
'wine', 'alcohol', 'continent'])
sns.heatmap(drinksdf.corr(),annot=True,cmap='YlGnBu')
With the above, we can have a quick couple of assessments: – there is a strong correlation between beer and alcohol and thus a strong overlap there. – wine and spirit are almost not correlated and thus it would be rare to have a place where wine and spirit consumption equally high. One would be preferred over other.
If we notice, upper and lower halves along the diagonal are same. Correlation of A is to B is same as B is to A. Further, A correlation with A will always be 1. Such case, we can make a small tweak to make it more presentable and avoid any correlation confusion.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
drinksdf = pd.read_csv(
'data-files/drinks.csv',
skiprows=1,
names = ['country', 'beer', 'spirit',
'wine', 'alcohol', 'continent'])
# correlation and masks
drinks_cr = drinksdf.corr()
drinks_mask = np.triu(drinks_cr)
# remove the last ones on both axes
drinks_cr = drinks_cr.iloc[1:,:-1]
drinks_mask = drinks_mask[1:, :-1]
sns.heatmap(drinks_cr,
mask=drinks_mask,
annot=True,
cmap='coolwarm')
It is the same correlation data but just the needed one is represented.
Data Image
It helps in displaying data as an image, i.e. on a 2D regular raster.
Images are internally just arrays. Any 2D numpy array can be displayed as an image.
import pandas as pd
import matplotlib.pyplot as plt
M,N = 25,30
data = np.random.random((M,N))
plt.imshow(data)
Real world example
Let’s read an image and then try to display it back to see how it looks
It read the image as an array of matrix and then drew it as plot that turned to be same as the image. Since, images are like any other plots, we can plot other objects (like annotations) on top of it.
Generally, it is used in comparing multiple variables (in pairs) against each other. With multiple plots stacked against each other in the same figure, it helps in quick assessment for correlation and distribution for a pair.
Parameters are: number of rows, number of columns, the index of the subplot
(Index are counted row wise starting with 1)
The widths of the different subplots may be different with use of GridSpec.
import numpy as np
import matplotlib.pyplot as plt
import math
# data setup
x = np.arange(1, 100, 5)
y1 = x**2
y2 = 2*x+4
y3 = [ math.sqrt(i) for i in x]
y4 = [ math.log(j) for j in x]
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2)
ax1.plot(x, y1)
ax1.set_title('f(x) = quadratic')
ax1.grid()
ax2.plot(x, y2)
ax2.set_title('f(x) = linear')
ax2.grid()
ax3.plot(x, y3)
ax3.set_title('f(x) = sqareroot')
ax3.grid()
ax4.plot(x, y4)
ax4.set_title('f(x) = log')
ax4.grid()
fig.tight_layout()
plt.show()
We can stack up m x n view of the variables and have a quick look on how they are correlated. With the above, we can quickly assess that second graph parameters are linearly correlated.
Data Representation
Plot Anatomy
Below picture will help with plots terminology and representation:
Credit: matplotlib.org
Figure above is the base space where the entire plot happens. Most of the parameters can be customized for better representation. For specific details, look here.
Plot annotations
It helps in highlighting few key findings or indicators on a plot. For advanced annotations, look here.
import numpy as np
import matplotlib.pyplot as plt
# A simple parabolic data
x = np.arange(-4, 4, 0.02)
y = x**2
# Setup plot with data
fig, ax = plt.subplots()
ax.plot(x, y)
# Setup axes
ax.set_xlim(-4,4)
ax.set_ylim(-1,8)
# Visual titles
ax.set_title('Annotation Sample')
ax.set_xlabel('X-values')
ax.set_ylabel('Parabolic values')
# Annotation
# 1. Highlighting specific data on the x,y data
ax.annotate('local minima of \n the parabola',
xy=(0, 0),
xycoords='data',
xytext=(2, 3),
arrowprops=
dict(facecolor='red', shrink=0.04),
horizontalalignment='left',
verticalalignment='top')
# 2. Highlighting specific data on the x/y axis
bbox_yproperties = dict(
boxstyle="round,pad=0.4", fc="w", ec="k", lw=2)
ax.annotate('Covers 70% of y-plot range',
xy=(0, 0.7),
xycoords='axes fraction',
xytext=(0.2, 0.7),
bbox=bbox_yproperties,
arrowprops=
dict(facecolor='green', shrink=0.04),
horizontalalignment='left',
verticalalignment='center')
bbox_xproperties = dict(
boxstyle="round,pad=0.4", fc="w", ec="k", lw=2)
ax.annotate('Covers 40% of x-plot range',
xy=(0.3, 0),
xycoords='axes fraction',
xytext=(0.1, 0.4),
bbox=bbox_xproperties,
arrowprops=
dict(facecolor='blue', shrink=0.04),
horizontalalignment='left',
verticalalignment='center')
plt.show()
Plot style | plt.style.use('style')
It helps in customizing representation of a plot, like color, fonts, line thickness, etc. Default styles get applied if the customization is not defined. Apart from adhoc customization, we can also choose one of the already defined template styles and apply them.
# To know all existing styles with package
for style in plt.style.available:
print(style)
# To use a defined style for plot
plt.style.use('seaborn')
# OR
with plt.style.context('Solarize_Light2'):
plt.plot(np.sin(np.linspace(0, 2 * np.pi)), 'r-o')
plt.show()
Saving plots | ax.savefig()
It helps in saving figure with plot as an image file of defined parameters. Parameters details are here. It will save the image file to the current directory by default.
It helps in filling missing data with some reasonable data as many statistical or machine learning packages do not work with data containing null values.
Data interpolation can be defined to use pre-defined functions such as linear, quadratic or cubic
import pandas as pd
import matplotlib.pyplot as plt
df = pd.DataFrame(np.random.randn(20,1))
df = df.where(df<0.5)
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(df)
ax1.set_title('f(x) = data missing')
ax1.grid()
ax2.plot(df.interpolate())
ax2.set_title('f(x) = data interpolated')
ax2.grid()
fig.tight_layout()
plt.show()
With the above, we see all the missing data replaced with some probably interpolation supported by dataframe based on valid previous and next data.
Animation
At times, it helps in presenting the data as an animation. On a high level, it would need data to be plugged in a loop with delta changes translating into a moving view.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib import animation
fig = plt.figure()
def f(x, y):
return np.sin(x) + np.cos(y)
x = np.linspace(0, 2 * np.pi, 80)
y = np.linspace(0, 2 * np.pi, 70).reshape(-1, 1)
im = plt.imshow(f(x, y), animated=True)
def updatefig(*args):
global x, y
x += np.pi / 5.
y += np.pi / 10.
im.set_array(f(x, y))
return im,
ani = animation.FuncAnimation(
fig, updatefig, interval=100, blit=True)
plt.show()
3-D Plotting
If needed, we can also have an interactive 3-D plot though it might be slow with large datasets.
This is to get started with pandas and try few concrete examples. pandas is a Python based library that helps in reading, transforming, cleaning and analyzing data. It is built on the NumPy package.
pandas is a fast, powerful, flexible and easy to use open source data analysis and manipulation tool, built on top of the Python programming language.
https://pandas.pydata.org
Key data structure in pandas is called DataFrame – it helps to work with tabular data translated as rows of observations and columns of features.
While reading for AI/ML (Artificial Intelligence/Machine Learning), I came across a discussion – if Python can be used as a “statistics workbench” to replace R, SPSS, etc? It was nice shareout by multiple knowledge folks related to languages used for problems of statistics, specifically R (read about R here).
For quick reference, I will quote few of the latest thoughts from there that are in favor of Python and how it has evolved. I too conquer with most of them:
1. Python is easily the most intuitive syntax of any programming language. This makes for extremely fast development time.
2. Python is performant. It opens large datasets reliably.
3. The packages in Python are fast catching up to R’s packages. Python usage has increased tremendously last few years.
4. Readability is one of the most important qualities good code can possess, and Python is one of the most readable language.
Overall, Python is a general purpose language with an easy to understand syntax which would be relatively easier for usual programmers to learn/adopt. R is developed keeping statisticians in mind. Thus it has many features around data visualization and is a tad ahead currently.
Final analysis in the paper shares R being ahead in comparison for data analysis but Python having potential to catch up quickly and easily.
My thoughts …
My intent was to understand which of the programming language serves as an essential tool to demonstrate AI/ML capabilities. Looking at them, Python seems good enough for me to serve as AI/ML tool to start and probably conquer it.
Ammunition needed …
There are many python based libraries and packages that are generally used for statistical work. Below are few of them that would help in our data analysis exploration going ahead:
scipy – python-based ecosystem of open-source software for mathematics, science, and engineering.
cookbook – many statistical facilities, a collection of various user-contributed recipes already available
This is to get started with NumPy and try few concrete examples. NumPy (Numerical Python) are packages for numerical computation designed for efficient work on large data sets.
