The dataset contains climate data, the data structure is:
I want to visualise the total hours of sunshine for the summer months (June, July, August) per year. The steps involved in preparing the data were:
import pandas as pd import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = [15, 10] df = pd.read_csv('weather.csv') print(df.head()) print(df.shape) months = [6,7,8] df = df[df['m'].isin(months)] print(df.head()) drop_cols = ['m','tmax','af','tmin','rainmm'] df = df.drop(drop_cols,axis=1) print(df.head()) sunh_sum = df.groupby('year').sum() sunh_sum.plot(kind='bar') plt.show() The plot:
0 Comments
The following code uses plotly to create a heat map on a globe. The data is country GDP and the Globe generated is interactive (below is only an image so not interactive. The code:
metricscale1=[[0, 'rgb(102,194,165)'], [0.05, 'rgb(102,194,165)'], [0.15, 'rgb(171,221,164)'], [0.2, 'rgb(230,245,152)'], [0.25, 'rgb(255,255,191)'], [0.35, 'rgb(254,224,139)'], [0.45, 'rgb(253,174,97)'], [0.55, 'rgb(213,62,79)'], [1.0, 'rgb(158,1,66)']] data = [ dict( type = 'choropleth', autocolorscale = False, colorscale = metricscale1, showscale = True, locations = df['Country'].values, z = df['GDP ($ per capita)'].values, locationmode = 'country names', text = df['Country'].values, marker = dict( line = dict(color = 'rgb(250,250,225)', width = 0.5)), colorbar = dict(autotick = True, tickprefix = '', title = 'GDP') ) ] layout = dict( title = 'World Map of GDP ($US per capita)', geo = dict( showframe = True, showocean = True, oceancolor = 'rgb(28,107,160)', #oceancolor = 'rgb(222,243,246)', projection = dict( type = 'orthographic', rotation = dict( lon = 60, lat = 10), ), lonaxis = dict( showgrid = False, gridcolor = 'rgb(102, 102, 102)' ), lataxis = dict( showgrid = False, gridcolor = 'rgb(102, 102, 102)' ) ), ) fig = dict(data=data, layout=layout) py.iplot(fig, validate=False, filename='worldmapGDP') The analysis of some data from OECD, required some reshaping of the data. OECD provided the data in the following format. In one column there is data about education, earnings, free time,...To work with this data I need these topics in separate columns: There were numerous columns with data I didn't need, so I had to drop these. The data I was interested in was all in one column, so the first x rows had data on average earnings, the next x rows had data on average earnings for males, the next x rows for females, the next x rows had data on years spent in education and so on. To test for linear correlation I needed the data in adjacent columns not all in one column. The following script was used to reshape the data. I extracted the data I needed into separate dataframes then combined these dataframes as necessary:
import pandas as pd import matplotlib.pyplot as plt from matplotlib import cm as cm def plot_corr(df,size=4): '''Function plots a graphical correlation matrix for each pair of columns in the dataframe. Input: df: pandas DataFrame size: vertical and horizontal size of the plot''' corr = df.corr() fig, ax = plt.subplots(figsize=(size, size)) ax.matshow(corr,cmap=cm.Greys) plt.xticks(range(len(corr.columns)), corr.columns); plt.yticks(range(len(corr.columns)), corr.columns); plt.show() #import data df = pd.read_csv('oecd.csv') #features available ''' print(df['Indicator'].unique()) ['Dwellings without basic facilities' 'Housing expenditure' 'Rooms per person' 'Household net adjusted disposable income' 'Household net financial wealth' 'Employment rate' 'Longterm unemployment rate' 'Personal earnings' 'Quality of support network' 'Educational attainment' 'Student skills' 'Years in education' 'Air pollution' 'Water quality' 'Voter turnout' 'Life expectancy' 'Selfreported health' 'Life satisfaction' 'Homicide rate' 'Employees working very long hours' 'Time devoted to leisure and personal care' 'Labour market insecurity' 'Stakeholder engagement for developing regulations' 'Feeling safe walking alone at night'] ''' #format data gender = 'Total' #there are t 3 values: total, male and female df_edu = df[(df['Indicator']=='Years in education') & (df['Inequality']==gender)] df_earn = df[(df['Indicator']=='Personal earnings') & (df['Inequality']==gender)] df_satis = df[(df['Indicator']=='Life satisfaction') & (df['Inequality']==gender)] df_person = df[(df['Indicator']=='Time devoted to leisure and personal care') & (df['Inequality']==gender)] drop=['LOCATION','INDICATOR','Indicator','MEASURE','Measure','INEQUALITY','Inequality','Unit Code','Unit','PowerCode Code','PowerCode','Reference Period Code', 'Reference Period', 'Flag Codes', 'Flags'] df_edu = df_edu.drop(drop,1) df_edu = df_edu.rename(columns={'Value': 'Edu'}) df_earn = df_earn.drop(drop,1) df_earn = df_earn.rename(columns={'Value': 'Earn'}) df_satis = df_satis.drop(drop,1) df_satis = df_satis.rename(columns={'Value': 'Satis'}) df_person = df_person.drop(drop,1) df_person = df_person.rename(columns={'Value': 'Person'}) df_combine = df_edu.merge(df_earn, on='Country',how='left') df_combine = df_combine.merge(df_satis, on='Country',how='left') df_combine = df_combine.merge(df_person, on='Country',how='left') df_combine = df_combine.drop('Country',1) #print(df_combine.corr(method='spearman')) #print(df_combine.head()) #visualise #plot_corr(df_combine) df_combine.plot(kind='scatter',y='Satis',x='Earn') plt.show() This script was used to visualise the correlation matrix for some of the OECD data analysis posted here. The output: The darker the shade of grey the stronger the correlation. The top left to bottom right diagonal can be ignored, this is comparing the same fields so equals 1.
Satis = life satisfaction earn = personal earnings person = available personal time (to pursue hobbies, relax and so on) Edu = time spent in full time education import pandas as pd import matplotlib.pyplot as plt from matplotlib import cm as cm def plot_corr(df,size=4): '''Function plots a graphical correlation matrix for each pair of columns in the dataframe. Input: df: pandas DataFrame size: vertical and horizontal size of the plot''' corr = df.corr() fig, ax = plt.subplots(figsize=(size, size)) ax.matshow(corr,cmap=cm.Greys) plt.xticks(range(len(corr.columns)), corr.columns); plt.yticks(range(len(corr.columns)), corr.columns); plt.show() #import data df = pd.read_csv('oecd.csv') #features available ''' print(df['Indicator'].unique()) ['Dwellings without basic facilities' 'Housing expenditure' 'Rooms per person' 'Household net adjusted disposable income' 'Household net financial wealth' 'Employment rate' 'Longterm unemployment rate' 'Personal earnings' 'Quality of support network' 'Educational attainment' 'Student skills' 'Years in education' 'Air pollution' 'Water quality' 'Voter turnout' 'Life expectancy' 'Selfreported health' 'Life satisfaction' 'Homicide rate' 'Employees working very long hours' 'Time devoted to leisure and personal care' 'Labour market insecurity' 'Stakeholder engagement for developing regulations' 'Feeling safe walking alone at night'] ''' #format data gender = 'Total' df_edu = df[(df['Indicator']=='Years in education') & (df['Inequality']==gender)] df_earn = df[(df['Indicator']=='Personal earnings') & (df['Inequality']==gender)] df_satis = df[(df['Indicator']=='Life satisfaction') & (df['Inequality']==gender)] df_person = df[(df['Indicator']=='Time devoted to leisure and personal care') & (df['Inequality']==gender)] drop = ['LOCATION','INDICATOR','Indicator','MEASURE','Measure','INEQUALITY','Inequality','Unit Code','Unit','PowerCode Code','PowerCode','Reference Period Code', 'Reference Period', 'Flag Codes', 'Flags'] df_edu = df_edu.drop(drop,1) df_edu = df_edu.rename(columns={'Value': 'Edu'}) df_earn = df_earn.drop(drop,1) df_earn = df_earn.rename(columns={'Value': 'Earn'}) df_satis = df_satis.drop(drop,1) df_satis = df_satis.rename(columns={'Value': 'Satis'}) df_person = df_person.drop(drop,1) df_person = df_person.rename(columns={'Value': 'Person'}) df_combine = df_edu.merge(df_earn, on='Country',how='left') df_combine = df_combine.merge(df_satis, on='Country',how='left') df_combine = df_combine.merge(df_person, on='Country',how='left') df_combine = df_combine.drop('Country',1) #print(df_combine.corr(method='spearman')) #print(df_combine.head()) #visualise #plot_corr(df_combine) df_combine.plot(kind='scatter',y='Satis',x='Earn') plt.show() The recent twitter spat between Elon Musk and Mark Zuckerberg shows that clever people are thinking about Artificial Intelligence (AI). The problem is these two people are on opposite sides of a debate on the possible risks and rewards of AI. Elon Musk is not the only influential person to warn about the potential negative impact of AI, Stephen Hawking and Bill Gates have also issued warnings. We are still a long way from the AI of science fiction stories which risesup and builds an army of human hating killing machines. The two most widespread forms of AI we have are machine learning (ML) and deep learning (DL). Both are examples of narrow AI that is they may be able outperform humans in one narrow task but unlike the multi functional human brain they are unable to carry out unrelated tasks, to reason or be selfaware. Our world is increasingly controlled by Artificial Intelligence (AI), and it is not just the self driving cars and chess playing computers that the media often report on. Google, Amazon, Facebook, your bank, the government, security/intelligence organizations, the police and others all use AI. Often this is Machine Learning (ML) but increasingly Deep Learning (DL) is being used to solve a diverse range of problems including medical issues, Amazon’s Echo and business applications. But what is it? Is it just another form of machine learning? Though they have some things in common DL and ML are not the same. To illustrate how DL works I will use a basic DL script written in Python, the script is available below. The problem we are going to attempt to solve involves creating a model which divides data into catagories. This type of problem is common in the real world, for example customers who renew their subscription/contract versus those who don’t, computer activity which is suspicious or benign, a fuzzy patch on an MRI scan that might be benign or might be cancer. The script can generate three types of dataset. The first, called moons, can be plotted on a 2 dimensional graph: The two classes are coloured red and blue. Our model will be represented by a decision boundary, a line, on the graph which separates the blue and red dots. For any new data point we will then be able to use our model to determine if it belongs to the reds or the blues. As you can see a simple straight line will not be a sufficient to solve the problem: Feeding the data into the DL script generates the following solution: The solution is not perfect, but it is pretty good. Note that we are not trying to get every single point on the correct side of the line – that situation is called over fitting, it is not a good thing. Real world data often contains outliers and noise, we don’t necessarily want to include this in our model. The Script import numpy as np
import sklearn from sklearn import datasets, linear_model import matplotlib.pyplot as plt def initialise(a,b,c,d): nn_input_dim = a #number of input nodes nn_output_dim = b #number of output nodes epsilon = c # learning rate for gradient descent reg_lambda = d # regularization strength return nn_input_dim, nn_output_dim, epsilon, reg_lambda def generate_data(data_type): np.random.seed(0) if data_type == 'moons': X, y = datasets.make_moons(200, noise=0.20) elif data_type == 'circles': X, y = sklearn.datasets.make_circles(200, noise=0.20) elif data_type == 'blobs': X, y = sklearn.datasets.make_blobs(centers=2, random_state=0) return X, y def visualize(X, y, model): plot_decision_boundary(lambda x:predict(model,x), X, y) def plot_decision_boundary(pred_func, X, y): # Set min and max values and give it some padding x_min, x_max = X[:, 0].min()  .5, X[:, 0].max() + .5 y_min, y_max = X[:, 1].min()  .5, X[:, 1].max() + .5 h = 0.01 # Generate a grid of points with distance h between them xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) # Predict the function value for the whole gid Z = pred_func(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) # Plot the contour and training examples plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral) plt.show() # Helper function to evaluate the total loss on the dataset def calculate_loss(model, X, y): num_examples = len(X) # training set size W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2'] # Forward propagation to calculate our predictions z1 = X.dot(W1) + b1 a1 = np.tanh(z1) z2 = a1.dot(W2) + b2 exp_scores = np.exp(z2) probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # Calculating the loss corect_logprobs = np.log(probs[range(num_examples), y]) data_loss = np.sum(corect_logprobs) # Add regulatization term to loss (optional) data_loss += reg_lambda / 2 * (np.sum(np.square(W1)) + np.sum(np.square(W2))) return 1. / num_examples * data_loss def predict(model, x): W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2'] # Forward propagation z1 = x.dot(W1) + b1 a1 = np.tanh(z1) z2 = a1.dot(W2) + b2 exp_scores = np.exp(z2) probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) return np.argmax(probs, axis=1) # This function learns parameters for the neural network and returns the model. #  nn_hdim: Number of nodes in the hidden layer #  num_passes: Number of passes through the training data for gradient descent #  print_loss: If True, print the loss every 1000 iterations def build_model(X, y, nn_hdim, num_passes=20000, print_loss=False): # Initialize the parameters to random values. We need to learn these. num_examples = len(X) np.random.seed(0) W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim) b1 = np.zeros((1, nn_hdim)) W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim) b2 = np.zeros((1, nn_output_dim)) # This is what we return at the end model = {} # Gradient descent. For each batch... for i in range(0, num_passes): # Forward propagation z1 = X.dot(W1) + b1 a1 = np.tanh(z1) z2 = a1.dot(W2) + b2 exp_scores = np.exp(z2) probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # Backpropagation delta3 = probs delta3[range(num_examples), y] = 1 dW2 = (a1.T).dot(delta3) db2 = np.sum(delta3, axis=0, keepdims=True) delta2 = delta3.dot(W2.T) * (1  np.power(a1, 2)) dW1 = np.dot(X.T, delta2) db1 = np.sum(delta2, axis=0) # Add regularization terms (b1 and b2 don't have regularization terms) dW2 += reg_lambda * W2 dW1 += reg_lambda * W1 # Gradient descent parameter update W1 += epsilon * dW1 b1 += epsilon * db1 W2 += epsilon * dW2 b2 += epsilon * db2 # Assign new parameters to the model model = {'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2} # Optionally print the loss. # This is expensive because it uses the whole dataset, so we don't want to do it too often. if print_loss and i % 1000 == 0: print("Loss after iteration %i: %f" % (i, calculate_loss(model, X, y))) return model nn_input_dim, nn_output_dim, epsilon, reg_lambda = initialise(2,2,0.01,0.01) X, y = generate_data('moons') model = build_model(X, y, 4, 10000, print_loss=True) visualize(X, y, model) Note: this script is derived from: https://github.com/dennybritz/nnfromscratch/blob/master/ann_classification.py This script was used to generate these visualisations:
import pandas as pd import plotly.offline as py import numpy as np df = pd.read_csv('VietnamConflict.csv') df_states = pd.read_csv('states.csv') #approx 1967 population by state death_by_state = df['STATE_CODE'].value_counts().reset_index().rename(columns={'index': 'STATE_CODE', 'STATE_CODE': 'COUNT'}) df_normalised = pd.merge(df_states,death_by_state,on='STATE_CODE',how='left') df_normalised['NORMALISED_COUNT'] = df_normalised['COUNT']/df_normalised['POPULATION'] df_normalised['NORMALISED_COUNT'] = df_normalised['NORMALISED_COUNT'].round() for col in df_normalised.columns: df_normalised[col] = df_normalised[col].astype(str) scl = [[0.0, 'rgb(242,240,247)'],[0.2, 'rgb(218,218,235)'],[0.4, 'rgb(188,189,220)'],\ [0.6, 'rgb(158,154,200)'],[0.8, 'rgb(117,107,177)'],[1.0, 'rgb(84,39,143)']] labels = df_normalised['STATE_CODE'] values = df_normalised['COUNT'] data = [ dict( type='choropleth', colorscale = scl, autocolorscale = False, locations = labels, z = np.array(values).astype(float), locationmode = 'USAstates', text = labels, marker = dict( line = dict ( color = 'rgb(255,255,255)', width = 2 ) ), colorbar = dict( title = "US casualties") ) ] layout = dict( #title = 'US casualties in Vietnam war<br>(Normalised by approximate 1967 state pop)', title = 'US casualties in Vietnam war', geo = dict( scope='usa', projection=dict( type='albers usa' ), showlakes = True, lakecolor = 'rgb(255, 255, 255)'), ) fig = dict( data=data, layout=layout ) py.plot( fig, filename='US_Vietnam_war_casualties.html' ) The dataset is available in numerous places, for example here. It is a passenger list for the Titanic and includes data on things like gender, ticket class and if the passenger survived or not. I converted the file to a csv file and gave it a shorter name. Our goal is to write code code that will take some details on a passenger and predict if he/she died or survived. Machine learning attempts to build a data model based on features of the data, for example did the passenger have a first, second or third class ticket, was the passenger male or female and so on. The model can then be used to predict the outcome for a given passenger or group of passengers. This dataset serves to illustrate some of the features of machine learning, but remember the code could with very little alteration also handle other data for example predicting if someone will develop diabetes. The first thing we need is a labelled training data set. The algorithm learns from this data then applies what it learnt to new data (test data). This problem is a classification problem as every passenger fell into one of two categories  they survived or they died so the 3 machine learning techniques used below are classification techniques, they are also supervised learning techniques which means we need to break the original data set into a training dataset and a test dataset
#the script was written and tested using idle, it should be compatible with both python 2 and 3 #import the necessary libraries import pandas as pd from sklearn import tree, preprocessing import sklearn.ensemble as ske from sklearn.model_selection import train_test_split #read the data into a pandas dataframe df = pd.read_csv('titanic_data.csv') #drop fields which have lots of missing data, then drop rows with missing data df = df.drop(['body','cabin','boat','home.dest','name','ticket'],axis=1) df = df.dropna() #machine learning needs numerical values not strings le = preprocessing.LabelEncoder() df.sex = le.fit_transform(df.sex) df.embarked = le.fit_transform(df.embarked) ''' a row from the original data looked like: pclass survived name sex age sibsp parch ticket fare cabin embarked boat body home.dest 1 1 Allen, Miss. Elisabeth Walton female 29 0 0 24160 211.3375 B5 S 2 St Louis, MO a typical row now looks like: pclass survived sex age sibsp parch fare embarked 1 1 0 29.0000 0 0 211.3375 2 ''' #create two new numpy arrays, X has the survived column values removed and y is only the survived column values X = df.drop(['survived'], axis=1).values y = df['survived'].values #we are using supervised learning so we need training and test data, the test_size parameter determines the relative sizes of the traing and test data sets X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.3, random_state=0) #use three different approaches and print out the success rate (1 = 100%), you can vary the parameters below and the test_size parameter above to try to #improve success rate clf_dt = tree.DecisionTreeClassifier(max_depth=10) clf_dt = clf_dt.fit(X_train, y_train) print(clf_dt.score(X_test,y_test)) clf_rf = ske.RandomForestClassifier(n_estimators=50) clf_rf = clf_rf.fit(X_train, y_train) print(clf_rf.score(X_test,y_test)) clf_gb = ske.GradientBoostingClassifier(n_estimators=50) clf_gb = clf_gb.fit(X_train, y_train) print(clf_gb.score(X_test,y_test)) ''' I found the gradient boosting technique gave the best results (about 82% accuracy) and the decision tree gave the worst results ''' Why visualise the data? We are visual creatures, it is often easier to see meaning in diagrams rather than in lists and tables of numbers, for example we have the following data, it could be the number of customers in a shop by day over a period of about three months.
The amount of data is small but it is still difficult to take in everything when it is presented as a table. But if we plot the data as a line graph with day number on the xaxis and number of customers on the yaxis: Straight away we can see that we can divide the data into pre40 days and post40 days. With much more activity including some prominent spikes in the post40 day data. Plotting the data makes the story much easier to see. We can't say why there is a difference, there is nothing in the data we have that could answer that question. A more technical plot is the box and whisker plot. It is less user friendly than a simple line graph but does give more information on the median, quartile and range of the data. The diagram below explains the different features in the above plot. Note the above plot also contains dots which indicate outliers in the data. Each box represents a day of the week starting at Monday. I would never use a box and whisker plot in a report or presentation aimed at people who are not familiar with statistics. One more possible plot is the waterfall graph: This plot starts at the beginning of week three. Each bar represents the increase or decrease in number of customers from the previous day. It is similar to the line graph above but can be used to highlight certain events/days. For example say one day we are expecting customer numbers to increase but instead we see a decline  the waterfall graph can illustrate this clearly: Other common graphs include the bar graph and the histogram, see here for a tutorial on these.
According to Wikipedia dizygotic (fraternal) twins usually occur when two fertilized eggs are implanted in the uterus wall at the same time while monozygotic (identical) twins occur when a single egg is fertilized to form one zygote (hence, "monozygotic") which then divides into two separate embryos.
Fraternal twins can be mm, mf, fm or ff (where m = male and f = female), identical twins can only be mm, or ff. For the sake of this example let's say the probability of each option is equal, so P(mm) = P(mf) = P(fm) = P(ff) = 0.25 for Fraternal twins and P(mm) = P(ff) = 0.5 for identical twins. The probability that twins are identical is P(I) = 0.1 so P(F) = 0.9 (probability of Fraternal), assuming twins must be either identical or fraternal (not strictly true but let's not make things too complicated). If we have two brothers who are twins what is the probability that they are identical twins? The nonBaysean answer might be 0.1 or 10%. But this is incorrect. The Baysean formula gives the correct answer: The probability of identical twins given that both twins are brothers written as P(IB) = P(BI)P(I)/P(B) and since we are assuming twins must be either identical or fraternal then: P(B) = P(BI)P(I) + P(BF)P(F) substituting this into the above gives: P(IB) = P(BI)P(I)/P(BI)P(I) + P(BF)P(F) then putting in the numbers gives (0.5 x 0.1)/((0.5 x 0.1) + (0.25 x 0.9)) = 2/11 (about 18.2%)  so the knowledge that both twins are male makes the probability they are identical higher. Let's say we gather some data on a group of people. This data will include height, weight and age. So the data may look something like:
We could plot this data on a three dimensional grid, we can also represent each row with a list of three values, for example the first row becomes: [58,1.56,23]. This list is a vector. Vectors can be used to represent all kinds of data including natural language, images and so on.

This blog includes:Scripts mainly in Python with a few in R covering NLP, Pandas, Matplotlib and others. See the home page for links to some of the scripts. Also includes some explanations of basic data science terminology. Archives
June 2018
