Some Data Processing and Analysis with Python

The following problems appeared as assignments in the edX course Analytics for Computing (by Gatech). The descriptions are taken from the assignments.

1. Association rule mining

First we shall implement the basic pairwise association rule mining algorithm.

Problem definition

Let’s say we have a fragment of text in some language. We wish to know whether there are association rules among the letters that appear in a word. In this problem:

  • Words are “receipts”
  • Letters within a word are “items”

We want to know whether there are association rules of the form, a⟹ b , where a and b are letters, for a given language (by calculating for each rule its confidencecon(⟹ b), which is an estimate of the conditional probability of b given a, or Pr[b|a].

Sample text input

Let’s carry out this analysis on a “dummy” text fragment, which graphic designers refer to as the lorem ipsum:

latin_text= """
Sed ut perspiciatis, unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam
rem aperiam eaque ipsa, quae ab illo inventore veritatis et quasi architecto beatae vitae dicta
sunt, explicabo. Nemo enim ipsam voluptatem, quia voluptas sit, aspernatur aut odit aut fugit, sed
quia consequuntur magni dolores eos, qui ratione voluptatem sequi nesciunt, neque porro quisquam est,
qui dolorem ipsum, quia dolor sit amet consectetur adipisci[ng] velit, sed quia non numquam [do] eius
modi tempora inci[di]dunt, ut labore et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima
veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, nisi ut aliquid ex ea commodi
consequatur? Quis autem vel eum iure reprehenderit, qui in ea voluptate velit esse, quam nihil molestiae
consequatur, vel illum, qui dolorem eum fugiat, quo voluptas nulla pariatur?

At vero eos et accusamus et iusto odio dignissimos ducimus, qui blanditiis praesentium voluptatum
deleniti atque corrupti, quos dolores et quas molestias excepturi sint, obcaecati cupiditate non
provident, similique sunt in culpa, qui officia deserunt mollitia animi, id est laborum et dolorum
fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est
eligendi optio, cumque nihil impedit, quo minus id, quod maxime placeat, facere possimus, omnis voluptas
assumenda est, omnis dolor repellendus. Temporibus autem quibusdam et aut officiis debitis aut rerum
necessitatibus saepe eveniet, ut et voluptates repudiandae sint et molestiae non recusandae. Itaque
earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur
aut perferendis doloribus asperiores repellat.
"""


Data cleaning

Like most data in the real world, this dataset is noisy. It has both uppercase and lowercase letters, words have repeated letters, and there are all sorts of non-alphabetic characters. For our analysis, we should keep all the letters and spaces (so we can identify distinct words), but we should ignore case and ignore repetition within a word.

For example, the eighth word of this text is “error.” As an itemset, it consists of the three unique letters{e,o,r}. That is, to treat the word as a set, meaning we only keep the unique letters. This itemset has six possible itempairs{e,o}{e,r}, and {o,r}.

  • We need to start by “cleaning up” (normalizing) the input, with all characters converted to lowercase and all non-alphabetic, non-space characters removed.
  • Next, we need to convert each word into an itemset like the following examples:

consequatur –> {‘a’, ‘e’, ‘c’, ‘s’, ‘n’, ‘o’, ‘u’, ‘t’, ‘q’, ‘r’}
voluptatem –> {‘l’, ‘a’, ‘e’, ‘o’, ‘p’, ‘u’, ‘m’, ‘t’, ‘v’}

Implementing the basic algorithm

The followed algorithm is implemented:

FindAssocRules--crop-small.png

 

First all item-pairs within an itemset are enumerated and a table that tracks the counts of those item-pairs is updated in-place.

  • Now, given tables of item-paircounts and individual item counts, as well as a confidence threshold, the rules that meet the threshold are returned.
  • The returned rules should be in the form of a dictionary whose key is the tuple(a,bcorresponding to the rule a⇒ b, and whose value is the confidence of the rule, conf(⇒ b).
  • The following functions were implemented to compute the association rules.
    from collections import defaultdict
    from itertools import combinations 
    
    def update_pair_counts (pair_counts, itemset):
        """
        Updates a dictionary of pair counts for all pairs of items 
        in a given itemset.
        """
        assert type (pair_counts) is defaultdict
    
        for item in list(combinations(itemset, 2)):
            pair_counts[item] += 1
            pair_counts[item[::-1]] += 1
        return pair_counts
    def update_item_counts(item_counts, itemset):
    
        for item in itemset:
            item_counts[item] += 1
        return item_counts
    def filter_rules_by_conf (pair_counts, item_counts, threshold):
        rules = {} # (item_a, item_b) -> conf (item_a => item_b)
    
        for (item_a, item_b) in pair_counts:
            conf = pair_counts[(item_a, item_b)] / float(item_counts[item_a])
            if conf >= threshold:
                rules[(item_a, item_b)] = conf
                                                         
        return rules
    def find_assoc_rules(receipts, threshold):
    
        pair_counts = defaultdict(int)
        item_counts = defaultdict(int)
        for receipt in receipts:
            update_pair_counts(pair_counts, receipt)
            update_item_counts(item_counts, receipt)
        return filter_rules_by_conf(pair_counts, item_counts, threshold)

 

  • For the Latin string, latin_text, the function find_assoc_rules() was used to compute the rules whose confidence is at least 0.75, with the following rules obtained as result.

    conf(q => u) = 1.000
    conf(x => e) = 1.000
    conf(x => i) = 0.833
    conf(h => i) = 0.833
    conf(v => t) = 0.818
    conf(r => e) = 0.800
    conf(v => e) = 0.773
    conf(f => i) = 0.750
    conf(b => i) = 0.750
    conf(g => i) = 0.750

 

  • Now, let’s look at rules common to the above Latin textandEnglish text obtained by a translation of the lorem ipsum text, as shown below:
    english_text = """
    But I must explain to you how all this mistaken idea of denouncing of a pleasure and praising pain was
    born and I will give you a complete account of the system, and expound the actual teachings of the great
    explorer of the truth, the master-builder of human happiness. No one rejects, dislikes, or avoids
    pleasure itself, because it is pleasure, but because those who do not know how to pursue pleasure
    rationally encounter consequences that are extremely painful. Nor again is there anyone who loves or
    pursues or desires to obtain pain of itself, because it is pain, but occasionally circumstances occur in
    which toil and pain can procure him some great pleasure. To take a trivial example, which of us
    ever undertakes laborious physical exercise, except to obtain some advantage from it? But who has any
    right to find fault with a man who chooses to enjoy a pleasure that has no annoying consequences, or
    one who avoids a pain that produces no resultant pleasure?
    
    On the other hand, we denounce with righteous indignation and dislike men who are so beguiled and
    demoralized by the charms of pleasure of the moment, so blinded by desire, that they cannot foresee the
    pain and trouble that are bound to ensue; and equal blame belongs to those who fail in their duty
    through weakness of will, which is the same as saying through shrinking from toil and pain. These
    cases are perfectly simple and easy to distinguish. In a free hour, when our power of choice is
    untrammeled and when nothing prevents our being able to do what we like best, every pleasure is to
    be welcomed and every pain avoided. But in certain circumstances and owing to the claims of duty or
    the obligations of business it will frequently occur that pleasures have to be repudiated and
    annoyances accepted. The wise man therefore always holds in these matters to this principle of
    selection: he rejects pleasures to secure other greater pleasures, or else he endures pains to
    avoid worse pains.
    """

 

  • Again, for the English string, english_text, the function find_assoc_rules()  was used to compute the rules whose confidence is at least 0.75, with the following rules obtained as result.

    conf(z => a) = 1.000
    conf(j => e) = 1.000
    conf(z => o) = 1.000
    conf(x => e) = 1.000
    conf(q => e) = 1.000
    conf(q => u) = 1.000
    conf(z => m) = 1.000
    conf(z => r) = 1.000
    conf(z => l) = 1.000
    conf(z => e) = 1.000
    conf(z => d) = 1.000
    conf(z => i) = 1.000
    conf(k => e) = 0.778
    conf(q => n) = 0.750

 

  • Let’s consider any rules with a confidence of at least 0.75 to be a “high-confidence rule“.  The common_high_conf_rules are all the high-confidence rules appearing in both the Latin text and the English text. The rules shown below are all such rules:High-confidence rules common to _lorem ipsum_ in Latin and English:

    q => u
    x => e

 

  • The following table and the figure show the high confidence rules for  the latin and the english texts.
    index rule confidence
    0 z=> o 1.000000 English
    1 z=> l 1.000000 English
    2 z=> m 1.000000 English
    3 q=> u 1.000000 English
    4 q=> e 1.000000 English
    5 x=> e 1.000000 English
    6 z=> e 1.000000 English
    7 j=> e 1.000000 English
    8 z=> a 1.000000 English
    9 z=> d 1.000000 English
    10 q=> u 1.000000 Latin
    11 z=> i 1.000000 English
    12 x=> e 1.000000 Latin
    13 z=> r 1.000000 English
    14 x=> i 0.833333 Latin
    15 h=> i 0.833333 Latin
    16 v=> t 0.818182 Latin
    17 r=> e 0.800000 Latin
    18 k=> e 0.777778 English
    19 v=> e 0.772727 Latin
    20 g=> i 0.750000 Latin
    21 q=> n 0.750000 English
    22 f=> i 0.750000 Latin
    23 b=> i 0.750000 Latin

    eng_lat.png

Putting it all together: Actual baskets!

Let’s take a look at some real data  from this link. First few lines of the transaction data is shown below:

citrus fruit,semi-finished bread,margarine,ready soups
tropical fruit,yogurt,coffee
whole milk
pip fruit,yogurt,cream cheese ,meat spreads
other vegetables,whole milk,condensed milk,long life bakery product
whole milk,butter,yogurt,rice,abrasive cleaner
rolls/buns
other vegetables,UHT-milk,rolls/buns,bottled beer,liquor (appetizer)
pot plants
whole milk,cereals
tropical fruit,other vegetables,white bread,bottled water,chocolate
citrus fruit,tropical fruit,whole milk,butter,curd,yogurt,flour,bottled water,dishes
beef
frankfurter,rolls/buns,soda
chicken,tropical fruit
butter,sugar,fruit/vegetable juice,newspapers
fruit/vegetable juice
packaged fruit/vegetables
chocolate
specialty bar
other vegetables
butter milk,pastry
whole milk
tropical fruit,cream cheese ,processed cheese,detergent,newspapers
tropical fruit,root vegetables,other vegetables,frozen dessert,rolls/buns,flour,sweet spreads,salty snack,waffles,candy,bathroom cleaner
bottled water,canned beer
yogurt
sausage,rolls/buns,soda,chocolate
other vegetables
brown bread,soda,fruit/vegetable juice,canned beer,newspapers,shopping bags
yogurt,beverages,bottled water,specialty bar

  • Our task is to mine this dataset for pairwise association rules to produce a final dictionary, basket_rules, that meet these conditions:
  1. The keys are pairs (a,b), where a and b are item names.
  2. The values are the corresponding confidence scores, conf(⇒ b).
  3. Only include rules ⇒ b where item a occurs at least MIN_COUNT times and conf(⇒ b) is at least THRESHOLD.

The result is shown below:

Found 19 rules whose confidence exceeds 0.5.
Here they are:

conf(honey => whole milk) = 0.733
conf(frozen fruits => other vegetables) = 0.667
conf(cereals => whole milk) = 0.643
conf(rice => whole milk) = 0.613
conf(rubbing alcohol => whole milk) = 0.600
conf(cocoa drinks => whole milk) = 0.591
conf(pudding powder => whole milk) = 0.565
conf(jam => whole milk) = 0.547
conf(cream => sausage) = 0.538
conf(cream => other vegetables) = 0.538
conf(baking powder => whole milk) = 0.523
conf(tidbits => rolls/buns) = 0.522
conf(rice => other vegetables) = 0.520
conf(cooking chocolate => whole milk) = 0.520
conf(frozen fruits => whipped/sour cream) = 0.500
conf(specialty cheese => other vegetables) = 0.500
conf(ready soups => rolls/buns) = 0.500
conf(rubbing alcohol => butter) = 0.500
conf(rubbing alcohol => citrus fruit) = 0.500

2. Simple string processing with Regex

Phone numbers

  • Write a function to parse US phone numbers written in the canonical “(404) 555-1212” format, i.e., a three-digit area code enclosed in parentheses followed by a seven-digit local number in three-hyphen-four digit format.
  • It should also ignore all leading and trailing spaces, as well as any spaces that appear between the area code and local numbers.
  • However, it should not accept any spaces in the area code (e.g., in ‘(404)’) nor should it in the local number.
  • It should return a triple of strings, (area_code, first_three, last_four).
  • If the input is not a valid phone number, it should raise a ValueError.
The following function implements the regex parser.
import re 
def parse_phone(s):
    pattern = re.compile("\s*\((\d{3})\)\s*(\d{3})-(\d{4})\s*")
    m = pattern.match(s)
    if not m:
        raise ValueError('not a valid phone number!')
    return m.groups()

#print(parse_phone1('(404) 201-2121'))    
#print(parse_phone1('404-201-2121'))  
  • Implement an enhanced phone number parser that can handle any of these patterns.
    • (404) 555-1212
    • (404) 5551212
    • 404-555-1212
    • 404-5551212
    • 404555-1212
    • 4045551212
  • As before, it should not be sensitive to leading or trailing spaces. Also, for the patterns in which the area code is enclosed in parentheses, it should not be sensitive to the number of spaces separating the area code from the remainder of the number.

The following function implements the enhanced regex parser.

import re 
def parse_phone2 (s):
    pattern = re.compile("\s*\((\d{3})\)\s*(\d{3})-?(\d{4})\s*")
    m = pattern.match(s)
    if not m:
        pattern2 = re.compile("\s*(\d{3})-?(\d{3})-?(\d{4})\s*")
        m = pattern2.match(s)
        if not m:
            raise ValueError('not a valid phone number!')
    return m.groups()

3. Tidy data and the Pandas

“Tidying data,” is all about cleaning up tabular data for analysis purposes.

Definition: Tidy datasets. More specifically, Wickham defines a tidy data set as one that can be organized into a 2-D table such that

  1. each column represents a variable;
  2. each row represents an observation;
  3. each entry of the table represents a single value, which may come from either categorical (discrete) or continuous spaces.

Definition: Tibbles. if a table is tidy, we will call it a tidy table, or tibble, for short.

Apply functions to data frames

Given the following pandas DataFrame (first few rows are shown in the next table),compute the prevalence, which is the ratio of cases to the population, using the apply() function, without modifying the original DataFrame.

country year cases population
0 Afghanistan ’99 745 19987071
1 Brazil ’99 37737 172006362
2 China ’99 212258 1272915272
3 Afghanistan ’00 2666 20595360
4 Brazil ’00 80488 174504898
5 China ’00 213766 1280428583

The next function does exactly the same thing.

def calc_prevalence(G):
    assert 'cases' in G.columns and 'population' in G.columns
    H = G.copy()
    H['prevalence'] = H.apply(lambda row: row['cases'] / row['population'], axis=1)
    return H

Tibbles and Bits

Now let’s start creating and manipulating tibbles.

Write a function, canonicalize_tibble(X), that, given a tibble X, returns a new copy Y of X in canonical order. We say Y is in canonical order if it has the following properties.

  1. The variables appear in sorted order by name, ascending from left to right.
  2. The rows appear in lexicographically sorted order by variable, ascending from top to bottom.
  3. The row labels (Y.index) go from 0 to n-1, where n is the number of observations.

The following code exactly does the same:

def canonicalize_tibble(X):
    # Enforce Property 1:
    var_names = sorted(X.columns)
    Y = X[var_names].copy()
    Y = Y.sort_values(by=var_names, ascending=True)
    Y.reset_index(drop=True, inplace=True)
    return Y

Basic tidying transformations: Implementing Melting and Casting

Given a data set and a target set of variables, there are at least two common issues that require tidying.

Melting

First, values often appear as columns. Table 4a is an example. To tidy up, we want to turn columns into rows:

tidy-9

Because this operation takes columns into rows, making a “fat” table more tall and skinny,  it is sometimes called melting.

To melt the table, we need to do the following.

  1. Extract the column values into a new variable. In this case, columns "1999"  and "2000" of table4 need to become the values of the variable, "year".
  2. Convert the values associated with the column values into a new variable as well. In this case, the values formerly in columns "1999" and "2000"become the values of the "cases" variable.

In the context of a melt, let’s also refer to "year" as the new key variable and
"cases" as the new value variable.

Implement the melt operation as a function,

def melt(df, col_vals, key, value):
        ...

It should take the following arguments:

  • df: the input data frame, e.g., table4 in the example above;
  • col_vals: a list of the column names that will serve as values;
  • key: name of the new variable, e.g., year in the example above;
  • value: name of the column to hold the values.

The next function implements the melt operation:

def melt(df, col_vals, key, value):
    assert type(df) is pd.DataFrame
    df2 = pd.DataFrame()
    for col in col_vals:
        df1 = pd.DataFrame(df[col].tolist(), columns=[value]) #, index=df.country)
        df1[key] = col
        other_cols = list(set(df.columns.tolist()) - set(col_vals))
        for col1 in other_cols:
            df1[col1] = df[col1]
        df2 = df2.append(df1, ignore_index=True)
    df2 = df2[other_cols + [key, value]]    
    return df2

with the following output

=== table4a ===
country 1999 2000
0 Afghanistan 745 2666
1 Brazil 37737 80488
2 China 212258 213766
=== melt(table4a) ===
country year cases
0 Afghanistan 1999 745
1 Brazil 1999 37737
2 China 1999 212258
3 Afghanistan 2000 2666
4 Brazil 2000 80488
5 China 2000 213766
=== table4b ===
country 1999 2000
0 Afghanistan 19987071 20595360
1 Brazil 172006362 174504898
2 China 1272915272 1280428583
=== melt(table4b) ===
country year population
0 Afghanistan 1999 19987071
1 Brazil 1999 172006362
2 China 1999 1272915272
3 Afghanistan 2000 20595360
4 Brazil 2000 174504898
5 China 2000 1280428583

Casting

The second most common issue is that an observation might be split across multiple rows. Table 2 is an example. To tidy up, we want to merge rows:

tidy-8.png

Because this operation is the moral opposite of melting, and “rebuilds” observations from parts, it is sometimes called casting.

Melting and casting are Wickham’s terms from his original paper on tidying data. In his more recent writing, on which this tutorial is based, he refers to the same operation as gathering. Again, this term comes from Wickham’s original paper, whereas his more recent summaries use the term spreading.

The signature of a cast is similar to that of melt. However, we only need to know the key, which is column of the input table containing new variable names, and the value, which is the column containing corresponding values.

Implement a function to cast a data frame into a tibble, given a key column containing new variable names and a value column containing the corresponding cells.

Observe that we are asking your cast() to accept an optional parameter, join_how, that may take the values 'outer' or 'inner' (with 'outer' as the default).

The following function implements the casting operation:

def cast(df, key, value, join_how='outer'):
    """Casts the input data frame into a tibble,
    given the key column and value column.
    """
    assert type(df) is pd.DataFrame
    assert key in df.columns and value in df.columns
    assert join_how in ['outer', 'inner']
    
    fixed_vars = df.columns.difference([key, value])
    tibble = pd.DataFrame(columns=fixed_vars) # empty frame
    
    fixed_vars = fixed_vars.tolist()
    #tibble[fixed_vars] = df[fixed_vars]
    cols = []
    for k,df1 in df.groupby(df[key]):
        #tibble = pd.concat([tibble.reset_index(drop=True), df1[value]], axis=1)
        #print(df1[fixed_vars+[value]].head())
        tibble = tibble.merge(df1[fixed_vars+[value]], on=fixed_vars, how=join_how)
        cols.append(str(k)) #list(set(df1[key]))[0])
    tibble.columns = fixed_vars + cols
 
    return tibble

with the following output:

=== table2 ===
country year type count
0 Afghanistan 1999 cases 745
1 Afghanistan 1999 population 19987071
2 Afghanistan 2000 cases 2666
3 Afghanistan 2000 population 20595360
4 Brazil 1999 cases 37737
5 Brazil 1999 population 172006362
6 Brazil 2000 cases 80488
7 Brazil 2000 population 174504898
8 China 1999 cases 212258
9 China 1999 population 1272915272
10 China 2000 cases 213766
11 China 2000 population 1280428583
=== tibble2 = cast (table2, "type", "count") ===
country year cases population
0 Afghanistan 1999 745 19987071
1 Afghanistan 2000 2666 20595360
2 Brazil 1999 37737 172006362
3 Brazil 2000 80488 174504898
4 China 1999 212258 1272915272
5 China 2000 213766 1280428583

Separating variables

Consider the following table.

 

country year rate
0 Afghanistan 1999 745/19987071
1 Afghanistan 2000 2666/20595360
2 Brazil 1999 37737/172006362
3 Brazil 2000 80488/174504898
4 China 1999 212258/1272915272
5 China 2000 213766/1280428583

In this table, the rate variable combines what had previously been the cases
andpopulation data. This example is an instance in which we might want to separate a column into two variables.

Write a function that takes a data frame (df) and separates an existing column (key) into new variables (given by the list of new variable names, into).  How will the separation happen? The caller should provide a function, splitter(x), that given a value returns a list containing the components.

 

The following code implements the function:

import re

def default_splitter(text):
    """Searches the given spring for all integer and floating-point
    values, returning them as a list _of strings_.
    
    E.g., the call
    
      default_splitter('Give me $10.52 in exchange for 91 kitten stickers.')
      
    will return ['10.52', '91'].
    """
    #fields = re.findall('(\d+\.?\d+)', text)
    fields = list(re.match('(\d+)/(\d+)', text).groups())
    return fields

def separate(df, key, into, splitter=default_splitter):
    """Given a data frame, separates one of its columns, the key,
    into new variables.
    """
    assert type(df) is pd.DataFrame
    assert key in df.columns    
    return (df.merge(df[key].apply(lambda s: pd.Series({into[i]:splitter(s)[i] for i in range(len(into))})), 
    left_index=True, right_index=True)).drop(key, axis=1)

with the following output:

=== table3 ===
country year rate
0 Afghanistan 1999 745/19987071
1 Afghanistan 2000 2666/20595360
2 Brazil 1999 37737/172006362
3 Brazil 2000 80488/174504898
4 China 1999 212258/1272915272
5 China 2000 213766/1280428583
=== tibble3 = separate (table3, ...) ===
country year cases population
0 Afghanistan 1999 745 19987071
1 Afghanistan 2000 2666 20595360
2 Brazil 1999 37737 172006362
3 Brazil 2000 80488 174504898
4 China 1999 212258 1272915272
5 China 2000 213766 1280428583
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