from dsc80_utils import *
📣 Announcements 📣¶
- Mid-quarter survey out, due tonight, Nov 9 at 11:59pm.
- https://forms.gle/khHDPRuhgTqZTW1e9
- If 90% of the class fills it out, everyone gets +1 point on the midterm.
- No discussion or OH tomorrow (Veteran's Day).
- Lab 6 due Monday.
- Project 3 due Friday, Nov 17.
Agenda¶
Lots and lots of regular expressions! Good resources:
- regex101.com, a helpful site to have open while writing regular expressions.
- Python
re
library documentation and how-to.- The "how-to" is great, read it!
- regex "cheat sheet" (taken from here).
Motivation¶
contact = '''
Thank you for buying our expensive product!
If you have a complaint, please send it to complaints@compuserve.com or call (800) 867-5309.
If you are happy with your purchase, please call us at (800) 123-4567; we'd love to hear from you!
Due to high demand, please allow one-hundred (100) business days for a response.
'''
Who called? 📞¶
- Goal: Extract all phone numbers from a piece of text, assuming they are of the form
'(###) ###-####'
.
print(contact)
Thank you for buying our expensive product! If you have a complaint, please send it to complaints@compuserve.com or call (800) 867-5309. If you are happy with your purchase, please call us at (800) 123-4567; we'd love to hear from you! Due to high demand, please allow one-hundred (100) business days for a response.
We can do this using the same string methods we've come to know and love.
Strategy:
- Split by spaces.
- Check if there are any consecutive "words" where:
- the first "word" looks like an area code, like
'(678)'
. - the second "word" looks like the last 7 digits of a phone number, like
'999-8212'
.
- the first "word" looks like an area code, like
Let's first write a function that takes in a string and returns whether it looks like an area code.
def is_possibly_area_code(s):
'''Does `s` look like (678)?'''
return (len(s) == 5 and
s.startswith('(') and
s.endswith(')') and
s[1:4].isnumeric())
is_possibly_area_code('(123)')
True
is_possibly_area_code('(99)')
False
Let's also write a function that takes in a string and returns whether it looks like the last 7 digits of a phone number.
def is_last_7_phone_number(s):
'''Does `s` look like 999-8212?'''
return len(s) == 8 and s[0:3].isnumeric() and s[3] == '-' and s[4:].isnumeric()
is_last_7_phone_number('999-8212')
True
is_last_7_phone_number('534 1100')
False
Finally, let's split the entire text by spaces, and check whether there are any instances where pieces[i]
looks like an area code and pieces[i+1]
looks like the last 7 digits of a phone number.
# Removes punctuation from the end of each string.
pieces = [s.rstrip('.,?;"\'') for s in contact.split()]
for i in range(len(pieces) - 1):
if is_possibly_area_code(pieces[i]):
if is_last_7_phone_number(pieces[i+1]):
print(pieces[i], pieces[i+1])
(800) 867-5309 (800) 123-4567
Is there a better way?¶
- This was an example of pattern matching.
- It can be done with string methods, but there is often a better approach: regular expressions.
print(contact)
Thank you for buying our expensive product! If you have a complaint, please send it to complaints@compuserve.com or call (800) 867-5309. If you are happy with your purchase, please call us at (800) 123-4567; we'd love to hear from you! Due to high demand, please allow one-hundred (100) business days for a response.
import re
re.findall(r'\(\d{3}\) \d{3}-\d{4}', contact)
['(800) 867-5309', '(800) 123-4567']
🤯
Basic regular expressions¶
Regular expressions¶
A regular expression, or regex for short, is a sequence of characters used to match patterns in strings.
- For example,
\(\d{3}\) \d{3}-\d{4}
describes a pattern that matches US phone numbers of the form'(XXX) XXX-XXXX'
. - Think of regex as a "mini-language" (formally: they are a grammar for describing a language).
- For example,
Pros: They are very powerful and are widely used (virtually every programming language has a module for working with them).
Cons: They can be hard to read and have many different "dialects."
Writing regular expressions¶
You will ultimately write most of your regular expressions in Python, using the
re
module. We will see how to do so shortly.However, a useful tool for designing regular expressions is regex101.com.
We will use it heavily during lecture; you should have it open as we work through examples. If you're trying to revisit this lecture in the future, you'll likely want to watch the podcast.
Literals¶
A literal is a character that has no special meaning.
Letters, numbers, and some symbols are all literals.
Some symbols, like
.
,*
,(
, and)
, are special characters.*Example:* The regex
hey
matches the string'hey'
. The regexhe.
also matches the string'hey'
.
Regex building blocks 🧱¶
The four main building blocks for all regexes are shown below (table source, inspiration).
operation | order of op. | example | matches ✅ | does not match ❌ |
---|---|---|---|---|
concatenation | 3 | AABAAB |
'AABAAB' |
every other string |
or | 4 | AA|BAAB |
'AA' , 'BAAB' |
every other string |
closure (zero or more) |
2 | AB*A |
'AA' , 'ABBBBBBA' |
'AB' , 'ABABA' |
parentheses | 1 | A(A|B)AAB (AB)*A |
'AAAAB' , 'ABAAB' 'A' , 'ABABABABA' |
every other string'AA' , 'ABBA' |
Note that |
, (
, )
, and *
are special characters, not literals. They manipulate the characters around them.
*Example (or, parentheses):*
- What does
DSC 30|80
match? - What does
DSC (30|80)
match?
*Example (closure, parentheses):*
- What does
blah*
match? - What does
(blah)*
match?
Exercise¶
Write a regular expression that matches 'billy'
, 'billlly'
, 'billlllly'
, etc.
- First, think about how to match strings with any even number of
'l'
s, including zero'l'
s (i.e.'biy'
). - Then, think about how to match only strings with a positive even number of
'l'
s.
✅ Click here to see the answer after you've tried it yourself at regex101.com.
bi(ll)*y
will match any even number of 'l'
s, including 0.
To match only a positive even number of 'l'
s, we'd need to first "fix into place" two 'l'
s, and then follow that up with zero or more pairs of 'l'
s. This specifies the regular expression bill(ll)*y
.
Exercise¶
Write a regular expression that matches 'billy'
, 'billlly'
, 'biggy'
, 'biggggy'
, etc.
Specifically, it should match any string with a positive even number of 'l'
s in the middle, or a positive even number of 'g'
s in the middle.
✅ Click here to see the answer after you've tried it yourself at regex101.com.
Possible answers: bi(ll(ll)*|gg(gg)*)y
or bill(ll)*y|bigg(gg)*y
.
Note, bill(ll)*|gg(gg)*y
is not a valid answer! This is because "concatenation" comes before "or" in the order of operations. This regular expression would match strings that match bill(ll)*
, like 'billll'
, OR strings that match gg(gg)*y
, like 'ggy'
.
Intermediate regex¶
More regex syntax¶
operation | example | matches ✅ | does not match ❌ |
---|---|---|---|
wildcard | .U.U.U. |
'CUMULUS' 'JUGULUM' |
'SUCCUBUS' 'TUMULTUOUS' |
character class | [A-Za-z][a-z]* |
'word' 'Capitalized' |
'camelCase' '4illegal' |
at least one | bi(ll)+y |
'billy' 'billlllly' |
'biy' 'bily' |
between $i$ and $j$ occurrences | m[aeiou]{1,2}m |
'mem' 'maam' 'miem' |
'mm' 'mooom' 'meme' |
.
, [
, ]
, +
, {
, and }
are also special characters, in addition to |
, (
, )
, and *
.
*Example (character classes, at least one):* [A-E]+
is just shortform for (A|B|C|D|E)(A|B|C|D|E)*
.
*Example (wildcard):*
- What does
.
match? - What does
he.
match? - What does
...
match?
*Example (at least one, closure):*
- What does
123+
match? - What does
123*
match?
*Example (number of occurrences):* What does tri{3, 5}
match? Does it match 'triiiii'
?
*Example (character classes, number of occurrences):* What does [1-6a-f]{3}-[7-9E-S]{2}
match?
Exercise¶
Write a regular expression that matches any lowercase string has a repeated vowel, such as 'noon'
, 'peel'
, 'festoon'
, or 'zeebraa'
.
✅ Click here to see the answer after you've tried it yourself at regex101.com.
One answer: [a-z]*(aa|ee|ii|oo|uu)[a-z]*
This regular expression matches strings of lowercase characters that have 'aa'
, 'ee'
, 'ii'
, 'oo'
, or 'uu'
in them anywhere. [a-z]*
means "zero or more of any lowercase characters"; essentially we are saying it doesn't matter what letters come before or after the double vowels, as long as the double vowels exist somewhere.
Exercise¶
Write a regular expression that matches any string that contains both a lowercase letter and a number, in any order. Examples include 'billy80'
, '80!!billy'
, and 'bil8ly0'
.
✅ Click here to see the answer after you've tried it yourself at regex101.com.
One answer: (.*[a-z].*[0-9].*)|(.*[0-9].*[a-z].*)
We can break the above regex into two parts – everything before the |
, and everything after the |
.
The first part, .*[a-z].*[0-9].*
, matches strings in which there is at least one lowercase character and at least one digit, with the lowercase character coming first.
The second part, .*[0-9].*[a-z].*
, matches strings in which there is at least one lowercase character and at least one digit, with the digit coming first.
Note, the .*
between the digit and letter classes is needed in the event the string has non-digit and non-letter characters.
This is the kind of task that would be easier to accomplish with regular Python string methods.
Even more regex syntax¶
operation | example | matches ✅ | does not match ❌ |
---|---|---|---|
escape character | ucsd\.edu |
'ucsd.edu' |
'ucsd!edu' |
beginning of line | ^ark |
'ark two' 'ark o ark' |
'dark' |
end of line | ark$ |
'dark' 'ark o ark' |
'ark two' |
zero or one | cat? |
'ca' 'cat' |
'cart' (matches 'ca' only) |
built-in character classes* | \w+ \d+ |
'billy' '231231' |
'this person' '858 people' |
character class negation | [^a-z]+ |
'KINGTRITON551' '1721$$' |
'porch' 'billy.edu' |
**Note: in Python's implementation of regex,*
\d
refers to digits.\w
refers to alphanumeric characters ([A-Z][a-z][0-9]_
).\s
refers to whitespace.\b
is a word boundary.
*Example (escaping):*
- What does
he.
match? - What does
he\.
match? - What does
(858)
match? - What does
\(858\)
match?
*Example (anchors):*
- What does
858-534
match? - What does
^858-534
match? - What does
858-534$
match?
Example (built-in character classes)¶
**Note: in Python's implementation of regex,*
\d
refers to digits.\w
refers to alphanumeric characters ([A-Z][a-z][0-9]_
).\s
refers to whitespace.\b
is a word boundary.What does
\d{3} \d{3}-\d{4}
match?What does
\bcat\b
match? Does it find a match in'my cat is hungry'
? What about'concatenate'
?
Exercise¶
Write a regular expression that matches any string that:
- is between 5 and 10 characters long, and
- is made up of only vowels (either uppercase or lowercase, including
'Y'
and'y'
), periods, and spaces.
Examples include 'yoo.ee.IOU'
and 'AI.I oey'
.
✅ Click here to see the answer after you've tried it yourself at regex101.com.
One answer: ^[aeiouyAEIOUY. ]{5,10}$
Key idea: Within a character class (i.e. [...]
), special characters do not generally need to be escaped.
Regex in Python¶
re
in Python¶
The re
package is built into Python. It allows us to use regular expressions to find, extract, and replace strings.
import re
re.search
takes in a string regex
and a string text
and returns the location and substring corresponding to the first match of regex
in text
.
re.search('AB*A',
'here is a string for you: ABBBA. here is another: ABBBBBBBA')
<re.Match object; span=(26, 31), match='ABBBA'>
re.findall
takes in a string regex
and a string text
and returns a list of all matches of regex
in text
. You'll use this most often.
re.findall('AB*A',
'here is a string for you: ABBBA. here is another: ABBBBBBBA')
['ABBBA', 'ABBBBBBBA']
re.sub
takes in a string regex
, a string repl
, and a string text
, and replaces all matches of regex
in text
with repl
.
re.sub('AB*A',
'billy',
'here is a string for you: ABBBA. here is another: ABBBBBBBA')
'here is a string for you: billy. here is another: billy'
Raw strings¶
When using regular expressions in Python, it's a good idea to use raw strings, denoted by an r
before the quotes, e.g. r'exp'
.
re.findall('\bcat\b', 'my cat is hungry')
[]
re.findall(r'\bcat\b', 'my cat is hungry')
['cat']
# Huh?
print('\bcat\b')
cat
Capture groups¶
- Surround a regex with
(
and)
to define a capture group within a pattern.
- Capture groups are useful for extracting relevant parts of a string.
re.findall(r'\w+@(\w+)\.edu',
'my old email was billy@notucsd.edu, my new email is notbilly@ucsd.edu')
['notucsd', 'ucsd']
- Notice what happens if we remove the
(
and)
!
re.findall(r'\w+@\w+\.edu',
'my old email was billy@notucsd.edu, my new email is notbilly@ucsd.edu')
['billy@notucsd.edu', 'notbilly@ucsd.edu']
- Earlier, we also saw that parentheses can be used to group parts of a regex together. When using
re.findall
, all groups are treated as capturing groups.
# A regex that matches strings with two of the same vowel followed by 3 digits
# We only want to capture the digits, but...
re.findall(r'(aa|ee|ii|oo|uu)(\d{3})', 'eeoo124')
[('oo', '124')]
Example: Log parsing¶
Web servers typically record every request made of them in the "logs".
s = '''132.249.20.188 - - [24/Feb/2023:12:26:15 -0800] "GET /my/home/ HTTP/1.1" 200 2585'''
Let's use our new regex syntax (including capturing groups) to extract the day, month, year, and time from the log string s
.
exp = '\[(.+)\/(.+)\/(.+):(.+):(.+):(.+) .+\]'
re.findall(exp, s)
[('24', 'Feb', '2023', '12', '26', '15')]
While above regex works, it is not very specific. It works on incorrectly formatted log strings.
other_s = '[adr/jduy/wffsdffs:r4s4:4wsgdfd:asdf 7]'
re.findall(exp, other_s)
[('adr', 'jduy', 'wffsdffs', 'r4s4', '4wsgdfd', 'asdf')]
The more specific, the better!¶
- Be as specific in your pattern matching as possible – you don't want to match and extract strings that don't fit the pattern you care about.
.*
matches every possible string, but we don't use it very often.
- A better date extraction regex:
\[(\d{2})\/([A-Z]{1}[a-z]{2})\/(\d{4}):(\d{2}):(\d{2}):(\d{2}) -\d{4}\]
- `\d{2}` matches any 2-digit number.
- `[A-Z]{1}` matches any single occurrence of any uppercase letter.
- `[a-z]{2}` matches any 2 consecutive occurrences of lowercase letters.
- Remember, special characters (`[`, `]`, `/`) need to be escaped with `\`.
s
'132.249.20.188 - - [24/Feb/2023:12:26:15 -0800] "GET /my/home/ HTTP/1.1" 200 2585'
new_exp = '\[(\d{2})\/([A-Z]{1}[a-z]{2})\/(\d{4}):(\d{2}):(\d{2}):(\d{2}) -\d{4}\]'
re.findall(new_exp, s)
[('24', 'Feb', '2023', '12', '26', '15')]
A benefit of new_exp
over exp
is that it doesn't capture anything when the string doesn't follow the format we specified.
other_s
'[adr/jduy/wffsdffs:r4s4:4wsgdfd:asdf 7]'
re.findall(new_exp, other_s)
[]
Limitations¶
Limitations of regexes¶
Writing a regular expression is like writing a program.
- You need to know the syntax well.
- They can be easier to write than to read.
- They can be difficult to debug.
Regular expressions are terrible at certain types of problems. Examples:
- Anything involving counting (same number of instances of a and b).
- Anything involving complex structure (palindromes).
- Parsing highly complex text structure (HTML, for instance).
Text features¶
Review: Regression and features¶
In DSC 40A, our running example was to use regression to predict a data scientist's salary, given their GPA, years of experience, and years of education.
After minimizing empirical risk to determine optimal parameters, $w_0^*, \dots, w_3^*$, we made predictions using:
GPA, years of experience, and years of education are features – they represent a data scientist as a vector of numbers.
- e.g. Your feature vector may be [3.5, 1, 7].
This approach requires features to be numerical.
Moving forward¶
Suppose we'd like to predict the sentiment of a piece of text from 1 to 10.
- 10: Very positive (happy).
- 1: Very negative (sad, angry).
Example:
Input: "DSC 80 is a pretty good class."
Output: 7.
We can frame this as a regression problem, but we can't directly use what we learned in 40A, because here our inputs are text, not numbers.
Text features¶
Big question: How do we represent a text document as a feature vector of numbers?
If we can do this, we can:
- use a text document as input in a regression or classification model (in a few lectures).
- quantify the similarity of two text documents (today).
Example: San Diego employee salaries¶
- Transparent California publishes the salaries of all City of San Diego employees.
- Let's look at the 2021 data.
salaries = pd.read_csv('https://transcal.s3.amazonaws.com/public/export/san-diego-2021.csv')
salaries['Employee Name'] = salaries['Employee Name'].str.split().str[0] + ' Xxxx'
salaries.head()
Employee Name | Job Title | Base Pay | Overtime Pay | ... | Year | Notes | Agency | Status | |
---|---|---|---|---|---|---|---|---|---|
0 | Mara Xxxx | City Attorney | 218759.0 | 0.0 | ... | 2021 | NaN | San Diego | FT |
1 | Todd Xxxx | Mayor | 218759.0 | 0.0 | ... | 2021 | NaN | San Diego | FT |
2 | Elizabeth Xxxx | Investment Officer | 259732.0 | 0.0 | ... | 2021 | NaN | San Diego | FT |
3 | Terence Xxxx | Police Officer | 212837.0 | 0.0 | ... | 2021 | NaN | San Diego | FT |
4 | Andrea Xxxx | Independent Budget Analyst | 224312.0 | 0.0 | ... | 2021 | NaN | San Diego | FT |
5 rows × 13 columns
Aside on privacy and ethics¶
Even though the data we downloaded is publicly available, employee names still correspond to real people.
Be careful when dealing with PII (personably identifiable information).
- Only work with the data that is needed for your analysis.
- Even when data is public, people have a reasonable right to privacy.
Remember to think about the impacts of your work outside of your Jupyter Notebook.
Goal: Quantifying similarity¶
Our goal is to describe, numerically, how similar two job titles are.
For instance, our similarity metric should tell us that
'Deputy Fire Chief'
and'Fire Battalion Chief'
are more similar than'Deputy Fire Chief'
and'City Attorney'
.Idea: Two job titles are similar if they contain shared words, regardless of order. So, to measure the similarity between two job titles, let's count the number of words they share in common.
Before we do this, we need to be confident that the job titles are clean and consistent – let's explore.
Exploring job titles¶
jobtitles = salaries['Job Title']
jobtitles.head()
0 City Attorney 1 Mayor 2 Investment Officer 3 Police Officer 4 Independent Budget Analyst Name: Job Title, dtype: object
How many employees are in the dataset? How many unique job titles are there?
jobtitles.shape[0], jobtitles.nunique()
(12305, 588)
What are the most common job titles?
jobtitles.value_counts().iloc[:100]
Police Officer 2123 Fire Fighter Ii 331 Assistant Engineer - Civil 284 ... Executive Assistant 26 Paralegal 26 Librarian Iv 25 Name: Job Title, Length: 100, dtype: int64
jobtitles.value_counts().iloc[:25].sort_values().plot(kind='barh')
Are there any missing job titles?
jobtitles.isna().sum()
2
There aren't many. To avoid having to deal with missing values later on, let's just drop the two missing job titles now.
jobtitles = jobtitles[jobtitles.notna()]
Canonicalization¶
Remember, our goal is ultimately to count the number of shared words between job titles. But before we start counting the number of shared words, we need to consider the following:
Some job titles may have punctuation, like
'-'
and'&'
, which may count as words when they shouldn't.'Assistant - Manager'
and'Assistant Manager'
should count as the same job title.
Some job titles may have "glue" words, like
'to'
and'the'
, which (we can argue) also shouldn't count as words.'Assistant To The Manager'
and'Assistant Manager'
should count as the same job title.
Let's address the above issues. The process of converting job titles so that they are always represented the same way is called canonicalization.
Punctuation¶
Are there job titles with unnecessary punctuation that we can remove?
To find out, we can write a regular expression that looks for characters other than letters, numbers, and spaces.
We can use regular expressions with the
.str
methods we learned earlier in the quarter just by usingregex=True
.
# Uses character class negation
jobtitles.str.contains(r'[^A-Za-z0-9 ]', regex=True).sum()
845
jobtitles[jobtitles.str.contains(r'[^A-Za-z0-9 ]', regex=True)].head()
281 Park & Recreation Director 539 Associate Engineer - Mechanical 1023 Associate Engineer - Civil 1376 Associate Engineer - Traffic 1460 Budget/Legislative Analyst I Name: Job Title, dtype: object
It seems like we should replace these pieces of punctuation with a single space.
"Glue" words¶
Are there job titles with "glue" words in the middle, such as 'Assistant to the Manager'
?
To figure out if any titles contain the word 'to'
, we can't just do the following, because it will evaluate to True
for job titles that have 'to'
anywhere in them, even if not as a standalone word.
# Why are we converting to lowercase?
jobtitles.str.lower().str.contains('to').sum()
1541
jobtitles[jobtitles.str.lower().str.contains('to')]
0 City Attorney 10 Assistant Retirement Administrator 25 Department Director ... 12190 Deputy Director 12210 City Attorney Investigator 12267 Test Monitor Ii Name: Job Title, Length: 1541, dtype: object
Instead, we need to look for 'to'
separated by word boundaries.
jobtitles.str.lower().str.contains(r'\bto\b', regex=True).sum()
11
jobtitles[jobtitles.str.lower().str.contains(r'\bto\b', regex=True)]
664 Assistant To The Fire Chief 1403 Principal Assistant To City Attorney 2358 Assistant To The Director ... 7544 Confidential Secretary To Mayor 9627 Principal Assistant To City Attorney 12061 Assistant To The Director Name: Job Title, Length: 11, dtype: object
We can look for other filler words too, like 'the'
and 'for'
.
jobtitles[jobtitles.str.lower().str.contains(r'\bthe\b', regex=True)]
664 Assistant To The Fire Chief 2358 Assistant To The Director 4459 Assistant To The Director 5685 Assistant To The Director 12061 Assistant To The Director Name: Job Title, dtype: object
jobtitles[jobtitles.str.lower().str.contains(r'\bfor\b', regex=True)]
3676 Assistant For Community Outreach 4451 Assistant For Community Outreach 11010 Assistant For Community Outreach Name: Job Title, dtype: object
We should probably remove these "glue" words.
Fixing punctuation and removing "glue" words¶
Let's put the following two steps together, and canonicalize job titles by:
- converting to lowercase,
- removing each occurrence of
'to'
,'the'
, and'for'
, - replacing each non-letter/digit/space character with a space, and
- replacing each sequence of multiple spaces with a single space.
jobtitles = (
jobtitles
.str.lower()
.str.replace(r'\bto\b|\bthe\b|\bfor\b', '', regex=True)
.str.replace('[^A-Za-z0-9 ]', ' ', regex=True)
.str.replace(' +', ' ', regex=True) # ' +' matches 1 or more occurrences of a space.
.str.strip() # Removes leading/trailing spaces if present.
)
jobtitles.sample(10)
5584 senior clerk typist 11658 assistant management analyst 8779 grounds maintenance worker ii ... 5751 associate engineer civil 9138 grounds maintenance worker ii 8213 payroll audit specialist ii Name: Job Title, Length: 10, dtype: object
Possible issue: inconsistent representations¶
Another possible issue is that some job titles may have inconsistent representations of the same word (e.g. 'Asst.'
vs 'Assistant'
).
jobtitles[jobtitles.str.contains('asst')].value_counts()
Series([], Name: Job Title, dtype: int64)
jobtitles[jobtitles.str.contains('assistant')].value_counts().head()
assistant engineer civil 284 library assistant i 127 library assistant ii 116 library assistant iii 107 clerical assistant ii 100 Name: Job Title, dtype: int64
The 2020 salaries dataset had several of these issues, but fortunately they appear to be fixed for us in the 2021 dataset (thanks, Transparent California).
Bag of words 💰¶
Text similarity¶
Recall, our idea is to measure the similarity of two job titles by counting the number of shared words between the job titles. How do we actually do that, for all of the job titles we have?
A counts matrix¶
Let's create a "counts" matrix, such that:
- there is 1 row per job title,
- there is 1 column per unique word that is used in job titles, and
- the value in row
title
and columnword
is the number of occurrences ofword
intitle
.
Such a matrix might look like:
senior | lecturer | teaching | professor | assistant | associate | |
---|---|---|---|---|---|---|
senior lecturer | 1 | 1 | 0 | 0 | 0 | 0 |
assistant teaching professor | 0 | 0 | 1 | 1 | 1 | 0 |
associate professor | 0 | 0 | 0 | 1 | 0 | 1 |
senior assistant to the assistant professor | 1 | 0 | 0 | 1 | 2 | 0 |
- Then, we can make statements like:
- "assistant teaching professor" is more similar to "associate professor" than to "senior lecturer".
- Next time!