Set Operations & Distinct Elements (np.unique, intersect1d, isin)0%

Dot Products & Matrix Multiplication (dot, @ operator, matmul)

Set Operations & Distinct Elements (np.unique, intersect1d, isin)

Beginner12 min read•Updated: Jul 11, 2026

Set Operations: unique(), intersect1d(), isin()

Working with categorical variables, database identifiers, and discrete groups frequently requires set-theoretic operations—such as finding distinct values, computing intersections between user cohorts, and testing membership across master lists.

NumPy provides high-performance 1D set operations implemented on sorted arrays, executing orders of magnitude faster than standard Python set objects.

1. Extracting Distinct Elements with `np.unique()`

np.unique(ar) finds all unique elements in an array and returns them in sorted order:

1import numpy as np
2 
3customer_ids = np.array([105, 102, 108, 102, 105, 109, 102, 108])
4 
5distinct_ids = np.unique(customer_ids)
6print("Unique customer IDs (sorted):", distinct_ids)

Output:

1Unique customer IDs (sorted): [102 105 108 109]

Advanced Features of `np.unique()`:

np.unique() provides three powerful optional parameters:

1
return_counts=True: Returns the frequency count of each distinct element.
2
return_index=True: Returns the index of the first occurrence of each unique element.
3
return_inverse=True: Returns integer indices to reconstruct the original array from the unique values (categorical label encoding!).

1labels = np.array(["Cat", "Dog", "Dog", "Bird", "Cat", "Dog"])
2 
3classes, counts = np.unique(labels, return_counts=True)
4print("Distinct classes:", classes)
5print("Frequency counts:", counts)
6 
7# Integer encoding (reconstruction indices):
8classes, encoded = np.unique(labels, return_inverse=True)
9print("Integer Encoded:", encoded)
10print("Reconstructed:   ", classes[encoded])

Output:

1Distinct classes: ['Bird' 'Cat' 'Dog']
2Frequency counts: [1 2 3]
3Integer Encoded: [1 2 2 0 1 2]
4Reconstructed:    ['Cat' 'Dog' 'Dog' 'Bird' 'Cat' 'Dog']

2. Testing Membership with `np.isin()`

To check whether elements in an array belong to a reference target list or cohort, use np.isin(element, test_elements). It returns a boolean array of the same shape:

1product_catalog = np.array([101, 102, 103, 104, 105, 106, 107])
2promotional_skus = np.array([102, 105, 999])
3 
4# Boolean mask of promotional products
5is_promo = np.isin(product_catalog, promotional_skus)
6print("Is promo mask:", is_promo)
7 
8# Filter catalog:
9print("Promotional products in stock:", product_catalog[is_promo])

3. Set Theoretic Operations: Union, Intersection, Difference

NumPy implements standard mathematical set algebra on 1D arrays:

1cohort_A = np.array([1, 2, 3, 4, 5, 6])
2cohort_B = np.array([4, 5, 6, 7, 8, 9])
3 
4# 1. Intersection: Elements present in BOTH sets (A ∩ B)
5common = np.intersect1d(cohort_A, cohort_B)
6print("Intersection (common):    ", common)  # [4 5 6]
7 
8# 2. Union: Elements present in EITHER set (A ∪ B)
9all_unique = np.union1d(cohort_A, cohort_B)
10print("Union (all unique):       ", all_unique)  # [1 2 3 4 5 6 7 8 9]
11 
12# 3. Difference: Elements in A that are NOT in B (A - B)
13only_A = np.setdiff1d(cohort_A, cohort_B)
14print("Difference (in A, not B): ", only_A)  # [1 2 3]
15 
16# 4. Symmetric Difference: Elements in A or B, but NOT both (XOR)
17exclusive = np.setxor1d(cohort_A, cohort_B)
18print("Exclusive (A XOR B):      ", exclusive)  # [1 2 3 7 8 9]

Interactive Quiz• Knowledge Check

Multiple Choice Questions

Question 1

In what order does np.unique() return the distinct elements?

Question 2

Which parameter of np.unique() returns the occurrence frequency of each distinct value?

Question 3

What does np.intersect1d(arr1, arr2) compute?

Question 4

Given catalog = np.array([10, 20, 30, 40]), what is the output of np.isin(catalog, [20, 99])?

Question 5

What does setting return_inverse=True in np.unique() provide?

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Dot Products & Matrix Multiplication (dot, @ operator, matmul)

Set Operations & Distinct Elements (np.unique, intersect1d, isin)

Beginner12 min read•Updated: Jul 11, 2026

Study Materials Cheatsheet

Set Operations: unique(), intersect1d(), isin()

NumPy provides high-performance 1D set operations implemented on sorted arrays, executing orders of magnitude faster than standard Python set objects.

1. Extracting Distinct Elements with `np.unique()`

np.unique(ar) finds all unique elements in an array and returns them in sorted order:

1import numpy as np
2 
3customer_ids = np.array([105, 102, 108, 102, 105, 109, 102, 108])
4 
5distinct_ids = np.unique(customer_ids)
6print("Unique customer IDs (sorted):", distinct_ids)

Output:

1Unique customer IDs (sorted): [102 105 108 109]

Advanced Features of `np.unique()`:

np.unique() provides three powerful optional parameters:

1
return_counts=True: Returns the frequency count of each distinct element.
2
return_index=True: Returns the index of the first occurrence of each unique element.
3
return_inverse=True: Returns integer indices to reconstruct the original array from the unique values (categorical label encoding!).

1labels = np.array(["Cat", "Dog", "Dog", "Bird", "Cat", "Dog"])
2 
3classes, counts = np.unique(labels, return_counts=True)
4print("Distinct classes:", classes)
5print("Frequency counts:", counts)
6 
7# Integer encoding (reconstruction indices):
8classes, encoded = np.unique(labels, return_inverse=True)
9print("Integer Encoded:", encoded)
10print("Reconstructed:   ", classes[encoded])

Output:

1Distinct classes: ['Bird' 'Cat' 'Dog']
2Frequency counts: [1 2 3]
3Integer Encoded: [1 2 2 0 1 2]
4Reconstructed:    ['Cat' 'Dog' 'Dog' 'Bird' 'Cat' 'Dog']

2. Testing Membership with `np.isin()`

To check whether elements in an array belong to a reference target list or cohort, use np.isin(element, test_elements). It returns a boolean array of the same shape:

1product_catalog = np.array([101, 102, 103, 104, 105, 106, 107])
2promotional_skus = np.array([102, 105, 999])
3 
4# Boolean mask of promotional products
5is_promo = np.isin(product_catalog, promotional_skus)
6print("Is promo mask:", is_promo)
7 
8# Filter catalog:
9print("Promotional products in stock:", product_catalog[is_promo])

3. Set Theoretic Operations: Union, Intersection, Difference

NumPy implements standard mathematical set algebra on 1D arrays:

1cohort_A = np.array([1, 2, 3, 4, 5, 6])
2cohort_B = np.array([4, 5, 6, 7, 8, 9])
3 
4# 1. Intersection: Elements present in BOTH sets (A ∩ B)
5common = np.intersect1d(cohort_A, cohort_B)
6print("Intersection (common):    ", common)  # [4 5 6]
7 
8# 2. Union: Elements present in EITHER set (A ∪ B)
9all_unique = np.union1d(cohort_A, cohort_B)
10print("Union (all unique):       ", all_unique)  # [1 2 3 4 5 6 7 8 9]
11 
12# 3. Difference: Elements in A that are NOT in B (A - B)
13only_A = np.setdiff1d(cohort_A, cohort_B)
14print("Difference (in A, not B): ", only_A)  # [1 2 3]
15 
16# 4. Symmetric Difference: Elements in A or B, but NOT both (XOR)
17exclusive = np.setxor1d(cohort_A, cohort_B)
18print("Exclusive (A XOR B):      ", exclusive)  # [1 2 3 7 8 9]

Interactive Quiz• Knowledge Check

Multiple Choice Questions

Question 1

In what order does np.unique() return the distinct elements?

Question 2

Which parameter of np.unique() returns the occurrence frequency of each distinct value?

Question 3

What does np.intersect1d(arr1, arr2) compute?

Question 4

Given catalog = np.array([10, 20, 30, 40]), what is the output of np.isin(catalog, [20, 99])?

Question 5

What does setting return_inverse=True in np.unique() provide?

Next Lesson

Dot Products & Matrix Multiplication (dot, @ operator, matmul)

Continue learning with hands-on practice, examples, and exercises in the upcoming topic.

Related Lessons

Previous Lesson	Next Lesson
Searching & Counting (argmax, argmin, nonzero, count_nonzero)	Dot Products & Matrix Multiplication (dot, @ operator, matmul)

Practice Quiz

Test your understanding of this lesson with 5 questions. Each question has one correct answer.

Previous Next

Set Operations: unique(), intersect1d(), isin()

1. Extracting Distinct Elements with np.unique()

Advanced Features of np.unique():

2. Testing Membership with np.isin()

3. Set Theoretic Operations: Union, Intersection, Difference

Multiple Choice Questions

Dot Products & Matrix Multiplication (dot, @ operator, matmul)

Related Lessons

Practice Quiz

Loading Page Content...

Set Operations: unique(), intersect1d(), isin()

1. Extracting Distinct Elements with np.unique()

Advanced Features of np.unique():

2. Testing Membership with np.isin()

3. Set Theoretic Operations: Union, Intersection, Difference

Multiple Choice Questions

Dot Products & Matrix Multiplication (dot, @ operator, matmul)

Related Lessons

Practice Quiz

1. Extracting Distinct Elements with `np.unique()`

Advanced Features of `np.unique()`:

2. Testing Membership with `np.isin()`

1. Extracting Distinct Elements with `np.unique()`

Advanced Features of `np.unique()`:

2. Testing Membership with `np.isin()`