get_subsequences_all_sequences()

get_subsequences_all_sequences() counts how many distinct subsequences exist in each sequence.

A subsequence is any sequence that can be derived by deleting some (or no) elements without changing the order of the remaining elements. For example, from sequence [A, B, A], we can get subsequences like [], [A], [B], [A, A], [A, B], [B, A], and [A, B, A].

This function helps you understand the complexity and diversity of your sequences. Higher numbers mean more possible subsequences, indicating more complex patterns.

Function Usage

A minimal example with only the required parameters (sufficient for most use cases):

result = get_subsequences_all_sequences(sequence_data)

A complete example with all available parameters (for advanced customization):

result = get_subsequences_all_sequences(
    sequence_data,
    dss=True,           # optional, default = True
    with_missing=False  # optional, default = False
)

Entry Parameters

Parameter	Required	Type	Description
seqdata	✓	SequenceData	A SequenceData object containing the sequences you want to analyze.
dss	✗	bool	If True, removes consecutive duplicate states before counting (e.g., [A, A, B, B] becomes [A, B]). Default = True.
with_missing	✗	bool	If True, includes missing values in the calculation. Default = False.

What It Does

• Processes each sequence in your dataset.

• If dss=True, applies distinct state sequence preprocessing: removes consecutive duplicate states (e.g., [A, A, B, B, A] → [A, B, A]).

• Counts distinct subsequences using a dynamic programming algorithm.

• Handles empty sequences (returns 1, representing the empty subsequence).

• Returns a Pandas DataFrame with one value per sequence.

Examples

1. Basic example

import pandas as pd
from sequenzo.define_sequence_data import SequenceData
from sequenzo.characteristics.simple_characteristics import get_subsequences_all_sequences

# Example dataset
df = pd.DataFrame({
    "ID": [1, 2, 3],
    "Y1": ["A", "A", "B"],
    "Y2": ["B", "A", "B"],
    "Y3": ["C", "C", "B"]
})

time_list = ["Y1", "Y2", "Y3"]
states = ["A", "B", "C"]

sequence_data = SequenceData(df, time=time_list, states=states, id_col="ID")

# Calculate number of subsequences
result = get_subsequences_all_sequences(sequence_data)
print(result)

Output:

   Subseq.
0        7
1        3
2        4

2. Without DSS preprocessing (dss=False)

result = get_subsequences_all_sequences(sequence_data, dss=False)
print(result)

When dss=False, consecutive duplicates are preserved, which may result in different counts:

   Subseq.
0        7
1        4
2        4

3. With real dataset (employment sequences)

result = get_subsequences_all_sequences(sequence_data)
print(result.head())

Output:

   Subseq.
0       15
1       23
2        8
...

Interpretation: Higher values indicate more complex sequences with more possible subsequences. This can help identify sequences with diverse patterns and structures.

Author

Code: Yuqi Liang

Documentation: Yuqi Liang