Ordinal Partition Network

class driada.recurrence.opn.OrdinalPartitionNetwork(data, d, tau, create_nx_graph=False)[source]

Bases: Network

Ordinal partition network from 1D time series.

Embeds with Takens delay embedding, ranks elements to get ordinal patterns. Nodes = unique patterns, directed weighted edges = transition probabilities between consecutive patterns.

Parameters:

data (array-like, 1D) – Raw time series values.
d (int) – Embedding dimension (pattern length). Must be <= 7.
tau (int) – Embedding delay.

Notes

Tied values in the time series are ranked by position (stable argsort), so equal values receive deterministic but position-dependent ordinal patterns. This is standard practice (Bandt & Pompe, 2002).

__init__(data, d, tau, create_nx_graph=False)[source]

Initialize a Network object from adjacency matrix or NetworkX graph.

Creates a network representation with automatic detection of directed/weighted properties if not specified. Supports preprocessing to extract connected components.

Parameters:

adj (scipy.sparse matrix or None) – Adjacency matrix. Mutually exclusive with graph parameter.
graph (networkx.Graph/DiGraph or None) – NetworkX graph object. Mutually exclusive with adj parameter.
preprocessing (str or None, default="giant_cc") –
Preprocessing method:
- None: No preprocessing
- ”remove_isolates”: Remove isolated nodes
- ”giant_cc”: Extract giant connected component
- ”giant_scc”: Extract giant strongly connected component (directed only)
name (str, default="") – Name identifier for the network.
pos (dict or None) – Node positions as {node: (x, y)} dictionary.
verbose (bool, default=False) – Whether to print progress messages.
create_nx_graph (bool, default=True) – Whether to create NetworkX graph from adjacency matrix.
node_attrs (dict or None) – Node attributes as {node: {attr: value}} nested dictionary.
logger (logging.Logger or None) – Logger instance for logging messages.
**network_args –
Additional network parameters:
- directed : bool or None (auto-detected if None)
- weighted : bool or None (auto-detected if None)
- real_world : bool (affects directionality validation)

adj

Adjacency matrix in sparse format.

Type:: scipy.sparse matrix

graph

NetworkX graph representation.

Type:: networkx.Graph/DiGraph or None

directed

Whether the network is directed.

Type:: bool

weighted

Whether the network has weighted edges.

Type:: bool

n

Number of nodes.

Type:: int

outdeg

Out-degree sequence (set by get_node_degrees()).

Type:: np.ndarray

indeg

In-degree sequence (set by get_node_degrees()).

Type:: np.ndarray

init_method

Initialization method used (‘adj’ or ‘graph’).

Type:: str

_calculated_directionality

Fraction of asymmetric edges (0.0 to 1.0).

Type:: float

network_params

Original network parameters passed to constructor.

Type:: dict

real_world

Whether this is a real-world network.

Type:: bool

_init_to_final_node_mapping

Mapping from initial to final node indices after preprocessing.

Type:: dict

lem_emb

Placeholder for Laplacian eigenmaps embedding.

Type:: None

trans, lap, nlap, rwlap, lap_out, lap_in

Various matrix representations (initialized to None).

Type:: None or array

n_cc

Number of connected components (set during some preprocessing).

Type:: int or None

n_scc

Number of strongly connected components (set during some preprocessing).

Type:: int or None

Raises:: ValueError – If both adj and graph are provided or neither is provided.

Notes

The constructor automatically computes node degrees after initialization. For large sparse matrices, auto-detection of directed/weighted properties uses efficient sparse operations to avoid memory issues.

property permutation_entropy

Permutation entropy normalized to [0, 1].

Shannon entropy of pattern visit frequencies divided by log2(d!). High (~1) = complex/random. Low (~0) = regular/periodic.

property missing_patterns: Number of d! ordinal patterns never visited.

property timeseries_data: Original time series data.