Vector Visibility Graph

This repository contains the Numba JIT-compiled implementation of the Vector Visibility Graphs (VVGs), which are a generalization of the Visibility Graphs (VGs) for multivariate time series. For a single time series, ts2vg (GitHub, PyPI) provides a detailed and thorough construction of VGs with a Cython-based approach for performance. However, this implementation is not directly applicable to multivariate time series. Therefore, in this package, we implement the construction of VVGs for multivariate time series using a Numba-based approach for performance.

Installation

You can install the package directly from PYPI using pip or poetry as follows:

pip install vector-vis-graph

or

poetry add vector-vis-graph

or directly from Conda

conda install -c conda-forge vector-vis-graph

Usage

Given a multivariate time series, the vector_vis_graph package can be used to construct a vector visibility graph (VVG). The package provides two functions natural_vvg() and horizontal_vvg() with the same input types for constructing Natural and Horizontal VVGs. They take a multivariate time series where the rows correspond to the time steps and the columns correspond to the vector components such that for a multivariate time series, mts, mts[i] is the vector at time step i. The functions also take the following optional arguments:

• timeline: The timeline of the multivariate time series. If not provided, the timeline is assumed to be [0, 1, 2, ...].
• weight_method: The method used to calculate the weight of the edges. The default is WeightMethod.UNWEIGHTED. There are a few other options available in the WeightMethod enum.
• penetrable_limit: The penetrable limit of the "visibility" of the vectors. For two vectors at different time steps to be visible to each other, the vectors at in-between time steps must satisfy certain conditions. The penetrable limit is the number of in-between time steps that can violate the conditions. The default is 0.
• directed: Whether the graph is directed or undirected. The visibility of the vectors is calculated in a left-to-right directed manner. If directed, the calculated graph adjacency matrix is returned, else its sum with its transpose is returned. The default is False, so undirected.

import numpy as np
from vector_vis_graph import WeightMethod, horizontal_vvg, natural_vvg

# Multivariate Time Series
TIME_LENGTH = 100
VEC_SIZE = 64
multivariate_ts = np.random.rand(TIME_LENGTH, VEC_SIZE)

# Natural Vector Visibility Graph with Default Parameters
# Timeline: [0, 1, 2, ...]
# Weight Method: Unweighted
# Penetrable Limit: 0
# Undirected Graph
nvvg_adj = natural_vvg(multivariate_ts)

# Horizontal Vector Visibility Graph with All Custom Parameters
# Timeline: [0, 2, 4, ...]
# Weight Method: Cosine Similarity
# Penetrable Limit: 2
# Directed Graph
hvvg_adj = horizontal_vvg(
    multivariate_ts,
    timeline=np.arange(0, 2 * TIME_LENGTH, 2), # [0, 2, 4, ...]
    weight_method=WeightMethod.COSINE_SIMILARITY,
    penetrable_limit=2,
    directed=True,
)