MMSBM Functions

functions.MMSBM_functions.omega_comp_arrays(Na, Nb, p_kl, theta, eta, K, L, links_array, links_ratings)[source]

Computes the omega matrix for a bipartite network.

Parameters:

  • Na (int) – Number of nodes in layer a

  • Nb (int) – Number of nodes in layer b

  • p_kl (np.array) – Probability matrix between groups k and l

  • theta (np.array) – Membership matrix for layer a

  • eta (np.array) – Membership matrix for layer b

  • K (int) – Number of groups in layer a

  • L (int) – Number of groups in layer b

  • links_array (np.array) – Array containing the links between nodes

  • links_ratings (np.array) – Array containing the ratings/labels for each link

Returns:

The computed omega matrix of shape (Na, Nb, K, L)

Return type:

np.array

functions.MMSBM_functions.omega_comp_arrays_exclusive(q_ka, N_att, theta, N_nodes, K, metas_links_arrays_nodes)[source]

Computes the omega matrix for exclusive metadata.

Parameters:

  • q_ka (np.array) – Probability matrix between groups k and attributes a

  • N_att (int) – Number of attributes

  • theta (np.array) – Membership matrix for nodes

  • N_nodes (int) – Number of nodes

  • K (int) – Number of groups

  • metas_links_arrays_nodes (np.array) – Array containing the links between nodes and metadata

Returns:

The computed omega matrix of shape (N_nodes, N_att, K)

Return type:

np.array

functions.MMSBM_functions.theta_comp_arrays_multilayer(BiNet, layer='a')[source]

Computes the membership matrix for a layer in a bipartite network.

Parameters:

  • BiNet (BiNet) – The bipartite network object

  • layer (str, default="a") – The layer to compute the membership matrix for (“a” or “b”)

Returns:

The computed membership matrix for the specified layer

Return type:

np.array

Raises:

TypeError – If layer is not “a” or “b”

functions.MMSBM_functions.theta_comp_array(N_nodes, K, omega, denominators, links, masks_list)[source]

Computes the membership matrix of a nodes layer with no metadata.

Parameters:

  • N_nodes (int) – Number of nodes

  • K (int) – Number of groups

  • omega (np.array) – The omega matrix

  • denominators (np.array) – Array of denominators for normalization

  • links (np.array) – Array containing the links

  • masks_list (list) – List of masks for each attribute

Returns:

The computed membership matrix of shape (N_nodes, K)

Return type:

np.array

functions.MMSBM_functions.q_ka_comp_arrays(K, N_att, omega, links, masks_att_list)[source]

Computes the probability matrix between nodes in group k and attribute a.

Parameters:

  • K (int) – Number of groups

  • N_att (int) – Number of attributes

  • omega (np.array) – The omega matrix of the BiNet

  • links (np.array) – The links of the BiNet

  • masks_att_list (list) – A list of masks for each attribute

Returns:

The probability matrix of shape (K, N_att) between nodes in group k and attribute a

Return type:

np.array

functions.MMSBM_functions.p_kl_comp_arrays(Ka, Kb, N_labels, links, omega, mask_list)[source]

Computes the probability matrix between groups in nodes_a layer and group nodes_b layer in a BiNet network.

Parameters:

  • Ka (int) – Number of groups in layer a

  • Kb (int) – Number of groups in layer b

  • N_labels (int) – Number of possible labels

  • links (np.array) – Array containing the links

  • omega (np.array) – The omega matrix

  • mask_list (list) – List of masks for each label

Returns:

The probability matrix of shape (Ka, Kb, N_labels) between nodes_a and nodes_b

Return type:

np.array

functions.MMSBM_functions.theta_meta(theta, meta)[source]

Computes the membership matrix for metadata.

Parameters:

  • theta (np.array) – The membership matrix

  • meta (metadata_layer) – The metadata layer object

Returns:

The computed membership matrix for the metadata

Return type:

np.array

functions.MMSBM_functions.log_like_comp(theta, eta, pkl, links, labels)[source]

Computes the log_likelihood given the membership matrices of two nodes layer and its matrix probabilities.

Parameters:

  • theta (np.array) – Membership matrix for layer a

  • eta (np.array) – Membership matrix for layer b

  • pkl (np.array) – Probability matrix between groups

  • links (np.array) – Array containing the indexes of the links

  • labels (np.array) – Array containing the indexes of the labels for each link

Returns:

The computed log likelihood

Return type:

float

functions.MMSBM_functions.total_p_comp_test(theta, eta, pkl, links)[source]

Computes the probabilities that two nodes are connected with each link label.

Parameters:

  • theta (np.array) – Membership matrix for layer a

  • eta (np.array) – Membership matrix for layer b

  • pkl (np.array) – Probability matrix between groups

  • links (np.array) – Array containing the links

Returns:

Array of probabilities for each link label

Return type:

np.array

functions.MMSBM_functions.log_like_comp_exclusive(theta, qka, links)[source]

Computes the log_likelihood of a bipartite network of exclusive metadata.

Parameters:

  • theta (np.array) – Membership matrix for nodes

  • qka (np.array) – Probability matrix between groups and attributes

  • links (np.array) – Array containing the indexes of the links

Returns:

The computed log likelihood for exclusive metadata

Return type:

float