diff --git a/main.py b/main.py index 3a5fb4e..a07d61c 100644 --- a/main.py +++ b/main.py @@ -1,301 +1,314 @@ import numpy as np import matplotlib.pyplot as plt from sklearn.metrics import mutual_info_score +def soft_moduarity(wc, dc_inv, xc, lc): + # Calculate the soft modularity as defined by equation (7) + + temp = np.linalg.multi_dot([dc_inv, xc, lc]) + temp_t = np.transpose(temp) + n = wc.shape[0] + + qc_s = np.trace(np.linalg.multi_dot([temp_t, wc, temp])) - np.linalg.multi_dot([np.ones((1, n)), temp, temp_t, wc, np.ones((n, 1))]) + return qc_s + def similarity(adj_mat, weighted, gamma=0.2): # calculate a similarity matrix from the adjacency matrix, basically an exponential scaling n, m = adj_mat.shape sim = np.zeros(adj_mat.shape) if weighted: for i in range(n): for j in range(m): if adj_mat[i, j] != 0: sim[i, j] = np.exp(-1.0/(gamma * adj_mat[i, j])) else: sim[i, j] = 0.0 else: sim = adj_mat / 2.0 for i in range(n): # populate the diagonal sim[i, i] = 1.0 sim /= np.sum(sim) return sim def normalize_rows(w: np.ndarray): # normalize matrix w row-wise return w / np.linalg.norm(w, ord=1, axis=1, keepdims=True) def normalize_cols(xc: np.ndarray): # normalize matrix xc column-wise return xc / np.linalg.norm(xc, ord=1, axis=0, keepdims=True) def kl_divergence(a_mat, b_mat): # Kullback-Leibler divergence for all non zero elements of a_mat and b_mat - #print("shape A: {}, ravel(A): {}".format(a_mat.shape, np.shape(np.ravel(a_mat)))) - #print("shape B: {}, ravel(B): {}".format(b_mat.shape, np.shape(np.ravel(b_mat)))) - assert a_mat.shape == b_mat.shape n, m = a_mat.shape res = 0.0 for i in range(n): for j in range(m): - if a_mat[i, j] != 0.0: - assert b_mat[i, j] != 0.0 + if a_mat[i, j] > 1e-20 and b_mat[i, j] > 1e-20: res += a_mat[i, j] * np.log(a_mat[i, j] / b_mat[i, j]) - a_mat[i, j] + b_mat[i, j] return res def param_update(xc, lc, wc, alpha): # Update function for xc (capital X and capital L), implementation of equations (4) and (5) yc = xc.dot(lc) n, m = yc.shape # xc_old = np.random.rand(xc.shape[0], xc.shape[1]) xc_old = xc xc_old = normalize_cols(xc_old) # lc_old = lc_new lc_old = lc np.fill_diagonal(lc_old, np.random.rand(lc.shape[0])) lc_old /= np.trace(lc_old) - eps = 1e-4 - # max_iter = int(1e6) - max_iter = int(1e2) + eps = 1e-5 + max_iter = int(1e3) gamma = np.zeros(max_iter) for it in range(max_iter): - # print("it: {}".format(it)) yc_old = xc_old.dot(lc_old) wc_approx = xc_old.dot(lc_old.dot(xc_old.T)) xc_new = np.zeros(xc.shape) lc_new = np.zeros(lc.shape) for k in range(m): for i in range(n): for j in range(n): - xc_new[i, k] += wc[i, j] * lc_old[k, k] * xc_old[j, k] / wc_approx[i, j] - lc_new[k, k] += wc[i, j] * xc_old[i, k] * xc_old[j, k] / wc_approx[i, j] + if wc[i, j] != 0: # avoid divisions by extremely small values in wc_approx + xc_new[i, k] += wc[i, j] * lc_old[k, k] * xc_old[j, k] / wc_approx[i, j] + lc_new[k, k] += wc[i, j] * xc_old[i, k] * xc_old[j, k] / wc_approx[i, j] xc_new[i, k] *= (2 * alpha * xc_old[i, k]) xc_new[i, k] += (1 - alpha) * yc_old[i, k] lc_new[k, k] *= (alpha * lc_old[k, k]) lc_new[k, k] += (1 - alpha) * sum(yc_old[:, k]) xc_new = normalize_cols(xc_new) lc_new /= np.trace(lc_new) - # print("xc_new = {}".format(xc_new)) - # print("lc_new = {}".format(lc_new)) - # print(np.sum(xc_new[:, 0])) - # print(np.sum(xc_new[:, 1])) - # print(np.sum(xc_new[:, 2])) - # print(np.sum(xc_new[:, 3])) - - gamma[it] = alpha * kl_divergence(wc, xc_new.dot(lc_new.dot(xc_new.T))) + (1 - alpha) * kl_divergence(yc, xc_new.dot(lc_new)) + gamma[it] = alpha * kl_divergence(wc, np.linalg.multi_dot([xc_new, lc_new, xc_new.T])) + (1 - alpha) * kl_divergence(yc, xc_new.dot(lc_new)) print("iter: {}, gamma: {}".format(it, gamma[it])) - if it > 1 and (gamma[it] - gamma[it - 1]) / gamma[it] > eps: - plt.plot(gamma[0:it]) - plt.show() - print("====> minimum found") - return xc_new, lc_new + if it == 0: + gamma_min = gamma[it] + else: + if gamma[it] < gamma[it - 1]: + gamma_min = gamma[it] + xc_res = xc_new + lc_res = lc_new + + elif abs((gamma[it] - gamma_min)) / gamma_min < eps: + plt.plot(gamma[0:it]) + plt.show() + print("====> minimum found") + return xc_res, lc_res xc_old = xc_new lc_old = lc_new raise Exception('Maximum iteration number reached: {}'.format(max_iter)) def read_edge_list(filename, weighted=False): idmap = set() edge_cache = {} with open(filename) as f: for line in f: if weighted: u, v, w = [int(x) for x in line.strip().split()] else: tmp = [int(x) for x in line.strip().split()] u, v, w = tmp[0], tmp[1], 1.0 edge_cache[(u, v)] = w idmap.add(u) idmap.add(v) idmap = list(idmap) idmap_inv = {nid: i for i, nid in enumerate(idmap)} n = len(idmap) adj_mat = np.zeros((n, n)) for (u, v), w in edge_cache.items(): adj_mat[idmap_inv[u], idmap_inv[v]] = w adj_mat += adj_mat.T return idmap, idmap_inv, adj_mat def alg(net_path, alpha, t_steps, n, m): # FacetNet with fixed number of communities and individuals xc = np.random.rand(n, m) + xc = normalize_cols(xc) lc = np.diag(np.random.rand(m)) - xc = np.matrix(xc / np.sum(xc, axis=0).reshape(1, m)) - lc = np.matrix(lc / np.sum(lc)) + lc /= np.trace(lc) for t in range(t_steps): idmap, idmap_inv, adj_mat = read_edge_list(net_path + "%d.edgelist" % t, weighted=False) - # TODO: not quite clear what this is for + # TODO: this similarity calculation is experiment specific and must be done outside this function # wc = similarity(adj_mat, weighted=True) wc = normalize_rows(adj_mat) xc_old = xc lc_old = lc xc, lc = param_update(xc, lc, wc, alpha) yc = xc.dot(lc) dc_inv = np.zeros(n) for i in range(n): dc_inv[i] = 1 / np.sum(yc[i, :]) dc_inv = np.matrix(np.diag(dc_inv)) print(dc_inv) print(yc) soft_comm = dc_inv.dot(yc) print("time:", t) - # print("community net") - # print(lc.dot(xc.dot(soft_comm))) - # - # print("evolution net") - # print(lc_old.dot(xc_old.dot(soft_comm))) - print("soft_comm") print(soft_comm) - print(np.sum(soft_comm, 1)) - print("Activity (dc)") - print(dc_inv) + print("community net") + print(np.linalg.multi_dot([lc, xc.T, soft_comm])) + print("evolution net") + print(np.linalg.multi_dot([lc_old, xc_old.T, soft_comm])) + + print("Activity (dc)") + print(np.diag(dc_inv)) -# do experiment with network stated in 4.1.2 -def exp1(): - t_steps = 15 - from synthetic import generate_evolution - print("generating synthetic graph") - generate_evolution("test_data/", tsteps=t_steps) - print("start the algorithm") - alpha = 0.5 - n, m = 128, 4 - np.random.seed(0) - alg("test_data/", alpha, t_steps, n, m) +def alg_extended(net_path, alpha, t_steps, m): + # FacetNet with for variable number of nodes, a solution for different community numbers is not implemented -# FacetNet with # of nodes and communities changed -def alg_extended(net_path, alpha, t_steps, m, with_truth=True): - idmap0, idmap_inv0 = [], {} for t in range(t_steps): print("time:", t) idmap, idmap_inv, adj_mat = read_edge_list(net_path + "%d.edgelist" % t, weighted=False) - if with_truth: - with open(net_path+"%d.comm" % t) as f: - comm_map = {} - for line in f: - id0, comm0 = line.strip().split() - comm_map[int(id0)] = int(comm0) n = len(idmap) - wc = similarity(adj_mat, weighted=False) + # wc = similarity(adj_mat, weighted=False) + wc = normalize_rows(adj_mat) + if t == 0: xc = np.random.rand(n, m) + xc = normalize_cols(xc) lc = np.diag(np.random.rand(m)) - xc = np.matrix(xc / np.sum(xc, axis=0).reshape(1, m)) - lc = np.matrix(lc / np.sum(lc)) - yc = xc * lc - else: # adjustment for changing of nodes + lc /= np.trace(lc) + + else: reserved_rows = [idmap_inv0[x] for x in idmap0 if x in idmap] num_new = len(set(idmap) - set(idmap0)) num_old = len(reserved_rows) - yc = yc[reserved_rows, :] - yc /= np.sum(yc) - yc = np.pad(yc, ((0, num_new), (0, 0)), mode='constant', constant_values=(0, 0)) - # not mentioned on the paper, but are necessary for node changing xc = xc[reserved_rows, :] - xc = np.matrix(xc / np.sum(xc, axis=0).reshape(1, m)) + xc = normalize_cols(xc) xc *= num_old / (num_old + num_new) xc = np.pad(xc, ((0, num_new), (0, 0)), mode='constant', constant_values=(1 / num_new, 1 / num_new)) - xc_new, lc_new, = param_update(xc, lc, wc, alpha) - yc = xc_new * lc_new - dc = np.zeros((n,)) + xc_old = xc + lc_old = lc + xc, lc, = param_update(xc, lc, wc, alpha) + + yc = xc.dot(lc) + + dc_inv = np.zeros(n) for i in range(n): - dc[i] = np.sum(yc[i, :]) - dc = np.matrix(np.diag(dc)) - soft_comm = dc.I * xc_new * lc_new + dc_inv[i] = 1 / np.sum(yc[i, :]) + dc_inv = np.matrix(np.diag(dc_inv)) - print("time:", t) + print(dc_inv) + print(yc) - print("community net") - print(lc * xc * soft_comm) + soft_comm = dc_inv.dot(yc) - print("evolution net") - print(lc_old * xc_old * soft_comm) + print("time:", t) print("soft_comm") print(soft_comm) + print("community net") + print(np.linalg.multi_dot([lc, xc.T, soft_comm])) + + print("evolution net") + print(np.linalg.multi_dot([lc_old, xc_old.T, soft_comm])) + print("Activity (dc)") - print(dc) + print(np.diag(dc_inv)) - xc = xc_new - ac = ac_new idmap0 = idmap idmap_inv0 = idmap_inv -# do experiment with adding and removing nodes -# def exp2(): -# tsteps = 15 -# from synthetic import generate_evolution2 - # print("generating synthetic graph") - # generate_evolution2("./data/syntetic2/", tsteps=tsteps) - # print("start the algorithm") - # alpha = 0.5 - # np.random.seed(0) - # alg_extended("./data/syntetic2/",alpha,tsteps,4) +def exp1(): + # Experiment with network stated in 4.1.2 + t_steps = 15 + from synthetic import generate_evolution_exp1 + print("generating synthetic graph") + generate_evolution_exp1("test_data/", tsteps=t_steps) + print("start the algorithm") + alpha = 0.5 + n, m = 128, 4 + np.random.seed(0) + alg("test_data/", alpha, t_steps, n, m) + + +def exp2(): + # Experiment with adding and removing nodes + t_steps = 15 + from synthetic import generate_evolution_exp2 + print("generating synthetic graph") + generate_evolution_exp2("./data/syntetic2/", tsteps=t_steps) + print("start the algorithm") + alpha = 0.5 + np.random.seed(0) + alg_extended("./data/syntetic2/", alpha, t_steps, 4) -# do experiment with network stated in 4.1.2, adding weight -# def exp3(): -# tsteps = 15 -# from synthetic import generate_evolution3 -# print("generating synthetic graph") -# generate_evolution3("./data/syntetic3/", tsteps=tsteps) -# print("start the algorithm") -# alpha = 0.9 -# N, M = 128, 4 -# np.random.seed(0) -# alg("./data/syntetic3/",alpha,tsteps,N,M) +def exp3(): + # Experiment with network stated in 4.1.2, adding weight + t_steps = 15 + from synthetic import generate_evolution_exp3 + print("generating synthetic graph") + generate_evolution_exp3("./data/syntetic3/", tsteps=t_steps) + print("start the algorithm") + alpha = 0.9 + n = 128 + m = 4 + np.random.seed(0) + alg("./data/syntetic3/", alpha, t_steps, n, m) + +def exp_raph(): + # Experiment with network stated in 4.1.2, adding weight + t_steps = 10 + print("start the algorithm") + alpha = 0.9 + n = 128 + m = 4 + np.random.seed(0) + alg("./data/syntetic3/", alpha, t_steps, n, m) if __name__ == "__main__": # path = "/home/matthias/Documents/CodeDataRaph/data_Danielle/24h_networks/col4" - # print(path) - # alg(path, 0.5, 11, 128, 2) + exp_raph() - print("do experiment with network stated in 4.1.2") - exp1() - # print("do experiment with network stated in 4.1.2") + # print("Experiment with network stated in 4.1.2") # exp1() - # print("\ndo experiment with adding and removing nodes") + + # print("Experiment with adding and removing nodes") # exp2() - # print("\ndo experiment with network stated in 4.1.2, adding weight") + # + # print("Experiment with network stated in 4.1.2, adding weight") # exp3() diff --git a/synthetic.py b/synthetic.py index 18c2874..4c39be1 100644 --- a/synthetic.py +++ b/synthetic.py @@ -1,133 +1,140 @@ import networkx as nx import numpy as np # import pandas as pd import os import matplotlib.pyplot as plt + def comm_exchanging(comm_affli,num_changing=3): idx = np.random.choice(np.arange(len(comm_affli)),num_changing,replace=False) for node in idx: comm_affli[node] = (comm_affli[node] + np.random.randint(1,4)) % 4 return comm_affli + def edge_aligning(comm_affli,z,avg_degree=16,idmap=[]): from itertools import combinations if idmap == []: idmap = [i for i in range(len(comm_affli))] G = nx.Graph() within_edges, inter_edges = [],[] for u,v in combinations(range(len(comm_affli)),2): if comm_affli[u] == comm_affli[v]: within_edges.append((u,v)) else: inter_edges.append((u, v)) within_edges_id = np.random.choice(range(len(within_edges)),int((avg_degree-z)*len(comm_affli)/2),replace=False) inter_edges_id = np.random.choice(range(len(inter_edges)), int(z*len(comm_affli)/2), replace=False) for i in within_edges_id: u,v = within_edges[i] G.add_edge(idmap[u],idmap[v]) for i in inter_edges_id: u,v = inter_edges[i] G.add_edge(idmap[u],idmap[v]) return G + def edge_aligning_weighted(comm_affli,z,avg_degree=16,idmap=[]): from itertools import combinations if idmap == []: idmap = [i for i in range(len(comm_affli))] G = nx.Graph() within_edges, inter_edges = [],[] for u,v in combinations(range(len(comm_affli)),2): if comm_affli[u] == comm_affli[v]: within_edges.append((u,v)) else: inter_edges.append((u, v)) within_edges_id = np.random.choice(range(len(within_edges)),int((avg_degree-z)*len(comm_affli)/2),replace=False) inter_edges_id = np.random.choice(range(len(inter_edges)), int(z*len(comm_affli)/2), replace=False) for i in within_edges_id: u,v = within_edges[i] G.add_edge(idmap[u],idmap[v],weight=2) for i in inter_edges_id: u,v = inter_edges[i] G.add_edge(idmap[u],idmap[v],weight=1) return G + def plot_graph_with_comm(G,comm_affli): colors = ["r","g","b","purple"] pos = nx.spring_layout(G) for comm in range(np.max(comm_affli)): nx.draw_networkx_nodes(G, pos, nodelist=np.where(comm_affli==comm)[0].tolist(), node_color=colors[comm]) nx.draw_networkx_edges(G, pos) plt.show() + def comm_exchanging2(idmax,comm_affli,idmap,idmap_inv): try: idx = np.random.choice(np.where(comm_affli == 3)[0],4,replace=False) comm_affli = np.array([comm for i,comm in enumerate(comm_affli) if not i in idx]) idmap = [nid for i,nid in enumerate(idmap) if not i in idx] idmap_inv = {nid: i for i, nid in enumerate(idmap)} except: pass idmap += [idmax, idmax + 1] idmap_inv[idmax] = len(comm_affli) idmap_inv[idmax+1] = len(comm_affli)+1 comm_affli = np.array(comm_affli.tolist()+[0,0]) idmax += 2 return idmax,comm_affli,idmap,idmap_inv + # generate an evolutional graph as is stated in 4.1.2 -def generate_evolution(output_path,z=3,avg_degree=16,tsteps=10): +def generate_evolution_exp1(output_path,z=3,avg_degree=16,tsteps=10): if not os.path.exists(output_path): os.makedirs(output_path) comm_affli = (np.arange(0, 128) / 32).astype(int) np.random.shuffle(comm_affli) for t in range(tsteps): G = edge_aligning(comm_affli, z, avg_degree) nx.write_weighted_edgelist(G, output_path+'%d.edgelist' % t) with open(output_path+"%d.comm" % t,"w") as f: f.write("\n".join("%d %d" % (i, comm) for i,comm in enumerate(comm_affli))) comm_affli = comm_exchanging(comm_affli,num_changing=3) # uncomment this line to plot the snapshot graph # plot_graph_with_comm(G, comm_affli) pass + # generate an evolutional graph such that at each timestamp: # 1. 4 nodes of community 3 was removed # 2. 2 new nodes of community 0 was added (with increased node id) -def generate_evolution2(output_path,z=3,avg_degree=16,tsteps=9): +def generate_evolution_exp2(output_path,z=3,avg_degree=16,tsteps=9): if not os.path.exists(output_path): os.makedirs(output_path) comm_affli = (np.arange(0, 128) / 32).astype(int) np.random.shuffle(comm_affli) idmap = [i for i in range(128)] # 数组下标与结点唯一id标识的映射 idmap_inv = {nid: i for i,nid in enumerate(idmap)} # 结点唯一id标识与数组下标的映射 idmax = 128 # 当前最大编号+1【出现过的总人次】 for t in range(tsteps): G = edge_aligning(comm_affli ,z, avg_degree, idmap) nx.write_weighted_edgelist(G, output_path+'%d.edgelist' % t) with open(output_path+"%d.comm" % t,"w") as f: f.write("\n".join("%d %d" % (idmap[i], comm) for i,comm in enumerate(comm_affli))) idmax,comm_affli,idmap,idmap_inv = comm_exchanging2(idmax,comm_affli,idmap,idmap_inv) pass # generate an evolutional graph as is stated in 4.1.2, adding weight -def generate_evolution3(output_path, z=3, avg_degree=16, tsteps=10): +def generate_evolution_exp3(output_path, z=3, avg_degree=16, tsteps=10): if not os.path.exists(output_path): os.makedirs(output_path) comm_affli = (np.arange(0, 128) / 32).astype(int) np.random.shuffle(comm_affli) for t in range(tsteps): G = edge_aligning_weighted(comm_affli, z, avg_degree) nx.write_weighted_edgelist(G, output_path + '%d.edgelist' % t) with open(output_path + "%d.comm" % t, "w") as f: f.write("\n".join("%d %d" % (i, comm) for i, comm in enumerate(comm_affli))) comm_affli = comm_exchanging(comm_affli, num_changing=3) # uncomment this line to plot the snapshot graph # plot_graph_with_comm(G, comm_affli) pass if __name__ == "__main__": - generate_evolution("./data/syntetic1/", tsteps=10) - generate_evolution2("./data/syntetic2/", tsteps=9) - generate_evolution3("./data/syntetic5/", tsteps=15) \ No newline at end of file + generate_evolution_exp1("./data/syntetic1/", tsteps=10) + generate_evolution_exp2("./data/syntetic2/", tsteps=9) + generate_evolution_exp3("./data/syntetic5/", tsteps=15) \ No newline at end of file diff --git a/test_data/0.comm b/test_data/0.comm index e8f1f44..e30eb78 100644 --- a/test_data/0.comm +++ b/test_data/0.comm @@ -1,128 +1,128 @@ 0 0 1 2 -2 3 +2 0 3 3 4 3 -5 1 -6 2 -7 3 -8 0 -9 1 -10 3 -11 3 -12 2 -13 1 -14 1 -15 0 -16 0 +5 3 +6 1 +7 2 +8 3 +9 3 +10 2 +11 1 +12 1 +13 3 +14 3 +15 1 +16 1 17 1 -18 3 -19 0 +18 0 +19 2 20 2 21 3 22 3 23 1 24 0 25 2 26 0 -27 1 -28 3 -29 3 -30 2 +27 0 +28 1 +29 2 +30 0 31 2 -32 2 +32 3 33 2 -34 2 -35 1 -36 0 -37 3 -38 2 -39 2 -40 1 -41 1 +34 1 +35 2 +36 2 +37 0 +38 0 +39 0 +40 3 +41 0 42 3 -43 1 -44 1 -45 2 +43 2 +44 3 +45 3 46 2 -47 1 +47 2 48 3 -49 3 -50 2 +49 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