def pyquest_spin_bintrees(data,row_alpha=0.5,col_alpha=0.5,beta=1.0,bal_constant=1.0,n_iters=3,n_spin=10): """ runs what is momentarily the standard questionnaire algorithm: initial affinity = mutual cosine similarity initial tree based on median of successive eigenvectors dual affinities based on earth mover distance. dual trees based on eigen_cut method """ #Generate initial affinity init_row_aff = affinity.mutual_cosine_similarity(data.T,False,0,threshold=0.1) #Compute diffusion embedding of initial affinities init_row_vecs,init_row_vals = markov.markov_eigs(init_row_aff, 12) #Generate median trees init_row_tree = bintree_construct.median_tree(init_row_vecs,init_row_vals,max_levels=12) row_trees, col_trees = [],[] for _ in xrange(n_spin): dual_col_trees = [] dual_row_trees = [init_row_tree] for _ in xrange(n_iters): dual_col_trees.append(bintree_construct.eigen_tree(data,dual_row_trees[-1],alpha=col_alpha,beta=beta,bal_constant=bal_constant)) dual_row_trees.append(bintree_construct.eigen_tree(data.T,dual_col_trees[-1],alpha=row_alpha,beta=beta,bal_constant=bal_constant)) row_trees.append(dual_row_trees[-1]) col_trees.append(dual_col_trees[-1]) return row_trees,col_trees
def flex_tree_diffusion(affinity, penalty_constant, n_eigs=12): """ affinity is an nxn affinity matrix. Creates a flexible tree by calculating the diffusion on the given affinity. Then clusters at each level by the flexible tree algorithm. For each level up, doubles the diffusion time. penalty_constant is the multiplier of the median diffusion distance. """ #First, we calculate the first n eigenvectors and eigenvalues of the #diffusion cluster_list = [] vecs, vals = markov.markov_eigs(affinity, n_eigs) diff_time = 1.0 q = np.eye(affinity.shape[0]) while 1: #now we calculate the diffusion distances between points at the #current diffusion time. diff_vecs = vecs.dot(np.diag(vals**diff_time)) diff_dists = spsp.distance.squareform(spsp.distance.pdist(diff_vecs)) #we take the affinity between clusters to be the average diffusion #distance between them. avg_dists = q.dot(diff_dists).dot(q.T) #now we cluster the points based on this distance cluster_list.append(cluster_from_distance(avg_dists, penalty_constant)) #if there is only one node left, then we are done. #otherwise, add another level to the tree, double the diffusion time #and keep going. if len(cluster_list[-1]) == 1: break temp_tree = clusterlist_to_tree(cluster_list) cpart = ClusteringPartition( [x.elements for x in temp_tree.dfs_level(2)]) q, _ = cluster_transform_matrices(cpart) diff_time *= 2.0 return clusterlist_to_tree(cluster_list)
def flex_tree_diffusion(affinity, penalty_constant, n_eigs=12): """ affinity is an nxn affinity matrix. Creates a flexible tree by calculating the diffusion on the given affinity. Then clusters at each level by the flexible tree algorithm. For each level up, doubles the diffusion time. penalty_constant is the multiplier of the median diffusion distance. """ # First, we calculate the first n eigenvectors and eigenvalues of the # diffusion cluster_list = [] vecs, vals = markov.markov_eigs(affinity, n_eigs) diff_time = 1.0 q = np.eye(affinity.shape[0]) while 1: # now we calculate the diffusion distances between points at the # current diffusion time. diff_vecs = vecs.dot(np.diag(vals ** diff_time)) diff_dists = spsp.distance.squareform(spsp.distance.pdist(diff_vecs)) # we take the affinity between clusters to be the average diffusion # distance between them. avg_dists = q.dot(diff_dists).dot(q.T) # now we cluster the points based on this distance cluster_list.append(cluster_from_distance(avg_dists, penalty_constant)) # if there is only one node left, then we are done. # otherwise, add another level to the tree, double the diffusion time # and keep going. if len(cluster_list[-1]) == 1: break temp_tree = clusterlist_to_tree(cluster_list) cpart = ClusteringPartition([x.elements for x in temp_tree.dfs_level(2)]) q, _ = cluster_transform_matrices(cpart) diff_time *= 2.0 return clusterlist_to_tree(cluster_list)
def pyquest_newtree(data,tree_constant=0.25,row_alpha=0.5,col_alpha=0.5,beta=1.0,n_iters=3): init_row_aff = affinity.mutual_cosine_similarity(data.T,False,0,threshold=0.1) #Compute diffusion embedding of initial affinities init_row_vecs,init_row_vals = markov.markov_eigs(init_row_aff, 12) init_row_vals[np.isnan(init_row_vals)] = 0.0 row_embedding = init_row_vecs.dot(np.diag(init_row_vals)) row_distances = spsp.distance.squareform(spsp.distance.pdist(row_embedding)) row_affinity = np.max(row_distances) - row_distances #Generate initial tree #print "call1 tree_constant:{}".format(tree_constant) init_row_tree = tree_building.make_tree_embedding(row_affinity,tree_constant) dual_col_trees = [] dual_row_trees = [init_row_tree] for _ in xrange(n_iters): #print "Beginning iteration {}".format(i) col_emd = dual_affinity.calc_emd(data,dual_row_trees[-1],alpha=col_alpha,beta=beta) col_aff = dual_affinity.emd_dual_aff(col_emd) #print "call2 tree_constant:{}".format(tree_constant) dual_col_trees.append(tree_building.make_tree_embedding(col_aff,tree_constant)) row_emd = dual_affinity.calc_emd(data.T,dual_col_trees[-1],alpha=row_alpha,beta=beta) row_aff = dual_affinity.emd_dual_aff(row_emd) #print "call3 tree_constant:{}".format(tree_constant) dual_row_trees.append(tree_building.make_tree_embedding(row_aff,tree_constant)) col_tree = dual_col_trees[-1] row_tree = dual_row_trees[-1] col_emd = dual_affinity.calc_emd(data,row_tree,alpha=col_alpha,beta=beta) row_emd = dual_affinity.calc_emd(data.T,col_tree,alpha=row_alpha,beta=beta) row_aff = dual_affinity.emd_dual_aff(row_emd) col_aff = dual_affinity.emd_dual_aff(col_emd) row_vecs,row_vals = markov.markov_eigs(row_aff, 12) col_vecs,col_vals = markov.markov_eigs(col_aff, 12) return row_tree,col_tree,row_vecs,col_vecs,row_vals,col_vals
def zero_eigen_cut(node,affinity): """ Returns the cut of the affinity matrix (cutting at zero) corresponding to the elements in node, under the condition of bal_constant. """ new_data = affinity[node.elements,:][:,node.elements] vecs,_ = markov.markov_eigs(new_data, 2) labels = vecs[:,1] < 0.0 return labels
def zero_eigen_cut(node, affinity): """ Returns the cut of the affinity matrix (cutting at zero) corresponding to the elements in node, under the condition of bal_constant. """ new_data = affinity[node.elements, :][:, node.elements] vecs, _ = markov.markov_eigs(new_data, 2) labels = vecs[:, 1] < 0.0 return labels
def random_dyadic_cut(node,affinity,left,right): """ Returns a randomized cut of the affinity matrix (cutting at zero) corresponding to the elements in node, under the condition of bal_constant. """ new_data = affinity[node.elements,:][:,node.elements] vecs,_ = markov.markov_eigs(new_data, 2) eig = vecs[:,1] eig_sorted = eig.argsort().argsort() cut_loc = np.random.randint(left,right+1) labels = eig_sorted < cut_loc return labels
def random_dyadic_cut(node, affinity, left, right): """ Returns a randomized cut of the affinity matrix (cutting at zero) corresponding to the elements in node, under the condition of bal_constant. """ new_data = affinity[node.elements, :][:, node.elements] vecs, _ = markov.markov_eigs(new_data, 2) eig = vecs[:, 1] eig_sorted = eig.argsort().argsort() cut_loc = np.random.randint(left, right + 1) labels = eig_sorted < cut_loc return labels
def break_node(train_data, col_tree_node, row_tree, regressors=None, k=5, alpha=0.0, beta=1.0, col_emd=None): """ First calculates the EMD on the columns of train_data in col_tree_node.elements using row_tree. Converts that to an affinity. Calculates the second eigenvector of the markov matrix based on that affinity. Then fits a linear model using the rows in regressors (all if it's None) and uses the LASSO path to identify the best k rows. Splits the node using the predicted eigenvector values. """ import sklearn.linear_model as sklm col_indices = col_tree_node.elements node_data = train_data[:, col_indices].astype(np.float64) if col_emd is None: col_emd = dual_affinity.calc_emd(node_data, row_tree, alpha, beta) col_aff = dual_affinity.emd_dual_aff(col_emd) else: col_aff = dual_affinity.emd_dual_aff( col_emd[:, col_indices][col_tree_node.elements, :]) vecs, _ = markov.markov_eigs(col_aff, 2) eig = vecs[:, 1] if regressors is None: regressors = range(row_tree.size) _, active, _ = sklm.lars_path(node_data[regressors, :].T, eig, max_iter=50) regr_indices = active[0:k] lm = sklm.LinearRegression() lm.fit(node_data[regr_indices, :].T, eig) pred_eigs = lm.predict(node_data[regr_indices, :].T) labels = pred_eigs > 0.0 partition = labels * np.ones(labels.shape[0]) col_tree_node.create_subclusters(partition) return np.array([regressors[x] for x in regr_indices]), lm
def eigen_cut_zero(node,emd,eps=1.0): affinity = dual_affinity.emd_dual_aff(emd[node.elements,:][:,node.elements] ,eps) try: vecs,_ = markov.markov_eigs(affinity,2) except: print affinity print emd print node.elements raise eig = vecs[:,1] n = len(eig) labels = np.ones(n) labels *= (eig > 0.0) return labels
def bal_eigen_cut(node,emd,bal_constant=1.0,eps=1.0): affinity = dual_affinity.emd_dual_aff(emd[node.elements,:][:,node.elements] ,eps) try: vecs,_ = markov.markov_eigs(affinity,2) except: print affinity print emd print node.elements raise eig = vecs[:,1] eig_sorted = np.argsort(eig) n = len(eig) l,r = bal_cut(n,bal_constant) cut_loc = np.random.randint(l,r+1) labels = np.zeros(n,np.int) labels[eig_sorted[0:cut_loc]] = 1 return labels
def break_node(train_data,col_tree_node,row_tree,regressors=None, k=5,alpha=0.0,beta=1.0,col_emd=None): """ First calculates the EMD on the columns of train_data in col_tree_node.elements using row_tree. Converts that to an affinity. Calculates the second eigenvector of the markov matrix based on that affinity. Then fits a linear model using the rows in regressors (all if it's None) and uses the LASSO path to identify the best k rows. Splits the node using the predicted eigenvector values. """ import sklearn.linear_model as sklm col_indices = col_tree_node.elements node_data = train_data[:,col_indices].astype(np.float64) if col_emd is None: col_emd = dual_affinity.calc_emd(node_data,row_tree,alpha,beta) col_aff = dual_affinity.emd_dual_aff(col_emd) else: col_aff = dual_affinity.emd_dual_aff(col_emd[:,col_indices][col_tree_node.elements,:]) vecs,_ = markov.markov_eigs(col_aff,2) eig = vecs[:,1] if regressors is None: regressors = range(row_tree.size) _,active,_ = sklm.lars_path(node_data[regressors,:].T,eig,max_iter=50) regr_indices = active[0:k] lm = sklm.LinearRegression() lm.fit(node_data[regr_indices,:].T,eig) pred_eigs = lm.predict(node_data[regr_indices,:].T) labels = pred_eigs > 0.0 partition = labels*np.ones(labels.shape[0]) col_tree_node.create_subclusters(partition) return np.array([regressors[x] for x in regr_indices]),lm
def eigen_cut(node,emd,noise,eps=1.0): affinity = dual_affinity.emd_dual_aff(emd[node.elements,:][:,node.elements] ,eps) try: vecs,_ = markov.markov_eigs(affinity,2) except: print affinity print emd print node.elements raise eig = vecs[:,1] eig_sorted = np.sort(eig) n = len(eig_sorted) rnoise = np.random.uniform(-noise,noise) if noise < 1e-8: labels = np.zeros(n) labels[np.argsort(eig)[0:int(n/2)]] = 1 else: cut_loc = eig_sorted[int((n/2)+(rnoise*n))] labels = np.ones(n)*(eig > cut_loc) return labels
def calc_col_embedding(self): self.col_vecs, self.col_vals = markov.markov_eigs(self.col_affinity, 8) Publisher.sendMessage("embed.col.calc")
def calc_row_embedding(self): self.row_vecs, self.row_vals = markov.markov_eigs(self.row_affinity, 8) Publisher.sendMessage("embed.row.calc")
def pyquest(data,params): #params should be a PyQuestParams object Publisher.sendMessage("status.bar", "Calculating initial affinity...") if params.init_aff_type == INIT_AFF_COS_SIM: init_row_aff = affinity.mutual_cosine_similarity( data.T,False,0,threshold=params.init_aff_threshold) elif params.init_aff_type == INIT_AFF_GAUSSIAN: #add KNN to the page init_row_aff = affinity.gaussian_euclidean( data.T, 5, params.init_aff_epsilon) #Compute diffusion embedding of initial affinities init_row_vecs,init_row_vals = markov.markov_eigs(init_row_aff, 12) init_row_vals[np.isnan(init_row_vals)] = 0.0 row_embedding = init_row_vecs.dot(np.diag(init_row_vals)) row_distances = spsp.distance.squareform(spsp.distance.pdist(row_embedding)) row_affinity = np.max(row_distances) - row_distances #Generate initial tree #print "call1 tree_constant:{}".format(tree_constant) Publisher.sendMessage("status.bar", "Calculating initial row tree...") if params.tree_type == TREE_TYPE_BINARY: init_row_tree = bintree_construct.median_tree( init_row_vecs,init_row_vals,max_levels=12) elif params.tree_type == TREE_TYPE_FLEXIBLE: # init_row_tree = tree_building.make_tree_embedding( # row_affinity,params.tree_constant) init_row_tree = tree_building.make_tree_embedding( row_affinity,params.tree_constant) dual_col_trees = [] dual_row_trees = [init_row_tree] row_tree_descs = ["Initial tree"] col_tree_descs = [] for i in xrange(params.n_iters): message = "Iteration {}: calculating column affinity...".format(i) Publisher.sendMessage("status.bar", message) #print "Beginning iteration {}".format(i) if params.col_affinity_type == DUAL_EMD: col_emd = dual_affinity.calc_emd(data,dual_row_trees[-1], params.col_alpha,params.col_beta) col_aff = dual_affinity.emd_dual_aff(col_emd) elif params.col_affinity_type == DUAL_GAUSSIAN: print "Gaussian dual affinity not supported at the moment." return None message = "Iteration {}: calculating column tree...".format(i) Publisher.sendMessage("status.bar", message) if params.tree_type == TREE_TYPE_BINARY: col_tree = bintree_construct.eigen_tree(data,dual_row_trees[-1], params.col_alpha,params.col_beta,params.tree_bal_constant) elif params.tree_type == TREE_TYPE_FLEXIBLE: col_tree = tree_building.make_tree_embedding(col_aff, params.tree_constant) dual_col_trees.append(col_tree) col_tree_descs.append("Iteration {}".format(i)) message = "Iteration {}: calculating row affinity...".format(i) Publisher.sendMessage("status.bar", message) if params.row_affinity_type == DUAL_EMD: row_emd = dual_affinity.calc_emd(data.T,dual_col_trees[-1], params.row_alpha,params.row_beta) row_aff = dual_affinity.emd_dual_aff(row_emd) elif params.row_affinity_type == DUAL_GAUSSIAN: print "Gaussian dual affinity not supported at the moment." return None message = "Iteration {}: calculating row tree...".format(i) Publisher.sendMessage("status.bar", message) if params.tree_type == TREE_TYPE_BINARY: row_tree = bintree_construct.eigen_tree(data.T,dual_col_trees[-1], params.row_alpha,params.row_beta,params.tree_bal_constant) elif params.tree_type == TREE_TYPE_FLEXIBLE: row_tree = tree_building.make_tree_embedding(row_aff, params.tree_constant) dual_row_trees.append(row_tree) row_tree_descs.append("Iteration {}".format(i)) quest_run_desc = "{}".format(datetime.datetime.now()) return PyQuestRun(quest_run_desc,dual_row_trees,dual_col_trees, row_tree_descs,col_tree_descs,params)