Recent works on representation learning for graph structured data predominantly focus on learning distributed representations of graph substructures such as nodes and subgraphs. However, many graph analytics tasks such as graph classification and clustering require representing entire graphs as fixed length feature vectors. While the aforementioned approaches are naturally unequipped to learn such representations, graph kernels remain as the most effective way of obtaining them. However, these graph kernels use handcrafted features (e.g., shortest paths, graphlets, etc.) and hence are hampered by problems such as poor generalization. To address this limitation, in this work, we propose a neural embedding framework named graph2vec to learn data-driven distributed representations of arbitrary sized graphs. graph2vec's embeddings are learnt in an unsupervised manner and are task agnostic. Hence, they could be used for any downstream task such as graph classification, clustering and even seeding supervised representation learning approaches. Our experiments on several benchmark and large real-world datasets show that graph2vec achieves significant improvements in classification and clustering accuracies over substructure representation learning approaches and are competitive with state-of-the-art graph kernels. 10 |
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41 | The code takes an input folder with json files. Every file is a graph and files have a numeric index as a name. The json files have two keys. The first key called "edges" corresponds to the edge list of the graph. The second key "features" corresponds to the node features. If the second key is not present the WL machine defaults to use the node degree as a feature. A sample graph dataset from NCI1 is included in the `dataset/` directory.
42 | 43 | ### Options 44 | 45 | Learning of the embedding is handled by the `src/graph2vec.py` script which provides the following command line arguments. 46 | 47 | #### Input and output options 48 | ``` 49 | --input-path STR Input folder. Default is `dataset/`. 50 | --output-path STR Embeddings path. Default is `features/nci1.csv`. 51 | ``` 52 | #### Model options 53 | ``` 54 | --dimensions INT Number of dimensions. Default is 128. 55 | --workers INT Number of workers. Default is 4. 56 | --epochs INT Number of training epochs. Default is 1. 57 | --min-count INT Minimal feature count to keep. Default is 5. 58 | --wl-iterations INT Number of feature extraction recursions. Default is 2. 59 | --learning-rate FLOAT Initial learning rate. Default is 0.025. 60 | --down-sampling FLOAT Down sampling rate for frequent features. Default is 0.0001. 61 | ``` 62 | 63 | ### Examples 64 |65 | The following commands learn an embedding of the graphs and writes it to disk. The node representations are ordered by the ID. Creating a graph2vec embedding of the default dataset with the default hyperparameter settings. Saving the embedding at the default path.
66 | 67 | ```sh 68 | $ python src/graph2vec.py 69 | ``` 70 | 71 | Creating an embedding of an other dataset. Saving the output in a custom place. 72 | 73 | ```sh 74 | $ python src/graph2vec.py --input-path new_data/ --output-path features/nci2.csv 75 | ``` 76 | 77 | Creating an embedding of the default dataset in 32 dimensions. 78 | 79 | ```sh 80 | $ python src/graph2vec.py --dimensions 32 81 | ``` 82 | ----------------------------------------------- 83 | 84 | **License** 85 | 86 | - [GNU License](https://github.com/benedekrozemberczki/graph2vec/blob/master/LICENSE) 87 | -------------------------------------------------------------------------------- /dataset/0.json: -------------------------------------------------------------------------------- 1 | {"edges": [[11, 10], [11, 13], [11, 7], [10, 12], [10, 5], [13, 14], [12, 15], [15, 14], [14, 9], [17, 19], [17, 8], [16, 8], [16, 6], [16, 18], [19, 20], [19, 4], [1, 7], [0, 7], [3, 9], [2, 9], [5, 6]], "features": {"0": "1", "1": "1", "2": "1", "3": "1", "4": "1", "5": "2", "6": "2", "7": "2", "8": "2", "9": "2", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3", "17": "3", "18": "3", "19": "3", "20": "3"}} -------------------------------------------------------------------------------- /dataset/1.json: -------------------------------------------------------------------------------- 1 | {"edges": [[20, 18], [20, 22], [21, 19], [21, 23], [22, 23], [1, 7], [1, 16], [0, 17], [3, 12], [2, 17], [2, 6], [5, 18], [5, 17], [4, 9], [4, 12], [4, 7], [7, 6], [6, 8], [9, 11], [9, 8], [8, 10], [11, 14], [10, 13], [13, 14], [12, 15], [19, 18]], "features": {"0": "4", "1": "1", "2": "1", "3": "1", "4": "2", "5": "2", "6": "3", "7": "3", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3", "17": "3", "18": "3", "19": "3", "20": "3", "21": "3", "22": "3", "23": "3"}} -------------------------------------------------------------------------------- /dataset/10.json: -------------------------------------------------------------------------------- 1 | {"edges": [[24, 19], [24, 26], [25, 27], [25, 23], [26, 27], [20, 21], [20, 22], [20, 7], [21, 17], [22, 18], [23, 19], [1, 16], [0, 12], [3, 7], [2, 7], [5, 12], [5, 4], [4, 8], [6, 13], [6, 16], [9, 8], [8, 10], [8, 11], [13, 12], [13, 14], [15, 18], [15, 14], [15, 17], [16, 19]], "features": {"0": "1", "1": "1", "2": "1", "3": "1", "4": "2", "5": "2", "6": "2", "7": "2", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3", "17": "3", "18": "3", "19": "3", "20": "3", "21": "3", "22": "3", "23": "3", "24": "3", "25": "3", "26": "3", "27": "3"}} -------------------------------------------------------------------------------- /dataset/11.json: -------------------------------------------------------------------------------- 1 | {"edges": [[11, 9], [11, 15], [10, 3], [10, 12], [10, 4], [13, 3], [13, 5], [12, 5], [12, 14], [15, 1], [15, 2], [14, 0], [14, 6], [16, 4], [16, 6], [3, 7], [7, 8], [9, 8]], "features": {"0": "4", "1": "1", "2": "1", "3": "2", "4": "2", "5": "2", "6": "2", "7": "3", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3"}} -------------------------------------------------------------------------------- /dataset/12.json: -------------------------------------------------------------------------------- 1 | {"edges": [[1, 7], [0, 8], [3, 8], [3, 5], [2, 9], [5, 7], [5, 6], [4, 9], [4, 8], [6, 9]], "features": {"0": "4", "1": "7", "2": "1", "3": "2", "4": "2", "5": "3", "6": "3", "7": "3", "8": "3", "9": "3"}} -------------------------------------------------------------------------------- /dataset/13.json: -------------------------------------------------------------------------------- 1 | {"edges": [[11, 8], [11, 12], [10, 13], [10, 6], [13, 2], [12, 9], [15, 1], [15, 0], [15, 4], [14, 3], [14, 7], [16, 0], [3, 4], [2, 7], [5, 8], [5, 7], [5, 6], [6, 9]], "features": {"0": "4", "1": "4", "2": "2", "3": "2", "4": "2", "5": "3", "6": "3", "7": "3", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3"}} -------------------------------------------------------------------------------- /dataset/14.json: -------------------------------------------------------------------------------- 1 | {"edges": [[24, 19], [24, 28], [25, 27], [25, 20], [26, 28], [26, 21], [27, 23], [20, 16], [21, 17], [22, 0], [22, 7], [22, 6], [23, 18], [29, 4], [1, 13], [3, 15], [2, 14], [5, 19], [5, 30], [4, 18], [7, 15], [6, 14], [9, 11], [9, 8], [9, 16], [8, 10], [8, 15], [8, 14], [11, 13], [10, 12], [10, 17], [13, 12], [17, 19], [16, 18]], "features": {"0": "4", "1": "1", "2": "1", "3": "1", "4": "1", "5": "1", "6": "2", "7": "2", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3", "17": "3", "18": "3", "19": "3", "20": "3", "21": "3", "22": "3", "23": "3", "24": "3", "25": "3", "26": "3", "27": "3", "28": "3", "29": "3", "30": "3"}} -------------------------------------------------------------------------------- /dataset/15.json: -------------------------------------------------------------------------------- 1 | {"edges": [[24, 21], [24, 22], [25, 22], [20, 18], [20, 23], [21, 18], [22, 23], [1, 16], [0, 11], [0, 13], [3, 15], [2, 15], [2, 17], [5, 13], [5, 16], [4, 9], [4, 10], [4, 14], [7, 9], [7, 8], [6, 18], [6, 16], [8, 11], [8, 12], [11, 10], [13, 12], [12, 15], [17, 19]], "features": {"0": "4", "1": "4", "2": "1", "3": "1", "4": "2", "5": "2", "6": "2", "7": "3", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3", "17": "3", "18": "3", "19": "3", "20": "3", "21": "3", "22": "3", "23": "3", "24": "3", "25": "3"}} -------------------------------------------------------------------------------- /dataset/16.json: -------------------------------------------------------------------------------- 1 | {"edges": [[11, 1], [11, 3], [11, 5], [10, 0], [10, 2], [10, 4], [3, 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"28": "3", "29": "3", "30": "3"}} -------------------------------------------------------------------------------- /dataset/18.json: -------------------------------------------------------------------------------- 1 | {"edges": [[11, 8], [11, 15], [10, 7], [13, 0], [13, 3], [13, 2], [12, 8], [12, 16], [15, 14], [14, 4], [14, 16], [17, 4], [18, 4], [1, 9], [3, 9], [2, 6], [5, 8], [5, 7], [5, 6], [6, 9]], "features": {"0": "4", "1": "1", "2": "2", "3": "2", "4": "2", "5": "3", "6": "3", "7": "3", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3", "17": "3", "18": "3"}} -------------------------------------------------------------------------------- /dataset/19.json: -------------------------------------------------------------------------------- 1 | {"edges": [[11, 0], [11, 3], [11, 4], [10, 7], [13, 8], [13, 15], [12, 8], [12, 14], [15, 16], [14, 16], [17, 2], [16, 2], [1, 9], [3, 6], [5, 8], [5, 7], [5, 6], [4, 9], [6, 9]], "features": 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-------------------------------------------------------------------------------- /dataset/20.json: -------------------------------------------------------------------------------- 1 | {"edges": [[11, 8], [11, 10], [10, 2], [10, 12], [13, 0], [13, 4], [13, 6], [12, 9], [15, 2], [14, 1], [14, 3], [14, 4], [3, 6], [5, 9], [5, 8], [5, 7], [7, 6]], "features": {"0": "5", "1": "4", "2": "1", "3": "2", "4": "2", "5": "3", "6": "3", "7": "3", "8": "3", "9": "3", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3"}} -------------------------------------------------------------------------------- /dataset/21.json: -------------------------------------------------------------------------------- 1 | {"edges": [[20, 0], [20, 21], [20, 18], [21, 19], [1, 13], [1, 14], [3, 12], [3, 6], [2, 15], [5, 12], [5, 17], [4, 11], [4, 15], [4, 14], [7, 9], [7, 6], [6, 8], [9, 10], [8, 10], [11, 13], [11, 12], [15, 16], [17, 19], [17, 16], [16, 18]], "features": {"0": "5", "1": "4", "2": "4", "3": 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"28": "3"}} -------------------------------------------------------------------------------- /dataset/23.json: -------------------------------------------------------------------------------- 1 | {"edges": [[24, 9], [24, 19], [25, 27], [25, 22], [26, 27], [26, 23], [27, 5], [20, 18], [20, 22], [20, 23], [21, 8], [21, 17], [28, 5], [1, 11], [1, 14], [0, 16], [3, 12], [2, 10], [4, 13], [7, 15], [6, 11], [6, 15], [6, 16], [11, 10], [10, 12], [13, 12], [13, 14], [15, 17], [17, 18], [16, 19], [19, 18]], "features": {"0": "4", "1": "1", "2": "1", "3": "1", "4": "1", "5": "1", "6": "2", "7": "2", "8": "2", "9": "2", "10": "3", "11": "3", "12": "3", "13": "3", "14": "3", "15": "3", "16": "3", "17": "3", "18": "3", "19": "3", "20": "3", "21": "3", "22": "3", "23": "3", "24": "3", "25": "3", "26": "3", "27": "3", "28": "3"}} -------------------------------------------------------------------------------- /dataset/24.json: 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53 | -------------------------------------------------------------------------------- /graph_embedding.jpeg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/benedekrozemberczki/graph2vec/27b998d2a009020eea7ff59802e440a35fef314a/graph_embedding.jpeg -------------------------------------------------------------------------------- /src/graph2vec.py: -------------------------------------------------------------------------------- 1 | """Graph2Vec module.""" 2 | 3 | import os 4 | import json 5 | import glob 6 | import hashlib 7 | import pandas as pd 8 | import networkx as nx 9 | from tqdm import tqdm 10 | from joblib import Parallel, delayed 11 | from param_parser import parameter_parser 12 | from gensim.models.doc2vec import Doc2Vec, TaggedDocument 13 | 14 | class WeisfeilerLehmanMachine: 15 | """ 16 | Weisfeiler Lehman feature extractor class. 17 | """ 18 | def __init__(self, graph, features, iterations): 19 | """ 20 | Initialization method which also executes feature extraction. 21 | :param graph: The Nx graph object. 22 | :param features: Feature hash table. 23 | :param iterations: Number of WL iterations. 24 | """ 25 | self.iterations = iterations 26 | self.graph = graph 27 | self.features = features 28 | self.nodes = self.graph.nodes() 29 | self.extracted_features = [str(v) for k, v in features.items()] 30 | self.do_recursions() 31 | 32 | def do_a_recursion(self): 33 | """ 34 | The method does a single WL recursion. 35 | :return new_features: The hash table with extracted WL features. 36 | """ 37 | new_features = {} 38 | for node in self.nodes: 39 | nebs = self.graph.neighbors(node) 40 | degs = [self.features[neb] for neb in nebs] 41 | features = [str(self.features[node])]+sorted([str(deg) for deg in degs]) 42 | features = "_".join(features) 43 | hash_object = hashlib.md5(features.encode()) 44 | hashing = hash_object.hexdigest() 45 | new_features[node] = hashing 46 | self.extracted_features = self.extracted_features + list(new_features.values()) 47 | return new_features 48 | 49 | def do_recursions(self): 50 | """ 51 | The method does a series of WL recursions. 52 | """ 53 | for _ in range(self.iterations): 54 | self.features = self.do_a_recursion() 55 | 56 | def path2name(path): 57 | base = os.path.basename(path) 58 | return os.path.splitext(base)[0] 59 | 60 | def dataset_reader(path): 61 | """ 62 | Function to read the graph and features from a json file. 63 | :param path: The path to the graph json. 64 | :return graph: The graph object. 65 | :return features: Features hash table. 66 | :return name: Name of the graph. 67 | """ 68 | name = path2name(path) 69 | data = json.load(open(path)) 70 | graph = nx.from_edgelist(data["edges"]) 71 | 72 | if "features" in data.keys(): 73 | features = data["features"] 74 | features = {int(k): v for k, v in features.items()} 75 | else: 76 | features = nx.degree(graph) 77 | features = {int(k): v for k, v in features} 78 | 79 | return graph, features, name 80 | 81 | def feature_extractor(path, rounds): 82 | """ 83 | Function to extract WL features from a graph. 84 | :param path: The path to the graph json. 85 | :param rounds: Number of WL iterations. 86 | :return doc: Document collection object. 87 | """ 88 | graph, features, name = dataset_reader(path) 89 | machine = WeisfeilerLehmanMachine(graph, features, rounds) 90 | doc = TaggedDocument(words=machine.extracted_features, tags=["g_" + name]) 91 | return doc 92 | 93 | def save_embedding(output_path, model, files, dimensions): 94 | """ 95 | Function to save the embedding. 96 | :param output_path: Path to the embedding csv. 97 | :param model: The embedding model object. 98 | :param files: The list of files. 99 | :param dimensions: The embedding dimension parameter. 100 | """ 101 | out = [] 102 | for f in files: 103 | identifier = path2name(f) 104 | out.append([identifier] + list(model.docvecs["g_"+identifier])) 105 | column_names = ["type"]+["x_"+str(dim) for dim in range(dimensions)] 106 | out = pd.DataFrame(out, columns=column_names) 107 | out = out.sort_values(["type"]) 108 | out.to_csv(output_path, index=None) 109 | 110 | def main(args): 111 | """ 112 | Main function to read the graph list, extract features. 113 | Learn the embedding and save it. 114 | :param args: Object with the arguments. 115 | """ 116 | graphs = glob.glob(os.path.join(args.input_path, "*.json")) 117 | print("\nFeature extraction started.\n") 118 | document_collections = Parallel(n_jobs=args.workers)(delayed(feature_extractor)(g, args.wl_iterations) for g in tqdm(graphs)) 119 | print("\nOptimization started.\n") 120 | 121 | model = Doc2Vec(document_collections, 122 | vector_size=args.dimensions, 123 | window=0, 124 | min_count=args.min_count, 125 | dm=0, 126 | sample=args.down_sampling, 127 | workers=args.workers, 128 | epochs=args.epochs, 129 | alpha=args.learning_rate) 130 | 131 | save_embedding(args.output_path, model, graphs, args.dimensions) 132 | 133 | if __name__ == "__main__": 134 | args = parameter_parser() 135 | main(args) 136 | -------------------------------------------------------------------------------- /src/param_parser.py: -------------------------------------------------------------------------------- 1 | """Parameter parser to set the model hyperparameters.""" 2 | 3 | import argparse 4 | 5 | def parameter_parser(): 6 | """ 7 | A method to parse up command line parameters. 8 | By default it gives an embedding of the partial NCI1 graph dataset. 9 | The default hyperparameters give a good quality representation without grid search. 10 | Representations are sorted by ID. 11 | """ 12 | parser = argparse.ArgumentParser(description="Run Graph2Vec.") 13 | 14 | parser.add_argument("--input-path", 15 | nargs="?", 16 | default="./dataset/", 17 | help="Input folder with jsons.") 18 | 19 | parser.add_argument("--output-path", 20 | nargs="?", 21 | default="./features/nci1.csv", 22 | help="Embeddings path.") 23 | 24 | parser.add_argument("--dimensions", 25 | type=int, 26 | default=128, 27 | help="Number of dimensions. Default is 128.") 28 | 29 | parser.add_argument("--workers", 30 | type=int, 31 | default=4, 32 | help="Number of workers. Default is 4.") 33 | 34 | parser.add_argument("--epochs", 35 | type=int, 36 | default=10, 37 | help="Number of epochs. Default is 10.") 38 | 39 | parser.add_argument("--min-count", 40 | type=int, 41 | default=5, 42 | help="Minimal structural feature count. Default is 5.") 43 | 44 | parser.add_argument("--wl-iterations", 45 | type=int, 46 | default=2, 47 | help="Number of Weisfeiler-Lehman iterations. Default is 2.") 48 | 49 | parser.add_argument("--learning-rate", 50 | type=float, 51 | default=0.025, 52 | help="Initial learning rate. Default is 0.025.") 53 | 54 | parser.add_argument("--down-sampling", 55 | type=float, 56 | default=0.0001, 57 | help="Down sampling rate of features. Default is 0.0001.") 58 | 59 | return parser.parse_args() 60 | --------------------------------------------------------------------------------