******************** UnsupervisedEdgeWise ******************** Overview -------- :class:`UnsupervisedEdgeWise` is an inductive edge representation learning algorithm which is able to leverage vertex and edge feature information. It can be applied to a wide variety of tasks, including edge classification and link prediction. `UnsupervisedEdgeWise` is based on top of the `GraphWise` model, leveraging the source vertex embedding and the destination vertex embedding generated by the `GraphWise` model to generate inductive edge embeddings. The training is based on [`Deep Graph Infomax (DGI)` by Velickovic et al.](https://arxiv.org/pdf/1809.10341.pdf) Model Structure --------------- A :class:`UnsupervisedEdgeWise` model consists of graph convolutional layers followed by an embedding layer which defaults to a DGI layer. First, the source and destination vertices of the target edge are processed through the convolutional layers. The forward pass through a convolutional layer for a vertex proceeds as follows 1. A set of neighbors of the vertex is sampled. 2. The previous layer representations of the neighbors are mean-aggregated, and the aggregated features are concatenated with the previous layer representation of the vertex. 3. This concatenated vector is multiplied with weights, and a bias vector is added. 4. The result is normalized such that the layer output has unit norm. The edge combination layer concatenates the source vertex embedding, the edge features and the destination vertex embedding forward it through a linear layer to get the edge embedding. The DGI Layer consists of three parts enabling unsupervised learning using embeddings produced by the convolution layers. 1. Corruption function: Shuffles the node features while preserving the graph structure to produce negative embedding samples using the convolution layers. 2. Readout function: Sigmoid activated mean of embeddings, used as summary of a graph 3. Discriminator: Measures the similarity of positive (unshuffled) embeddings with the summary as well as the similarity of negative samples with the summary from which the loss function is computed. Since none of these contains mutable hyperparameters, the default DGI layer is always used and cannot be adjusted. Functionalities --------------- We describe here the usage of the main functionalities of `UnsupervisedEdgeWise` in PGX, using the [Movielens](https://movielens.org) graph as an example. Loading a graph ~~~~~~~~~~~~~~~ First, we create a session and an analyst: .. code-block:: python :linenos: session = pypgx.get_session() analyst = session.analyst .. code-block:: python :linenos: full_graph = session.read_graph_with_properties(cpath) train_edge_filter = EdgeFilter.from_pgql_result_set( session.query_pgql("SELECT e FROM movielens MATCH (v1) -[e]-> (v2) WHERE ID(e) % 4 > 0"), "e" ) train_graph = full_graph.filter(train_edge_filter) test_edge_filter = EdgeFilter.from_pgql_result_set( session.query_pgql("SELECT e FROM movielens MATCH (v1) -[e]-> (v2) WHERE ID(e) % 4 = 0"), "e" ) test_graph = full_graph.filter(test_edge_filter) test_edges = test_graph.get_edges() Example: computing edge embeddings on the Movielens Dataset ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We describe here the usage of `UnsupervisedEdgeWise` in PGX using the [Movielens](https://movielens.org) graph as an example. This data set consists of 100,000 ratings (1-5) from 943 users on 1682 movies, with simple demographic info for the users (age, gender, occupation) and movies (year, avg_rating, genre). Users and movies are vertices, while ratings of users to movies are edges with a `rating` feature. We will use `EgdeWise` to compute the edges embeddings. We first build the model and fit it on the `trainGraph`: .. code-block:: python :linenos: conv_layer_config = dict(num_sampled_neighbors=10) conv_layer = analyst.graphwise_conv_layer_config(**conv_layer_config) params = dict(conv_layer_config=[conv_layer], pred_layer_config=[pred_layer], vertex_input_property_names=["movie_year", "avg_rating", "movie_genres", "user_occupation_label", "user_gender", "raw_user_age"], edge_input_property_names=["user_rating"], num_epochs=10, embedding_dim=32, learning_rate=0.003, normalize=False, # recommended seed=0) model = analyst.unsupervised_edgewise_builder(**params) model.fit(trainGraph) Since `EdgeWise` is inductive, we can infer the compute the embeddings for unseen edges: .. code-block:: python :linenos: embeddings = model.infer_embeddings(full_graph, test_edges) embeddings.print() This returns the embeddings for any edge as: ``` +-----------------------------------------+---------------------+ | edgeId | embedding | +-----------------------------------------+---------------------+ ``` Building an EdgeWise Model (minimal) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We build a ``EdgeWise`` model using the minimal configuration and default hyperparameters. Note that even though only one feature property is needed (either on vertices with ``vertex_input_property_names`` or edges with ``edge_input_property_names``) for the model to work, you can specify arbitrarily many. .. code-block:: python :linenos: params = dict( vertex_input_property_names=["features"], edge_input_property_names=["edge_features"] ) model = analyst.unsupervised_edgewise_builder(**params) Advanced hyperparameter customization ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The implementation allows for very rich hyperparameter customization. Internally, GraphWise for each node it applies an aggregation of the representations of neighbors, this operation can be configured through a sub-config class: either :class:`GraphWiseConvLayerConfig` or :class:`GraphWiseAttentionLayerConfig`. * GraphWiseConvLayer is based on `Inductive Representation Learning on Large Graphs (GraphSage) by Hamilton et al. `_ * GraphWiseAttentionLayer is based on `Graph Attention neTworks (GAT) by Velickovic et al. `_ which makes the aggregation smarter but comes with larger computation cost In the following, we build such a configuration and use it in a model. We specify a weight decay of ``0.001`` and dropout with dropping probability ``0.5`` to counteract overfitting. Also, we recommend to disable normalization of embeddings when intended to use them in downstream classfication tasks. To enable or disable GPU, we can use the parameter `enable_accelerator`. By default this feature is enabled, however if there's no GPU device and the cuda toolkit is not installed, the feature will be disabled and CPU will be the device used for all mllib operations. .. code-block:: python :linenos: weight_property = analyst.pagerank(train_graph).name conv_layer_config = dict( num_sampled_neighbors=25, activation_fn='tanh', weight_init_scheme='xavier', neighbor_weight_property_name=weight_property, dropout_rate=0.5 ) conv_layer = analyst.graphwise_conv_layer_config(**conv_layer_config) params = dict( conv_layer_config=[conv_layer], pred_layer_config=[pred_layer], vertex_input_property_names=["vertex_features"], edge_input_property_names=["edge_features"], seed=17, weight_decay=0.001, normalize=False, # recommended enable_accelerator=True # Enable or Disable GPU ) model = analyst.unsupervised_edgewise_builder(**params) The above code uses :class:`GraphWiseConvLayerConfig` for the convolutional layer configuration. It can be replaced with :class:`GraphWiseAttentionLayerConfig` if a graph attention network model is desired. If the number of sampled neighbors is set to `-1` using `setNumSampledNeighbors`, all neighboring nodes will be sampled. .. code-block:: python :linenos: conv_layer_config = dict( num_sampled_neighbors=25, activation_fn='leaky_relu', weight_init_scheme='xavier_uniform', num_heads=4, dropout_rate=0.5 ) conv_layer = analyst.graphwise_attention_layer_config(**conv_layer_config) For a full description of all available hyperparameters and their default values, see the :class:`pypgx.api.mllib.UnsupervisedEdgeWiseModel`, :class:`pypgx.api.mllib.GraphWiseConvLayerConfig`, :class:`pypgx.api.mllib.GraphWiseAttentionLayerConfig`, :class:`pypgx.api.mllib.GraphWiseDgiLayerConfig` and :class:`pypgx.api.mllib.GraphWiseDominantLayerConfig` docs. Property types supported ~~~~~~~~~~~~~~~~~~~~~~~~ The model supports two types of properties for both vertices and edges: * ``continuous`` properties (boolean, double, float, integer, long) * ``categorical`` properties (string) For ``categorical`` properties, two categorical configurations are possible: * ``one-hot-encoding``: each category is mapped to a vector, that is concatenated to other features (default) * ``embedding table``: each category is mapped to an embedding that is concatenated to other features and is trained along with the model One-hot-encoding converts each category into an independent vector. Therefore, it is suitable if we want each category to be interpreted as an equally independent group. For instance, if there are categories ranging from A to E without meaning anything by each alphabet, one-hot-encoding can be a good fit. Embedding table is recommended if the semantics of the properties matter, and we want certain categories to be closer to each other than the others. For example, let's assume there is a "day" property with values ranging from Monday to Sunday and we want to preserve our intuition that "Tuesday" is closer to "Wednesday" than "Saturday". Then by choosing the embedding table configuration, we can let the vectors that represent the categories to be learned during training so that the vector that is mapped to "Tuesday" becomes close to that of "Wednesday". Although the embedding table approach has an advantage over one-hot-encoding that we can learn more suitable vectors to represent each category, this also means that a good amount of data is required to train the embedding table properly. The one-hot-encoding approach might be better for use-cases with limited training data. When using the embedding table, we let users set the out-of-vocabulary probability. With the given probability, the embedding will be set to the out-of-vocabulary embedding randomly during training, in order to make the model more robust to unseen categories during inference. .. code-block:: python :linenos: vertex_input_property_configs = [ analyst.one_hot_encoding_categorical_property_config( property_name="vertex_str_feature_1", max_vocabulary_size=100, ), analyst.learned_embedding_categorical_property_config( property_name="vertex_str_feature_2", embedding_dim=4, shared=False, # set whether to share the vocabulary or not when several types have a property with the same name oov_probability=0.001 # probability to set the word embedding to the out-of-vocabulary embedding ), ] model_params = dict( vertex_input_property_names=[ "vertex_int_feature_1", # continuous feature "vertex_str_feature_1", # string feature using one-hot-encoding "vertex_str_feature_2", # string feature using embedding table "vertex_str_feature_3", # string feature using one-hot-encoding (default) ], vertex_input_property_configs=vertex_input_property_configs, ) model = analyst.unsupervised_edgewise_builder(**model_params) Setting the edge embedding production method ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The edge embedding is computed by default by combining the source vertex embedding, the destination vertex embedding and the edge features. You can manually set which of them are used by setting the :class:`EdgeCombinationMethod`: .. code-block:: python :linenos: from pypgx.api.mllib import ConcatEdgeCombinationMethod method_config = dict( use_source_vertex=True, use_destination_vertex=False, use_edge=True ) method = ConcatEdgeCombinationMethod(**method_config) params = dict( vertex_input_property_names=["vertex_features"], edge_input_property_names=["edge_features"], edge_combination_method=method, seed=17 ) model = analyst.unsupervised_edgewise_builder(**params) Training the UnsupervisedEdgeWiseModel ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We can train a ``UnsupervisedEdgeWiseModel`` on a graph: .. code-block:: python :linenos: model.fit(train_graph) We can also add a validation step to the training. When training a model, the optimal number of training epochs is not known in advance and it is one of the key parameters that determine the model quality. Being able to monitor the training and validation losses helps us to identify a good value for the model parameters and gain visibility in the training process. The evaluation frequency can be specified in terms of epoch or step. To configure a validation step, create a `GraphWiseValidationConfig` and pass it to the model builder: .. code-block:: python :linenos: val_config = analyst.graphwise_validation_config( evaluation_frequency=1, evaluation_frequency_scale="epoch", ) params = dict( vertex_input_property_names=["vertex_features"], edge_input_property_names=["edge_features"], validation_config=val_config, seed=17 ) model = analyst.unsupervised_edgewise_builder(**params) After configuring a validation step, pass a graph for validation to the fit method together with the graph for training: .. code-block:: python :linenos: model.fit(train_graph, test_graph) Getting Loss value ~~~~~~~~~~~~~~~~~~ We can fetch the training loss value: .. code-block:: python :linenos: loss = model.get_training_loss() Getting Training log ~~~~~~~~~~~~~~~~~~ If a validation step was configured, we can fetch the training log that has training and validation loss information: .. code-block:: python :linenos: training_log = model.get_training_log() training_log.print() The output frame will be similar to the following example output: +---------------------------------------------------+ | epoch | training_loss | validation_loss | +---------------------------------------------------+ | 1 | 1.1378216743469238 | 0.7227532917802985 | | 2 | 0.47905975580215454 | 0.36742845245383005 | | 3 | 0.28058260679244995 | 0.32146902856501663 | +---------------------------------------------------+ The first column will be named according to the evaluation frequency scale that was set in the validation configuration ("epoch" or "step"). Note that the validation loss is the average of the losses evaluated on all batches of the validation graph, while the training loss is the loss value logged at that epoch or step (i.e., the loss evaluated on the last batch). Also, please note that the training log will be overwritten if the fit method is called multiple times. Inferring embeddings ~~~~~~~~~~~~~~~~~~~~ We can use a trained model to infer embeddings for unseen edges and store in a ``CSV`` file: .. code-block:: python :linenos: edge_vectors = model.infer_embeddings(full_graph, test_edges).flatten_all() edge_vectors.store(file_format="csv", path="/edge_vectors.csv", overwrite=True) The schema for the ``edge_vectors`` would be as follows without flattening (``flatten_all`` splits the vector column into separate double-valued columns): +-----------------------------------------+---------------------+ | edgeId | embedding | +-----------------------------------------+---------------------+ Classifying the edges using the obtained embeddings ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We can use the obtained embeddings in downstream edge classification tasks. The following shows how we can train a MLP classifier which takes the embeddings as input. We assume that the edge label information is stored under the edge property "labels". .. code-block:: python :linenos: import pandas as pd from sklearn.metrics import accuracy_score, make_scorer from sklearn.model_selection import RepeatedStratifiedKFold, cross_val_score from sklearn.neural_network import MLPClassifier from sklearn.preprocessing import StandardScaler # prepare input data edge_vectors_df = edge_vectors.to_pandas().astype({"edgeId": int}) edge_labels_df = pd.DataFrame([ {"edgeId": e.id, "labels": properties} for e, properties in graph.get_edge_property("labels").get_values() ]).astype(int) edge_vectors_with_labels_df = edge_vectors_df.merge(edge_labels_df, on="edgeId") feature_columns = [c for c in edge_vectors_df.columns if c.startswith("embedding")] x = edge_vectors_with_labels_df[feature_columns].to_numpy() y = edge_vectors_with_labels_df["labels"].to_numpy() scaler = StandardScaler() x = scaler.fit_transform(x) # define a MLP classifier model = MLPClassifier( hidden_layer_sizes=(6,), learning_rate_init=0.05, max_iter=2000, random_state=42, ) # define a metric and evaluate with cross-validation cv = RepeatedStratifiedKFold(n_splits=5, n_repeats=3, random_state=42) scorer = make_scorer(accuracy_score, greater_is_better=True) scores = cross_val_score(model, x, y, scoring=scorer, cv=cv, n_jobs=-1) Storing a trained model ~~~~~~~~~~~~~~~~~~~~~~~ Models can be stored either to the server file system, or to a database. The following shows how to store a trained :class:`UnsupervisedEdgeWise` model to a specified file path: .. code-block:: python :linenos: model.export().file("/", key) When storing models in database, they are stored as a row inside a model store table. The following shows how to store a trained :class:`UnsupervisedEdgeWise` model in database in a specific model store table: .. code-block:: python :linenos: model.export().db( "modeltablename", "model_name", username="user", password="password", jdbc_url="jdbcUrl" ) Loading a pre-trained model ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Similarly to storing, models can be loaded from a file in the server file system, or from a database. We can load a pre-trained :class:`UnsupervisedEdgeWise` model from a specified file path as follows: .. code-block:: python :linenos: model = analyst.load_unsupervised_edgewise_model("/", "key") We can load a pre-trained :class:`UnsupervisedEdgeWise` model from a model store table in database as follows: .. code-block:: python :linenos: model = analyst.get_supervised_edgewise_model_loader().db( "modeltablename", "model_name", username="user", password="password", jdbc_url="jdbcUrl" ) Destroying a model ~~~~~~~~~~~~~~~~~~ We can destroy a model as follows: .. code-block:: python :linenos: model.destroy()