Graph Embeddings Alicia Frame, PhD October 10, 2019 Overview - - PowerPoint PPT Presentation

Graph Embeddings

Alicia Frame, PhD October 10, 2019

What’s an embedding? How do these work?

• Motivating Example - Word2Vec
• Motivating Example - DeepWalk

Graph embeddings overview Graph embedding techniques Graph embeddings with Neo4j

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Overview

What does the internet say?

• Google: “An embedding is a relatively

low-dimensional space into which you can translate high-dimensional vectors”

• Wikipedia: “In mathematics, an embedding

is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.”

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TL;DR - what’s an embedding?

A way of mapping something (a document, an image, a graph) into a fixed length vector (or matrix) that captures key features while reducing the dimensionality

Graph embeddings are a specific type of embedding that translate graphs, or parts of graphs, to fixed length vectors (or tensors)

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So what’s a graph embedding?

An embedding translates something complex into something a machine can work with

• Represents the important features of the input object in a

compact, low dimensional format

• Embedded representation can be used as a feature for ML, for

direct comparisons, or as an input representation for a DL model Embeddings - typically - learn what’s important in an unsupervised, generalizable way.

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But why bother?

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Motivating Examples

How can I represent words in a way that I can use them mathematically?

• How similar are two words?
• Can I use the representation of a word in a model?

Naive approach - how similar are the strings?

• Hand engineered rules?
• How many of each letter?

CAT = [10100000000000000001000000]

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Motivating example: Word Embeddings

Frequency matrix:

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Motivating example: Word Embeddings

Weighted term frequency (TF-IDF) Can we use documents to encode words?

Word order probably matters too: Words that occur together have similar contexts.

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Motivating example: Word Embeddings

• “Tylenol is a pain reliever,”

“Paracetamol is a pain reliever” same context

• Co-occurence: how often do two

words appear in the same context window?

• Context window: specific

number and direction He is not lazy He is intelligent He is smart He is not lazy He is intelligent He is smart

Word order probably matters too: Words that occur together have similar contexts.

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Motivating example: Word Embeddings

• “Tylenol is a pain reliever,”

“Paracetamol is a pain reliever” same context

• Co-occurence: how often do two

words appear in the same context window?

• Context window: specific

number and direction

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Why not stop here?

• You need more documents to really understand context … but

the more documents you have the bigger your matrix is

• Giant sparse matrices or vectors are cumbersome and

uninformative We need to reduce the dimensionality of our matrix

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Motivating example: Word Embeddings

Count Based Methods: Linear algebra to the rescue? Pros: Preserves semantic relationships, accurate, known methods Cons: Huge memory requirements, not trained for a specific task

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Motivating Example: Word Embeddings

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Motivating Example: Word Embeddings

Predictive Methods: learn an embedding for a specific task

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Motivating Example: Word Embeddings

Predictive Methods: learn an embedding for a specific task

The SkipGram model learns a vector representation for each word that maximizes the probability of that word given the previous words

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Motivating Example: Word Embeddings

input word - one hot encoded vector

• utput prediction -

probability, for each word in the corpus, that it’s the next word

The SkipGram model learns a vector representation for each word that maximizes the probability of that word given the previous words

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Motivating Example: Word Embeddings

input word - one hot encoded vector

• utput prediction -

probability, for each word in the corpus, that it’s the next word

The SkipGram model learns a vector representation for each word that maximizes the probability of that word given the previous words

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Motivating Example: Word Embeddings

The hidden layer is a weight matrix with

• ne row per word,

and one column per neuron -- this is the embedding!

Maximize the probability that the next word is w_t given h: Train model by maximizing the log-likelihood over the training set: Skipgram model calculates:

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(if we really want to get into the math)

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Motivating Example: Word Embeddings

Word embeddings condense representations of the words while preserving context:

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Cool, but what’s this got to do with graphs?

Motivating example: DeepWalk

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How do we represent a node in a graph mathematically? Can we adapt word2vec?

• Each node is like a word
• Neighborhood around the node is the context window

Extract the context for each node by sampling random walks from the graph: For every node in the graph, take n fixed length random walks (equivalent to sentences)

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Motivating example: DeepWalk

Once we have our sentences, we can extract the context windows and learn weights using the same skip-gram model (Objective is to predict neighboring nodes given the target node)

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Motivating example: DeepWalk

Embeddings are the hidden layer weights from the skipgram model Note: there are also equivalent methodologies to the matrix factorization approaches or hand engineered approaches we talked about for words as well

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Motivating example: DeepWalk

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Graph Embeddings Overview

There are lots of graph embeddings...

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What type of graph are you trying to create an embedding for?

• Monopartite graphs (DeepWalk is designed for these)
• Multipartite graphs (eg. Knowledge Graphs)

What aspect of the graph are you trying to represent?

• Vertex embeddings: describe connectivity of each node
• Path embeddings: traversals across the graph
• Graph embeddings: encode an entire graph into a single vector

What tp

Most techniques consist of:

• A similarity function that measures the similarity between nodes
• An encoder function: generates the node embedding
• A decoder function to reconstruct pairwise similarity
• A loss function that measures how good your reconstruction is

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Node embedding overview

Shallow - Encoder function is an embedding lookup Matrix Factorization:

• These techniques all rely on an adjacency matrix input
• Matrix factorization is applied either directly to the input or

some transformation of the input Random Walk:

• Obtain node co-occurrence via random walks
• Learn weight to optimize similarity measure

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Shallow Graph Embedding Techniques

Shallow - Encoder function is an embedding lookup Matrix Factorization:

• These techniques all rely on an adjacency matrix input
• Matrix factorization is applied either directly to the input or

some transformation of the input Random Walk:

• Obtain node co-occurrence via random walks
• Learn weight to optimize similarity measure

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Shallow Graph Embedding Techniques

Massive memory footprint Computationally intense

Shallow - Encoder function is an embedding lookup Matrix Factorization:

• These techniques all rely on an adjacency matrix input
• Matrix factorization is applied either directly to the input or

some transformation of the input Random Walk:

• Obtain node co-occurrence via random walks
• Learn weight to optimize similarity measure

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Shallow Graph Embedding Techniques

Massive memory footprint Computationally intense Local-only perspective Assumes similar nodes are close together

Matrix Factorization:

• These techniques all rely on an adjacency matrix input
• Matrix factorization is applied either directly to the input or

some transformation of the input Random Walk:

• Obtain node co-occurrence via random walks
• Learn weight to optimize similarity measure

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Shallow Graph Embedding Techniques

Massive memory footprint Computationally intense Local-only perspective Assumes similar nodes are close together

Why not stick with these?

• Shallow embeddings are inefficient - no parameters shared

between nodes

• Can’t leverage node attributes
• Only generate embeddings for nodes present when the

embedding was trained - problematic for large, evolving graphs Newer methodologies - compress information

• Neighborhood autoencoder methods
• Neighborhood aggregation
• Convolutional autoencoders

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Shallow Embeddings

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Autoencoder methods

Using Graph Embeddings

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Why are we going to all this trouble?

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Visualization & pattern discovery:

• Leveraging lots of existing
• t-SNE plots
• PCA

Clustering and community detection:

• Apply generic tabular data approaches (eg. k-means) but allows

capture of both functional and structural roles

• KNN graphs based on embedding similarity

Node classification/semi-supervised learning Predict missing node attributes Link prediction

• predict edges not present in the graph
• Either using similarity measures/heuristics or ML pipelines

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Why are we going to all this trouble?

Embeddings can make the graph algorithm library even more powerful!

Graph Embeddings in Neo4j

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Two prototype implementations from Labs: DeepWalk & DeepGL

• DeepGL is more similar to a “hand crafted” embedding
• Uses graph algorithms to generate features
• Diffusion of values across edges, dimensionality reduction

Neither is ready for production use - but lessons learned!

• Lots of demand
• Memory intensive and not turned for performance
• Deep Learning is not easy in Java

Python is easy to get started with for experimentation, but doesn’t perform at scale

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Neo4j Labs Implementations

We’re actively exploring the best ways to implement graph embeddings at scale so please stay tuned

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...So what’s next?

1. A graph embedding is a fixed length vector of a. Numbers b. Letters c. Nodes

• 2. An embedding is a ______________ representation of your data

a. Human readable b. Lower dimensional c. Binary

• 3. What’s the name of the graph embedding we walked through in

this presentation?

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Hunger Games!