A fuzzy matching & clustering library for python.

# Fog

A fuzzy matching/clustering library for Python.

## Installation

You can install fog with pip with the following command:

pip install fog


## Usage

### Evaluation

#### best_matching_macro_average

Efficient implementation of the "macro average best matching F1" evaluation metric for clusters.

Note that this metric is not symmetric and will match truth -> predicted.

Arguments

• truth iterable: the truth clusters.
• predicted iterable: the predicted clusters.
• allow_additional_items ?bool [False]: Whether to allow additional items that don't exist in truth clusters to be found in predicted ones. Those additional items will then be ignored when computing the metrics instead of raising an error when found.

### Graph

#### floatsam_sparsification

Function using an iterative algorithm to try and find the best weight threshold to apply to trim the given graph's edges while keeping the underlying community structures.

It works by iteratively increasing the threshold and stopping as soon as a significant connected component starts to drift away from the principal one.

This is basically a very naive gradient descent with a very naive cost function but it works decently for typical cases.

Arguments

• graph nx.Graph: Graph to sparsify.
• starting_treshold ?float [0.0]: Starting similarity threshold.
• learning_rate ?float [0.05]: How much to increase the threshold at each step of the algorithm.
• max_drifter_size ?int: Max size of component to detach itself from the principal one before stopping the algorithm. If not provided it will default to the logarithm of the graph's total number of nodes.
• weight ?str [weight wrt networkx conventions]: Name of the weight attribute.
• remove_edges ?bool [False]: Whether to remove edges from the graph having a weight less than found threshold or not. Note that if True, this will mutate the given graph.

#### monopartite_projection

Function computing a monopartite projection of the given bipartite graph. This projection can be basic and create a weighted edge each time two nodes in target partition share a common neighbor. Or it can be weighted and filtered using a similarity metric such as Jaccard or cosine similarity, for instance.

Arguments

• bipartite nx.Graph: Target bipartite graph.
• project str: Name of the partition to project.
• part ?str [bipartite]: Name of the node attribute on which the graph partition is built e.g. "color" or "type" etc.
• weight ?str [weight]: Name of the weight edge attribute.
• metric ?str [None]: Metric to use. If None, the basic projection will be returned. Also accepts jaccard, overlap, dice, cosine or binary_cosine.
• threshold ?float [None]: Optional similarity threshold under which edges won't be added to the monopartite projection.
• use_topology ?bool: Whether to use the bipartite graph's topology to attempt a subquadratic time projection. Intuitively, this works by not computing similarities of all pairs of nodes but only of pairs of nodes that share at least a common neighbor. It generally works better than the quadratic approach but can sometimes hurt your performance by losing time on graph traversals when your graph is very dense.
• bipartition_check ?bool: This function will start by checking whether your graph is bipartite because it can get stuck in an infinite loop if given graph is not truly bipartite. Be sure to disable this kwarg if you know beforehand that your graph is bipartite and for better performance.

### Keyers

#### omission_key

Function returning a string's omission key which is constructed thusly:

1. First we record the string's set of consonant in an order where most frequently mispelled consonants will be last.
2. Then we record the string's set of vowels in the order of first appearance.

This key is very useful when searching for mispelled strings because if sorted using this key, similar strings will be next to each other.

Arguments

• string str: The string to encode.

#### skeleton_key

Function returning a string's skeleton key which is constructed thusly:

1. The first letter of the string
2. Unique consonants in order of appearance
3. Unique vowels in order of appearance

This key is very useful when searching for mispelled strings because if sorted using this key, similar strings will be next to each other.

Arguments

• string str: The string to encode.

### Metrics

#### cosine_similarity

Function computing the cosine similarity of the given sequences. Runs in O(n), n being the sum of A & B's sizes.

Arguments

• A iterable: First sequence.
• B iterable: Second sequence.

#### sparse_cosine_similarity

Function computing cosine similarity on sparse weighted sets represented as python dicts.

Runs in O(n), n being the sum of A & B's sizes.

from fog.metrics import sparse_cosine_similarity

# Basic
sparse_cosine_similarity({'apple': 34, 'pear': 3}, {'pear': 1, 'orange': 1})
>>> ~0.062


Arguments

• A Counter: First weighted set.
• B Counter: Second weighted set.

#### sparse_dot_product

Function used to compute the dotproduct of sparse weighted sets represented by python dicts.

Runs in O(n), n being the size of the smallest set.

Arguments

• A Counter: First weighted set.
• B Counter: Second weighted set.

#### binary_cosine_similarity

Function computing the binary cosine similarity of the given sequences. Runs in O(n), n being the size of the smallest set.

Arguments

• A iterable: First sequence.
• B iterable: Second sequence.

#### sparse_binary_cosine_similarity

Function computing binary cosine similarity on sparse vectors represented as python sets.

Runs in O(n), n being the size of the smaller set.

Arguments

• A Counter: First set.
• B Counter: Second set.

#### dice_coefficient

Function computing the Dice coefficient. That is to say twice the size of the intersection of both sets divided by the sum of both their sizes.

Runs in O(n), n being the size of the smallest set.

from fog.metrics import dice_coefficient

# Basic
dice_coefficient('context', 'contact')
>>> ~0.727


Arguments

• A iterable: First sequence.
• B iterable: Second sequence.

#### jaccard_similarity

Function computing the Jaccard similarity. That is to say the intersection of input sets divided by their union.

Runs in O(n), n being the size of the smallest set.

from fog.metrics import jaccard_similarity

# Basic
jaccard_similarity('context', 'contact')
>>> ~0.571


Arguments

• A iterable: First sequence.
• B iterable: Second sequence.

#### weighted_jaccard_similarity

Function computing the weighted Jaccard similarity. Runs in O(n), n being the sum of A & B's sizes.

from fog.metrics import weighted_jaccard_similarity

# Basic
weighted_jaccard_similarity({'apple': 34, 'pear': 3}, {'pear': 1, 'orange': 1})
>>> ~0.026


Arguments

• A Counter: First weighted set.
• B Counter: Second weighted set.

#### overlap_coefficient

Function computing the overlap coefficient of the given sets, i.e. the size of their intersection divided by the size of the smallest set.

Runs in O(n), n being the size of the smallest set.

Arguments

• A iterable: First sequence.
• B iterable: Second sequence.

## Project details

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