Basic Evaluation Metrics for Embeddings
In the field of natural language processing (NLP), evaluating the quality of word embeddings is crucial for understanding how well they capture semantic meanings. In this section, we will discuss several basic evaluation metrics commonly used for assessing the performance of embeddings like Word2Vec and GloVe.
1. Intrinsic Evaluation Metrics
Intrinsic evaluation metrics involve direct measurement of the embeddings based on the properties of the vectors themselves. These metrics usually focus on how well embeddings reflect semantic relationships.1.1 Cosine Similarity
Cosine similarity is a measure that calculates the cosine of the angle between two non-zero vectors in an inner product space. It is widely used to determine how similar two word vectors are.Formula
The cosine similarity is computed as:$$ ext{Cosine Similarity}(A, B) = rac{A ullet B}{||A|| ||B||} $$
Where: - $A ullet B$ is the dot product of vectors A and B. - $||A||$ and $||B||$ are the magnitudes (or lengths) of vectors A and B.
Example
Consider the word vectors forking, queen, and man:
`python
from sklearn.metrics.pairwise import cosine_similarity
import numpy as npExample word vectors (random values)
king = np.array([0.5, 0.2, 0.1]) queen = np.array([0.4, 0.3, 0.2]) man = np.array([0.3, 0.1, 0.4])Calculate cosine similarity between king and queen
similarity_kq = cosine_similarity([king], [queen])[0][0]Calculate cosine similarity between king and man
similarity_km = cosine_similarity([king], [man])[0][0]print(f'Cosine Similarity between king and queen: {similarity_kq}')
print(f'Cosine Similarity between king and man: {similarity_km}')
`
1.2 Word Analogy Tasks
Word analogy tasks evaluate embeddings based on their ability to solve analogies such as “king - man + woman = queen.” The goal is to find a word vector that approximates this equation.Example
Using the analogy formula:`python
Compute the analogy vector
analogy_vector = king - man + womanFind the closest word vector to the analogy_vector
This can be done using cosine similarity to all other word vectors in the vocabulary.
`2. Extrinsic Evaluation Metrics
Extrinsic evaluation metrics assess embeddings based on their performance in downstream tasks, such as text classification, sentiment analysis, or clustering.2.1 Classification Accuracy
One way to evaluate embeddings is by measuring their performance in a classification task. For example, using embeddings as features in a supervised learning model.Example
1. Train a classifier using embeddings as input. 2. Measure the accuracy on the test set.2.2 Clustering
Embedding quality can also be evaluated by clustering similar words together. Metrics like Silhouette Score can be used to measure how well-separated the clusters of words are.Example
Using k-means clustering:`python
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_scoreAssume word_vectors is a matrix of word embeddings
kmeans = KMeans(n_clusters=10) clusters = kmeans.fit_predict(word_vectors)Evaluate clustering
silhouette_avg = silhouette_score(word_vectors, clusters) print(f'Silhouette Score: {silhouette_avg}')`