Sure, let's break down the concepts of TF-IDF, cosine similarity, and top-ranked documents:
1. TF-IDF (Term Frequency-Inverse Document Frequency):
TF-IDF is a numerical statistic used to evaluate the importance of a term (word) within a collection of documents (corpus). It is widely used in information retrieval and text mining. TF-IDF consists of two main components:
Term Frequency (TF): This measures the frequency of a term in a document. It quantifies how often a term appears in a document. A higher TF indicates that a term is more important in a document.
Inverse Document Frequency (IDF): This measures the importance of a term in the entire corpus. It quantifies how unique or rare a term is across the entire collection of documents. A higher IDF indicates that a term is less common and potentially more significant.
The TF-IDF score for a term in a document is calculated by multiplying its TF by its IDF. The goal is to assign higher scores to terms that are frequent within a document but rare across the entire corpus, as these terms are likely to be more informative.
2. Cosine Similarity:
Cosine similarity is a measure of similarity between two non-zero vectors in an inner product space. In the context of information retrieval and text analysis, cosine similarity is often used to determine how similar two documents are based on the angle between their TF-IDF vectors.
The cosine similarity between two vectors A and B is calculated as:
[ \text{Cosine Similarity}(A, B) = \frac{A \cdot B}{|A| |B|} ]
Where:
- A and B are the TF-IDF vectors of two documents or text samples.
- (A \cdot B) is the dot product of the vectors A and B.
- (|A|) and (|B|) are the Euclidean norms (lengths) of the vectors A and B, respectively.
Cosine similarity ranges from -1 (completely dissimilar) to 1 (completely similar). A value of 0 indicates no similarity.
Cosine similarity is commonly used in document retrieval and recommendation systems to find documents or items that are most similar to a query or reference document. In your case, it was used to rank documents based on their similarity to a query.
3. Top-Ranked Documents:
Top-ranked documents are the documents that receive the highest scores when ranked according to a similarity measure, such as cosine similarity. In the context of your previous question, you had a query ("The early bird gets the worm") and a collection of documents (D1, D2, D3, D4, D5). By calculating the TF-IDF vectors for the query and each document and then computing cosine similarities between the query and each document, you ranked the documents based on their relevance to the query.
The top-ranked documents are the ones with the highest cosine similarity scores to the query. These documents are considered the most relevant or similar to the query based on the TF-IDF and cosine similarity measure. In your case, D3 and D5 were identified as the top-ranked documents for the given query.