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| wn.ic | ||
| ===== | ||
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| .. automodule:: wn.ic | ||
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| The mathematical formulae for information content are defined in | ||
| `Formal Description`_, and the corresponding Python API function are | ||
| described in `Calculating Information Content`_. These functions | ||
| require information content weights obtained either by `computing them | ||
| from a corpus <Computing Corpus Weights_>`_, or by `loading | ||
| pre-computed weights from a file <Reading Pre-computed Information | ||
| Content Files_>`_. | ||
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| .. note:: | ||
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| The term *information content* can be ambiguous. It often, and most | ||
| accurately, refers to the result of the :func:`information_content` | ||
| function (:math:`\text{IC}(c)` in the mathematical notation), but | ||
| is also sometimes used to refer to the corpus frequencies/weights | ||
| (:math:`\text{freq}(c)` in the mathematical notation) returned by | ||
| :func:`load` or :func:`compute`, as these weights are the basis of | ||
| the value computed by :func:`information_content`. The Wn | ||
| documentation tries to consistently refer to former as the | ||
| *information content value*, or just *information content*, and the | ||
| latter as *information content weights*, or *weights*. | ||
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| Formal Description | ||
| ------------------ | ||
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| The Information Content (IC) of a concept (synset) is a measure of its | ||
| specificity computed from the wordnet's taxonomy structure and corpus | ||
| frequencies. It is defined by Resnik 1995 ([RES95]_), following | ||
| information theory, as the negative log-probability of a concept: | ||
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| .. math:: | ||
| \text{IC}(c) = -\log{p(c)} | ||
| A concept's probability is the empirical probability over a corpus: | ||
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| .. math:: | ||
| p(c) = \frac{\text{freq}(c)}{N} | ||
| Here, :math:`N` is the total count of words of the same category as | ||
| concept :math:`c` ([RES95]_ only considered nouns) where each word has | ||
| some representation in the wordnet, and :math:`\text{freq}` is defined | ||
| as the sum of corpus counts of words in :math:`\text{words}(c)`, which | ||
| is the set of words subsumed by concept :math:`c`: | ||
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| .. math:: | ||
| \text{freq}(c) = \sum_{w \in \text{words}(c)}{\text{count}(w)} | ||
| It is common for :math:`\text{freq}` to not contain actual frequencies | ||
| but instead weights distributed evenly among the synsets for a | ||
| word. These weights are calculated as the word frequency divided by | ||
| the number of synsets for the word: | ||
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| .. math:: | ||
| \text{freq}_{\text{distributed}}(c) | ||
| = \sum_{w \in \text{words}(c)}{\frac{\text{count}(w)}{|\text{synsets}(w)|}} | ||
| .. [RES95] Resnik, Philip. "Using information content to evaluate | ||
| semantic similarity." In Proceedings of the 14th International | ||
| Joint Conference on Artificial Intelligence (IJCAI-95), Montreal, | ||
| Canada, pp. 448-453. 1995. | ||
| Example | ||
| ------- | ||
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| In the Princeton WordNet, the frequency of a concept like **stone | ||
| fruit** is not the number of occurrences of *stone fruit*, but also | ||
| includes the counts of the words for its hyponyms (*almond*, *olive*, | ||
| etc.) and other taxonomic descendants (*Jordan almond*, *green olive*, | ||
| etc.). The word *almond* has two synsets: one for the fruit or nut, | ||
| another for the plant. Thus, if the word *almond* is encountered | ||
| :math:`n` times in a corpus, then the weight (either the frequency | ||
| :math:`n` or distributed weight :math:`\frac{n}{2}`) is added to the | ||
| total weights for both synsets and to those of their ancestors, but | ||
| not for descendant synsets, such as for **Jordan almond**. The fruit/nut | ||
| synset of almond has two hypernym paths which converge on **fruit**: | ||
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| 1. **almond** ⊃ **stone fruit** ⊃ **fruit** | ||
| 2. **almond** ⊃ **nut** ⊃ **seed** ⊃ **fruit** | ||
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| The weight is added to each ancestor (**stone fruit**, **nut**, | ||
| **seed**, **fruit**, ...) once. That is, the weight is not added to | ||
| the convergent ancestor for **fruit** twice, but only once. | ||
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| Calculating Information Content | ||
| ------------------------------- | ||
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| .. autofunction:: information_content | ||
| .. autofunction:: synset_probability | ||
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| Computing Corpus Weights | ||
| ------------------------ | ||
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| If pre-computed weights are not available for a wordnet or for some | ||
| domain, they can be computed given a corpus and a wordnet. | ||
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| The corpus is an iterable of words. For large corpora it may help to | ||
| use a generator for this iterable, but the entire vocabulary (i.e., | ||
| unique words and counts) will be held at once in memory. Multi-word | ||
| expressions are also possible if they exist in the wordnet. For | ||
| instance, the Princeton WordNet has *stone fruit*, with a single space | ||
| delimiting the words, as an entry. | ||
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| The :class:`wn.Wordnet` object must be instantiated with a single | ||
| lexicon, although it may have expand-lexicons for relation | ||
| traversal. For best results, the wordnet should use a lemmatizer to | ||
| help it deal with inflected wordforms from running text. | ||
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| .. autofunction:: compute | ||
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| Reading Pre-computed Information Content Files | ||
| ---------------------------------------------- | ||
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| The :func:`load` function reads pre-computed information content | ||
| weights files as used by the `WordNet::Similarity | ||
| <http://wn-similarity.sourceforge.net/>`_ Perl module or the `NLTK | ||
| <http://www.nltk.org/>`_ Python package. These files are computed for | ||
| a specific version of a wordnet using the synset offsets from the | ||
| `WNDB <https://wordnet.princeton.edu/documentation/wndb5wn>`_ format, | ||
| which Wn does not use. These offsets therefore must be converted into | ||
| an identifier that matches those used by the wordnet. By default, | ||
| :func:`load` uses the lexicon identifier from its *wordnet* argument | ||
| with synset offsets (padded with 0s to make 8 digits) and | ||
| parts-of-speech from the weights file to format an identifier, such as | ||
| ``pwn-00001174-n``. For wordnets that use a different identifier | ||
| scheme, the *get_synset_id* parameter of :func:`load` can be given a | ||
| callable created with :func:`wn.util.synset_id_formatter`. It can also | ||
| be given another callable with the same signature as shown below: | ||
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| .. code-block:: python | ||
| get_synset_id(*, offset: int, pos: str) -> str | ||
| .. warning:: | ||
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| The weights files are only valid for the version of wordnet for | ||
| which they were created. Files created for the Princeton WordNet | ||
| 3.0 do not work for the Princeton WordNet 3.1 because the offsets | ||
| used in its identifiers are different, although the *get_synset_id* | ||
| parameter of :func:`load` could be given a function that performs a | ||
| suitable mapping. Some `Open Multilingual Wordnet | ||
| <https://github.com/globalwordnet/OMW>`_ wordnets use the Princeton | ||
| WordNet 3.0 offsets in their identifiers and can therefore | ||
| technically use the weights, but this usage is discouraged because | ||
| the distributional properties of text in another language and the | ||
| structure of the other wordnet will not be compatible with that of | ||
| the Princeton WordNet. For these cases, it is recommended to | ||
| compute new weights using :func:`compute`. | ||
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| .. autofunction:: load |
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