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559 lines
22 KiB
Plaintext
559 lines
22 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"![](images/EscUpmPolit_p.gif \"UPM\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Course Notes for Learning Intelligent Systems"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Department of Telematic Engineering Systems, Universidad Politécnica de Madrid, © Carlos A. Iglesias"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Vector Representation"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Table of Contents\n",
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"* [Objectives](#Objectives)\n",
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"* [Tools](#Tools)\n",
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"* [Vector representation: Count vector](#Vector-representation:-Count-vector)\n",
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"* [Binary vectors](#Binary-vectors)\n",
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"* [Bigram vectors](#Bigram-vectors)\n",
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"* [Tf-idf vector representation](#Tf-idf-vector-representation)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Objectives"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"In this notebook we are going to transform text into feature vectors, using several representations as presented in class.\n",
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"\n",
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"We are going to use the examples from the slides."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"doc1 = 'Summer is coming but Summer is short'\n",
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"doc2 = 'I like the Summer and I like the Winter'\n",
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"doc3 = 'I like sandwiches and I like the Winter'\n",
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"documents = [doc1, doc2, doc3]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Tools"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The different tools we have presented so far (NLTK, Scikit-Learn, TextBlob and CLiPS) provide overlapping functionalities for obtaining vector representations and apply machine learning algorithms.\n",
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"\n",
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"We are going to focus on the use of scikit-learn so that we can also use easily Pandas as we saw in the previous topic.\n",
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"\n",
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"Scikit-learn provides specific facililities for processing texts, as described in the [manual](http://scikit-learn.org/stable/modules/feature_extraction.html)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Vector representation: Count vector"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Scikit-learn provides two classes for binary vectors: [CountVectorizer](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.CountVectorizer.html#sklearn.feature_extraction.text.CountVectorizer) and [HashingVectorizer](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.HashingVectorizer.html). The latter is more efficient but does not allow to understand which features are more important, so we use the first class. Nevertheless, they are compatible, so, they can be interchanged for production environments.\n",
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"\n",
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"The first step for vectorizing with scikit-learn is creating a CountVectorizer object and then we should call 'fit_transform' to fit the vocabulary."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>CountVectorizer(max_features=5000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">CountVectorizer</label><div class=\"sk-toggleable__content\"><pre>CountVectorizer(max_features=5000)</pre></div></div></div></div></div>"
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],
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"text/plain": [
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"CountVectorizer(max_features=5000)"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"from sklearn.feature_extraction.text import CountVectorizer\n",
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"\n",
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"vectorizer = CountVectorizer(analyzer = \"word\", max_features = 5000) \n",
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"vectorizer"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"As we can see, [CountVectorizer](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.CountVectorizer.html#sklearn.feature_extraction.text.CountVectorizer) comes with many options. We can define many configuration options, such as the maximum or minimum frequency of a term (*min_fd*, *max_df*), maximum number of features (*max_features*), if we analyze words or characters (*analyzer*), or if the output is binary or not (*binary*). *CountVectorizer* also allows us to include if we want to preprocess the input (*preprocessor*) before tokenizing it (*tokenizer*) and exclude stop words (*stop_words*).\n",
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"\n",
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"We can use NLTK preprocessing and tokenizer functions to tune *CountVectorizer* using these parameters.\n",
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"\n",
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"We are going to see how the vectors look like."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<3x10 sparse matrix of type '<class 'numpy.int64'>'\n",
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"\twith 15 stored elements in Compressed Sparse Row format>"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"vectors = vectorizer.fit_transform(documents)\n",
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"vectors"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We see the vectors are stored as a sparse matrix of 3x6 dimensions.\n",
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"We can print the matrix as well as the feature names."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[0 1 1 2 0 0 1 2 0 0]\n",
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" [1 0 0 0 2 0 0 1 2 1]\n",
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" [1 0 0 0 2 1 0 0 1 1]]\n",
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"['and' 'but' 'coming' 'is' 'like' 'sandwiches' 'short' 'summer' 'the'\n",
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" 'winter']\n"
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]
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}
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],
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"source": [
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"print(vectors.toarray())\n",
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"print(vectorizer.get_feature_names_out())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"As you can see, the pronoun 'I' has been removed because of the default token_pattern. \n",
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"We can change this as follows."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array(['and', 'but', 'coming', 'i', 'is', 'like', 'sandwiches', 'short',\n",
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" 'summer', 'the', 'winter'], dtype=object)"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"vectorizer = CountVectorizer(analyzer=\"word\", stop_words=None, token_pattern='(?u)\\\\b\\\\w+\\\\b') \n",
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"vectors = vectorizer.fit_transform(documents)\n",
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"vectorizer.get_feature_names_out()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We can now filter the stop words (it will remove 'and', 'but', 'I', 'is' and 'the')."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/home/cif/anaconda3/lib/python3.10/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function get_feature_names is deprecated; get_feature_names is deprecated in 1.0 and will be removed in 1.2. Please use get_feature_names_out instead.\n",
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" warnings.warn(msg, category=FutureWarning)\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"['coming', 'like', 'sandwiches', 'short', 'summer', 'winter']"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"vectorizer = CountVectorizer(analyzer=\"word\", stop_words='english', token_pattern='(?u)\\\\b\\\\w+\\\\b') \n",
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"vectors = vectorizer.fit_transform(documents)\n",
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"vectorizer.get_feature_names_out()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"frozenset({'or', 'be', 'least', 'ours', 'very', 'noone', 'more', 'can', 'front', 'last', 'co', 'where', 'beyond', 'you', 'was', 'to', 'nine', 'here', 'describe', 'than', 'rather', 'therefore', 'except', 'at', 'again', 'ourselves', 'most', 'anyway', 'thick', 'whither', 'thereupon', 'someone', 'hereupon', 'besides', 'among', 'hasnt', 'across', 'namely', 'because', 'is', 'out', 'same', 'yourself', 'somehow', 'sincere', 'con', 'hereby', 'towards', 'interest', 'much', 'up', 'why', 'myself', 'all', 'nobody', 'though', 'every', 'show', 'not', 'there', 'whether', 'still', 'name', 'when', 'the', 'each', 'six', 'nor', 'and', 'under', 'thereby', 'less', 'either', 'thence', 'into', 'seemed', 'something', 'four', 'sometimes', 'himself', 'those', 'nowhere', 'almost', 'are', 'empty', 'must', 'while', 'afterwards', 'perhaps', 'from', 'detail', 'through', 'any', 'have', 'may', 'he', 'anywhere', 'alone', 'without', 'beforehand', 'had', 'too', 'yourselves', 'our', 'see', 'how', 'please', 'what', 'am', 'do', 'it', 'serious', 'yet', 'down', 'top', 'amount', 'then', 'both', 'fire', 'been', 'wherein', 'done', 'etc', 'whose', 'whereafter', 'who', 'ltd', 'meanwhile', 'further', 'few', 'first', 'behind', 'made', 'yours', 'until', 'toward', 'amoungst', 'anyhow', 'we', 'with', 'give', 'go', 'no', 'back', 'else', 'becomes', 'your', 'fill', 'together', 'another', 'throughout', 'onto', 'de', 'me', 'ten', 'system', 'became', 'per', 'therein', 'everyone', 'often', 'ie', 'put', 'hers', 'herself', 'nevertheless', 'itself', 'eg', 'herein', 'his', 'this', 'cry', 'due', 'bill', 'one', 'on', 'being', 'themselves', 'of', 'some', 'their', 'neither', 'elsewhere', 'since', 'whole', 'eight', 'i', 'a', 'whoever', 'own', 'call', 'them', 'mostly', 'she', 'my', 'cannot', 'us', 'never', 'as', 'thin', 'upon', 'cant', 'un', 'before', 'her', 'otherwise', 'full', 'these', 'next', 'they', 'side', 'somewhere', 'fifty', 'hence', 'so', 'along', 'already', 'three', 'latter', 'anything', 'whom', 'could', 'indeed', 'nothing', 'whereby', 'which', 'sometime', 'become', 'ever', 'amongst', 'by', 'in', 'five', 'after', 'mine', 'fifteen', 'wherever', 'found', 'thereafter', 'third', 'keep', 'anyone', 'will', 'bottom', 'off', 'seem', 'none', 'an', 'whatever', 'over', 'during', 'also', 'latterly', 'via', 'take', 'former', 'above', 'now', 'becoming', 'hereafter', 'such', 'two', 'only', 'about', 'sixty', 're', 'everything', 'others', 'hundred', 'twelve', 'thus', 'even', 'well', 'always', 'once', 'beside', 'get', 'mill', 'seems', 'if', 'whereupon', 'find', 'forty', 'inc', 'whenever', 'around', 'other', 'should', 'many', 'enough', 'however', 'move', 'against', 'several', 'everywhere', 'has', 'whereas', 'that', 'whence', 'eleven', 'its', 'within', 'twenty', 'part', 'although', 'thru', 'couldnt', 'moreover', 'him', 'formerly', 'might', 'seeming', 'but', 'below', 'would', 'between', 'were', 'for'})\n"
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]
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}
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],
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"source": [
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"#stop words in scikit-learn for English\n",
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"print(vectorizer.get_stop_words())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Vectors\n",
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"f_array = vectors.toarray()\n",
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"f_array"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We can compute now the **distance** between vectors."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from scipy.spatial.distance import cosine\n",
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"d12 = cosine(f_array[0], f_array[1])\n",
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"d13 = cosine(f_array[0], f_array[2])\n",
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"d23 = cosine(f_array[1], f_array[2])\n",
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"print(d12, d13, d23)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Binary vectors"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We can also get **binary vectors** as follows."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"vectorizer = CountVectorizer(analyzer=\"word\", stop_words='english', binary=True) \n",
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"vectors = vectorizer.fit_transform(documents)\n",
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"vectorizer.get_feature_names()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"vectors.toarray()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Bigram vectors"
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]
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},
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{
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"cell_type": "markdown",
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|
"metadata": {},
|
|
"source": [
|
|
"It is also easy to get bigram vectors."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"vectorizer = CountVectorizer(analyzer=\"word\", stop_words='english', ngram_range=[2,2]) \n",
|
|
"vectors = vectorizer.fit_transform(documents)\n",
|
|
"vectorizer.get_feature_names()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"vectors.toarray()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Tf-idf vector representation"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Finally, we can also get a tf-idf vector representation using the class [TfidfVectorizer](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html#sklearn.feature_extraction.text.TfidfVectorizer) instead of CountVectorizer."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from sklearn.feature_extraction.text import TfidfVectorizer\n",
|
|
"\n",
|
|
"vectorizer = TfidfVectorizer(analyzer=\"word\", stop_words='english')\n",
|
|
"vectors = vectorizer.fit_transform(documents)\n",
|
|
"vectorizer.get_feature_names()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"vectors.toarray()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We can now compute the similarity of a query and a set of documents as follows."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"train = [doc1, doc2, doc3]\n",
|
|
"vectorizer = TfidfVectorizer(analyzer=\"word\", stop_words='english')\n",
|
|
"\n",
|
|
"# We learn the vocabulary (fit) and tranform the docs into vectors\n",
|
|
"vectors = vectorizer.fit_transform(train)\n",
|
|
"vectorizer.get_feature_names()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"vectors.toarray()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Scikit-learn provides a method to calculate the cosine similarity between one vector and a set of vectors. Based on this, we can rank the similarity. In this case, the ranking for the query is [d1, d2, d3]."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from sklearn.metrics.pairwise import cosine_similarity\n",
|
|
"\n",
|
|
"query = ['winter short']\n",
|
|
"\n",
|
|
"# We transform the query into a vector of the learnt vocabulary\n",
|
|
"vector_query = vectorizer.transform(query)\n",
|
|
"\n",
|
|
"# Here we calculate the distance of the query to the docs\n",
|
|
"cosine_similarity(vector_query, vectors)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The same result can be obtained with pairwise metrics (kernels in ML terminology) if we use the linear kernel."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from sklearn.metrics.pairwise import linear_kernel\n",
|
|
"cosine_similarity = linear_kernel(vector_query, vectors).flatten()\n",
|
|
"cosine_similarity"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## References\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"* [Scikit-learn](http://scikit-learn.org/stable/datasets/twenty_newsgroups.html#converting-text-to-vectors) Scikit-learn Convert Text to Vectors"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Licence"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The notebook is freely licensed under under the [Creative Commons Attribution Share-Alike license](https://creativecommons.org/licenses/by/2.0/). \n",
|
|
"\n",
|
|
"© Carlos A. Iglesias, Universidad Politécnica de Madrid."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
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},
|
|
"language_info": {
|
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"codemirror_mode": {
|
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
|
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"mimetype": "text/x-python",
|
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"name": "python",
|
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"nbconvert_exporter": "python",
|
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"pygments_lexer": "ipython3",
|
|
"version": "3.10.10"
|
|
},
|
|
"latex_envs": {
|
|
"LaTeX_envs_menu_present": true,
|
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"autocomplete": true,
|
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"bibliofile": "biblio.bib",
|
|
"cite_by": "apalike",
|
|
"current_citInitial": 1,
|
|
"eqLabelWithNumbers": true,
|
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"eqNumInitial": 1,
|
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"hotkeys": {
|
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"equation": "Ctrl-E",
|
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"itemize": "Ctrl-I"
|
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},
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"labels_anchors": false,
|
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|
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"report_style_numbering": false,
|
|
"user_envs_cfg": false
|
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}
|
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|
|
"nbformat": 4,
|
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"nbformat_minor": 1
|
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