The Luhn algorithm is a text summarization technique that uses statistical properties of the text to identify and extract the most important sentences from a document. The algorithm was developed by H.P. Luhn in the 1950s, and is still widely used in various forms today.
The Luhn algorithm works by first analyzing the frequency of each word in the document, and then assigning a score to each sentence based on the frequency of the words it contains. Sentences that contain words that are more frequent in the document as a whole are considered to be more important, and are assigned higher scores. The algorithm then selects the top-scoring sentences and concatenates them together to form the summary. The length of the summary is usually determined in advance by the user, and the algorithm selects the most important sentences that fit within that length limit.
It works by identifying the most salient or important sentences in a document based on the frequency of important words and their distribution within each sentence. First, the algorithm removes stopwords, which are common words such as “the”, “and”, and “a” that do not carry much meaning. Additionally, one could apply stemming, which reduces words to their base or root form. For example, “likes” and “liked” are reduced to “like”. Then, the algorithm looks for important words in each sentence. These are typically nouns, verbs, and adjectives that carry the most meaning. The specific method for identifying important words may vary depending on the implementation of the algorithm, but in general, they are selected based on their frequency and relevance to the topic of the text.
The algorithm counts the number of important words in each sentence and divides it by the span, or the distance between the first and last occurrence of an important word. This gives a measure of how densely the important words are distributed within the sentence. Finally, the algorithm ranks the sentences based on their scores, with the highest scoring sentences considered the most important and selected for the summary.
Here are the step-by-step instructions for the Luhn algorithm:
- Preprocess the text: Remove any stop words, punctuation, and other non-textual elements from the document, and convert all the remaining words to lowercase.
- Calculate the word frequency: Count the number of occurrences of each word in the document, and store this information in a frequency table.
- For each sentence, calculate the score by:
a. Identifying the significant words (excluding stop words) that occur in the sentence.
b. Ordering the significant words by their position in the sentence.
c. Determining the distance between adjacent significant words (the “span”).
d. Calculating a score for the sentence as the sum of the square of the number of significant words divided by the span for each adjacent pair of significant words.
- Select the top-scoring sentences: Sort the sentences in the document by their score, and select the top-scoring sentences up to a maximum length L. The length L is typically chosen by the user in advance, and represents the maximum number of words or sentences that the summary can contain.
- Generate the summary: Concatenate the selected sentences together to form the summary.
Below I summarize the topic of fructose malabsorption by generating a summary using the Luhn algorithm. To create the summary, I selected several articles from sources like Wikipedia and PubMed. The important words were selected based on their total frequency in all of the text. I chose the top 25 words to focus on, and then used the algorithm to identify the most important sentences based on the frequency and distribution of these words. The summary was generated using the top 15 sentences.
Symptoms and signs of Fructose malabsorption may cause gastrointestinal symptoms such as abdominal pain, bloating, flatulence or diarrhea. Although often assumed to be an acceptable alternative to wheat, spelt flour is not suitable for people with fructose malabsorption, just as it is not appropriate for those with wheat allergies or celiac disease. However, fructose malabsorbers do not need to avoid gluten, as those with celiac disease must. Many fructose malabsorbers can eat breads made from rye and corn flour. This can cause some surprises and pitfalls for fructose malabsorbers. Foods (such as bread) marked “gluten-free” are usually suitable for fructose malabsorbers, though they need to be careful of gluten-free foods that contain dried fruit or high fructose corn syrup or fructose itself in sugar form. Food-labeling Producers of processed food in most or all countries, including the US, are not currently required by law to mark foods containing “fructose in excess of glucose”.
Stone fruit: apricot, nectarine, peach, plum (caution – these fruits contain sorbitol);Berry fruit: blackberry, boysenberry, cranberry, raspberry, strawberry, loganberry; Citrus fruit: kumquat, grapefruit, lemon, lime, mandarin, orange, tangelo; Other fruits: ripe banana, jackfruit, passion fruit, pineapple, rhubarb, tamarillo.
The fructose and glucose contents of foods listed on the Australian food standards would appear to indicate that most of the listed foods have higher fructose levels.
Glucose enhances absorption of fructose, so fructose from foods with fructose-to-glucose ratio <1, like white potatoes, are readily absorbed, whereas foods with fructose-to-glucose ratio >1, like apples and pears, are often problematic regardless of the total amount of fructose in the food.
Foods with high fructose-to-glucose ratio.
Dietary supplements of xylose isomerase may improve some symptoms of fructose malabsorption, although there is currently only a single scientific study available.
This can lead to issues such as bloating, heartburn and constipation.
It is called a hydrogen breath test and is the method currently used for a clinical diagnosis.
People with fructose malabsorption absorb less than 25 g per sitting.
Fructose malabsorption should be considered in patients with symptoms of depression and disturbances of tryptophan metabolism. This prospective cross-sectional study aimed to investigate the potential association between primary-adult lactose malabsorption, fructose malabsorption, tryptophan (TRP) metabolism and the presence of depressive signs.
High intestinal fructose concentration seems to interfere with L-tryptophan metabolism, and it may reduce availability of tryptophan for the biosynthesis of serotonin (5-hydroxytryptamine).
After obtaining the top sentences above, I used them as input into ChatGPT to generate another summary. The summary ended up with some mistakes, such as “People with this condition should avoid foods like spelt flour that contain fructose.“, as spelt does not contain fructose, it contains fructans. But it was still a fun exercise.
Fructose malabsorption can cause gastrointestinal symptoms such as abdominal pain, bloating, flatulence, and diarrhea. People with this condition should avoid foods like spelt flour that contain fructose. However, they do not need to avoid gluten, and many can eat breads made from rye and corn flour. Foods marked “gluten-free” are generally suitable for fructose malabsorbers, but they need to be careful of gluten-free foods that contain dried fruit or high fructose corn syrup. Certain fruits such as apricots, nectarines, peaches, and plums can cause issues due to their sorbitol content. The fructose-to-glucose ratio of foods can also play a role in absorption, with foods with a higher ratio often being problematic. A hydrogen breath test is used for clinical diagnosis, and dietary supplements of xylose isomerase may help with symptoms. Fructose malabsorption may also be associated with depressive signs due to the interference with L-tryptophan metabolism.