# Latent Semantic Analysis: intuition, math, implementation (2023)

## How do we extract themes and topic from text using unsupervised learning

TL;DR — Text data suffers heavily from high-dimensionality. Latent Semantic Analysis (LSA) is a popular, dimensionality-reduction techniques that follows the same method as Singular Value Decomposition. LSA ultimately reformulates text data in terms of r latent (i.e. hidden) features, where r is less than m, the number of terms in the data. I’ll explain the conceptual and mathematical intuition and run a basic implementation in Scikit-Learn using the 20 newsgroups dataset.

Language is more than the collection of words in front of you. When you read a text your mind conjures up images and notions. When you read many texts, themes begin to emerge, even if they’re never stated explicitly. Our innate ability to understand and process language defies an algorithmic expression (for the moment). LSA is one of the most popular Natural Language Processing (NLP) techniques for trying to determine themes within text mathematically. LSA is an unsupervised learning technique that rests on two pillars:

• The distributional hypothesis, which states that words with similar meanings appear frequently together. This is best summarised by JR Firth’s quote “You shall know a word by the company it keeps” [1, p106]
• Singular Value Decomposition (SVD — Figure 1) a mathematical technique that we’ll be looking at in greater depth.

Note that LSA is an unsupervised learning technique — there is no ground truth. The latent concepts might or might not be there! In the dataset we’ll use later we know there are 20 news categories and we can perform classification on them, but that’s only for illustrative purposes. It’ll often be the case that we’ll use LSA on unstructured, unlabelled data.

Like all Machine Learning concepts, LSA can be broken down into 3 parts: the intuition, the maths and the code. Feel free to use the links in Contents to skip to the part most relevant to you. The full code is available in this Github repo.

A note on terminology: generally when decomposition of this kind is done on text data, the terms SVD and LSA (or LSI) are used interchangeably. From now on I’ll be using LSA, for simplicity’s sake.

This article assumes some understanding of basic NLP preprocessing and of word vectorisation (specifically tf-idf vectorisation).

## Contents:

1. Intuition: explanation with political news topics
2. The Math: SVD as a weighted, ordered sum of matrices or as a set of 3 linear transformations
3. The code implementation: in Python3 with Scikit-Learn and 20Newsgroups data
4. References

In simple terms: LSA takes meaningful text documents and recreates them in n different parts where each part expresses a different way of looking at meaning in the text. If you imagine the text data as a an idea, there would be n different ways of looking at that idea, or n different ways of conceptualising the whole text. LSA reduces our table of data to a table of latent (hidden) concepts.

Suppose that we have some table of data, in this case text data, where each row is one document, and each column represents a term (which can be a word or a group of words, like “baker’s dozen” or “Downing Street”). This is the standard way to represent text data (in a document-term matrix, as shown in Figure 2). The numbers in the table reflect how important that word is in the document. If the number is zero then that word simply doesn’t appear in that document.

Different documents will be about different topics. Let’s say all the documents are politics articles and there are 3 topics: foreign policy (F.P.), elections and reform.

Let’s say that there are articles strongly belonging to each category, some that are in two and some that belong to all 3 categories. We could plot a table where each row is a different document (a news article) and each column is a different topic. In the cells we would have a different numbers that indicated how strongly that document belonged to the particular topic (see Figure 3).

Now if we shift our attention conceptually to the topics themselves, we should ask ourselves the following question: do we expect certain words to turn up more often in either of these topics?

If we’re looking at foreign policy, we might see terms like “Middle East”, “EU”, “embassies”. For elections it might be “ballot”, “candidates”, “party”; and for reform we might see “bill”, “amendment” or “corruption”. So, if we plotted these topics and these terms in a different table, where the rows are the terms, we would see scores plotted for each term according to which topic it most strongly belonged. Naturally there will be terms that feature in all three documents (“prime minister”, “Parliament”, “decision”) and these terms will have scores across all 3 columns that reflect how much they belong to either category — the higher the number, the greater its affiliation to that topic. So, our second table (Figure 4) consists of terms and topics.

Now the last component is a bit trickier to explain as a table. It’s actually a set of numbers, one for each of our topics. What do the numbers represent? They represent how much each of the topics explains our data.

How do they “explain” the data? Well, suppose that actually, “reform” wasn’t really a salient topic across our articles, and the majority of the articles fit in far more comfortably in the “foreign policy” and “elections”. Thus “reform” would get a really low number in this set, lower than the other two. An alternative is that maybe all three numbers are actually quite low and we actually should have had four or more topics — we find out later that a lot of our articles were actually concerned with economics! By sticking to just three topics we’ve been denying ourselves the chance to get a more detailed and precise look at our data. The technical name for this array of numbers is the “singular values”.

So that’s the intuition so far. You’ll notice that our two tables have one thing in common (the documents / articles) and all three of them have one thing in common — the topics, or some representation of them.

Now let’s explain how this is a dimensionality reduction technique. It’s easier to see the merits if we specify a number of documents and topics. Suppose we had 100 articles and 10,000 different terms (just think of how many unique words there would be all those articles, from “amendment” to “zealous”!). In our original document-term matrix that’s 100 rows and 10,000 columns. When we start to break our data down into the 3 components, we can actually choose the number of topics — we could choose to have 10,000 different topics, if we genuinely thought that was reasonable. However, we could probably represent the data with far fewer topics, let’s say the 3 we originally talked about. That means that in our document-topic table, we’d slash about 99,997 columns, and in our term-topic table, we’d do the same. The columns and rows we’re discarding from our tables are shown as hashed rectangles in Figure 6. M is the original document-term table; U is the document-topic table, 𝚺 (sigma) is the array of singular values and V-transpose (the superscript T means that the original matrix T has been flipped along its diagonal) is the document-topic table, but flipped on its diagonal (I’ll explain why in the math section).

As for the set of numbers denoting topic importance, from a set of 10,000 numbers, each number getting smaller and smaller as it corresponds to a less important topic, we cut down to only 3 numbers, for our 3 remaining topics. This is why the Python implementation for LSA is called Truncated SVD by the way: we’re cutting off part of our table, but we’ll get to the code later. It’s also worth noting that we don’t know what the 3 topics are in advance, we merely hypothesised that there would be 3 and, once we’ve gotten our components, we can explore them and see what the terms are.

Of course, we don’t just want to return to the original dataset: we now have 3 lower-dimensional components we can use. In the code and maths parts we’ll go through which one we actually take forward. In brief, once we’ve truncated the tables (matrices), the product we’ll be getting out is the document-topic table (U) times the singular values (𝚺). This can be interpreted as the documents (all our news articles) along with how much they belong to each topic then weighted by the relative importance of each topic. You’ll notice that in that case something’s been left out of this final table — the words. Yes, we’ve gone beyond the words, we’re discarding them but keeping the themes, which is a much more compact way to express our text.

(Video) Intro to Latent Semantic Analysis -1 | LSA | NLP | LearnAI

For the maths, I’ll be going through two different interpretations of SVD: first the general geometric decomposition that you can use with a real square matrix M and second the separable-models decomposition which is more pertinent to our example. SVD is also used in model-based recommendation systems. It is very similar to Principal Component Analysis (PCA), but it operates better on sparse data than PCA does (and text data is almost always sparse). Whereas PCA performs decomposition on the correlation matrix of a dataset, SVD/LSA performs decomposition directly on the dataset as it is.

We will be factorising this matrix into constituent matrices. When I say factorising this is essentially the same as when we’re taking a number and representing it its factors, which when multiplied together, give us the original number, e.g. A = B * C * D .

This is also why it’s called Singular Value Decomposition — we’re decomposing it into its constituent parts.

## General geometric decomposition

The extra dimension that wasn’t available to us in our original matrix, the r dimension, is the amount of latent concepts. Generally we’re trying to represent our matrix as other matrices that have one of their axes being this set of components. You will also note that, based on dimensions, the multiplication of the 3 matrices (when V is transposed) will lead us back to the shape of our original matrix, the r dimension effectively disappearing.

What matters in understanding the math is not the algebraic algorithm by which each number in U, V and 𝚺 is determined, but the mathematical properties of these products and how they relate to each other.

First of all, it’s important to consider first what a matrix actually is and what it can be thought of — a transformation of vector space. In the top left corner of Figure 7 we have two perpendicular vectors. If we have only two variables to start with then the feature space (the data that we’re looking at) can be plotted anywhere in this space that is described by these two basis vectors. Now moving to the right in our diagram, the matrix M is applied to this vector space and this transforms it into the new, transformed space in our top right corner. In the diagram below the geometric effect of M would be referred to as “shearing” the vector space; the two vectors 𝝈1 and 𝝈2 are actually our singular values plotted in this space.

Now, just like with geometric transformations of points that you may remember from school, we can reconsider this transformation M as three separate transformations:

1. The rotation (or reflection) caused by V*. Note that V* = V-transpose as V is a real unitary matrix, so the complex conjugate of V is the same as its transpose. In vector terms, the transformation by V or V* keeps the length of the basis vectors the same;
2. 𝚺 has the effect of stretching or compressing all coordinate points along the values of its singular values. Imagine our disc in the bottom left corner as we squeeze it vertically down in the direction of 𝝈2 and stretch it horizontally along the direction of 𝝈1. These two singular values now can be pictured as the major and minor semi-axes of an ellipse. You can of course generalise this to n-dimensions.
3. Lastly, applying U rotates (or reflects) our feature space. We’ve arrived at the same output as a transformation directly from M.

I also recommend the excellent Wikipedia entry on SVD as it has a particularly good explanation and GIF of the process.

So, in other words, where x is any column vector:

One of the properties of the matrices U and V* is that they’re unitary, so we can say that the columns of both of these matrices form two sets of orthonormal basis vectors. In other words, the column vectors you can get from U would form their own coordinate space, such that if there were two columns U1 and U2, you could write out all of the coordinates of the space as combinations of U1 and U2. The same applies to the columns of V, V1 and V2, and this would generalise to n-dimensions (you’d have n-columns).

We can arrive at the same understanding of PCA if we imagine that our matrix M can be broken down into a weighted sum of separable matrices, as shown below.

The matrices 𝐴𝑖 are said to be separable because they can be decomposed into the outer product of two vectors, weighted by the singular value 𝝈i. Calculating the outer product of two vectors with shapes (m,) and (n,) would give us a matrix with a shape (m,n). In other words, every possible product of any two numbers in the two vectors is computed and placed in the new matrix. The singular value not only weights the sum but orders it, since the values are arranged in descending order, so that the first singular value is always the highest one.

In Figure 8 you can see how you could visualise this. Previously we had the tall U, the square Σ and the long 𝑉-transpose matrices. Now you can picture taking the first vertical slice from U, weighting (multiplying) all its values by the first singular value and then, by doing an outer product with the first horizontal slice of 𝑉-transpose, creating a new matrix with the dimensions of those slices. Then we add those products together and we get M. Or, if we don’t do the full sum but only complete it partially, we get the truncated version.

(Video) LSA

So, for our data:

• where M is our original (m, n) data matrix — m rows, n columns; m documents, n terms
• U is a (m, r) matrix — m documents and r concepts
• Σ is a diagonal (r , r) matrix — all values except those in the diagonal are zero. (But what do the non-zero values represent?
• V is a (n, r) matrix — n terms, r concepts

The values in 𝚺 represent how much each latent concept explains the variance in our data. When these are multiplied by the u column vector for that latent concept, it will effectively weigh that vector.

If we were to decompose this to 5 components, this would look something like this:

where there would be originally r number of u vectors; 5 singular values and n number of 𝑣-transpose vectors.

In this last section we’ll see how we can implement basic LSA using Scikit-Learn.

## Extract, Transform and Load our text data

`from sklearn.datasets import fetch_20newsgroupsX_train, y_train = fetch_20newsgroups(subset='train', return_X_y=True)X_test, y_test = fetch_20newsgroups(subset='test', return_X_y=True)`

## Cleaning and Preprocessing

The cleaning of text data is often a very different beast from cleaning of numerical data. You’ll often find yourself having prepared your vectoriser, you model and you’re ready to Gridsearch and then extract features, only to find that the most important features in cluster x is the string “___” … so you go back…and do more cleaning. The code block below came about as a result of me realizing that I needed to remove website URLs, numbers and emails from the dataset.

`from nltk.corpus import stopwordsfrom nltk.tokenize import RegexpTokenizerimport retokenizer = RegexpTokenizer(r'\b\w{3,}\b')stop_words = list(set(stopwords.words("english")))stop_words += list(string.punctuation)stop_words += ['__', '___']# Uncomment and run the 3 lines below if you haven't got these packages already# nltk.download('stopwords')# nltk.download('punkt')# nltk.download('wordnet')def rmv_emails_websites(string): """Function removes emails, websites and numbers""" new_str = re.sub(r"\S+@\S+", '', string) new_str = re.sub(r"\S+.co\S+", '', new_str) new_str = re.sub(r"\S+.ed\S+", '', new_str) new_str = re.sub(r"[0-9]+", '', new_str) return new_strX_train = list(map(rmv_emails_websites, X_train))X_test = list(map(rmv_emails_websites, X_test))`

## Tokenising and vectorising text data

Our models work on numbers, not string! So we tokenise the text (turning all documents into smaller observational entities — in this case words) and then turn them into numbers using Sklearn’s TF-IDF vectoriser. I recommend with any transformation process (especially ones that take time to run) you do them on the first 10 rows of your data and inspect results: are they what you expected to see? Is the shape of the dataframe what you hoped for? Once you’re feeling confident of your code, feed in the whole corpus.

`tfidf = TfidfVectorizer(lowercase=True,  stop_words=stop_words,  tokenizer=tokenizer.tokenize,  max_df=0.2, min_df=0.02 )tfidf_train_sparse = tfidf.fit_transform(X_train)tfidf_train_df = pd.DataFrame(tfidf_train_sparse.toarray(),  columns=tfidf.get_feature_names())tfidf_train_df.head()`

This should give you your vectorised text data — the document-term matrix. Repeat the steps above for the test set as well, but only using transform, not fit_transform.

## LSA for Exploratory Data Analysis (EDA)

Just for the purpose of visualisation and EDA of our decomposed data, let’s fit our LSA object (which in Sklearn is the TruncatedSVD class) to our train data and specifying only 20 components.

`from sklearn.decomposition import TruncatedSVDlsa_obj = TruncatedSVD(n_components=20, n_iter=100, random_state=42)tfidf_lsa_data = lsa_obj.fit_transform(tfidf_train_df)Sigma = lsa_obj.singular_values_V_T = lsa_obj.components_.T`

Now let’s visualise the singular values — is the barplot below showing us what we expected of them?

`sns.barplot(x=list(range(len(Sigma))), y = Sigma)`

Let’s explore our reduced data through the term-topic matrix, V-tranpose. TruncatedSVD will return it to as a numpy array of shape (num_documents, num_components), so we’ll turn it into a Pandas dataframe for ease of manipulation.

`term_topic_matrix = pd.DataFrame(data=lsa_term_topic,  index = eda_train.columns,  columns = [f'Latent_concept_{r}' for r in range(0,V_T.shape)])`

Let’s slice our term-topic matrix into Pandas Series (single column data-frames), sort them by value and plot them. The code below plots this for our 2nd latent component (recall that in python we start counting from 0) and returns the plot in Figure 10:

`data = term_topic_matrix[f'Latent_concept_1']data = data.sort_values(ascending=False)top_10 = data[:10]plt.title('Top terms along the axis of Latent concept 1')fig = sns.barplot(x= top_10.values, y=top_10.index)`

These are the words that rank highly along our 2nd latent component. What about the words at the other end of this axis (see Fig 11)?

You can make your own mind up about that this semantic divergence signifies. Adding more preprocessing steps would help us cleave through the noise that words like “say” and “said” are creating, but we’ll press on for now. Let’s do one more pair of visualisations for the 6th latent concept (Figures 12 and 13).

At this point it’s up to us to infer some meaning from these plots. The negative end of concept 5’s axis seems to correlate very strongly with technological and scientific themes (‘space’, ‘science’, ‘computer’), but so does the positive end, albeit more focused on computer related terms (‘hard’, ‘drive’, ‘system’).

Now just to be clear, determining the right amount of components will require tuning, so I didn’t leave the argument set to 20, but changed it to 100. You might think that’s still a large number of dimensions, but our original was 220 (and that was with constraints on our minimum document frequency!), so we’ve reduced a sizeable chunk of the data. I’ll explore in another post how to choose the optimal number of singular values. For now we’ll just go forward with what we have.

## Using our latent components in our modelling task

Although LSA is an unsupervised technique often used to find patterns in unlabelled data, we’re using it here to reduce the dimensions of labelled data before feeing it into a model. We’ll compare our accuracy on the LSA data with the accuracy on our standard TF-IDF data to gauge how much useful information the LSA has captured from the original dataset. We now have a train dataset of shape (11314, 100). The number of documents is preserved and we have created 100 latent concepts. Now let’s run a model on this and on our standard TF-IDF data. The aim of the implementation below isn’t to get a great model, but to compare the two very different datasets. I’ve included basic cross validation through GridSearchCV and performed a tiny amount of tuning for the tolerance hyperparameter. If you were to do this for the sake of building an actual model, you would go much farther than what’s written below. This is just to help you get a basic implementation going:

`logreg_lsa = LogisticRegression()logreg = LogisticRegression()logreg_param_grid = [{'penalty':['l1', 'l2']}, {'tol':[0.0001, 0.0005, 0.001]}]grid_lsa_log = GridSearchCV(estimator=logreg_lsa, param_grid=logreg_param_grid,  scoring='accuracy', cv=5, n_jobs=-1)grid_log = GridSearchCV(estimator=logreg, param_grid=logreg_param_grid,  scoring='accuracy', cv=5, n_jobs=-1)best_lsa_logreg = grid_lsa_log.fit(tfidf_lsa_data, y_train).best_estimator_best_reg_logreg = grid_log.fit(tfidf_train_df, y_train).best_estimator_print("Accuracy of Logistic Regression on LSA train data is :", best_lsa_logreg.score(tfidf_lsa_data, y_train))print("Accuracy of Logistic Regression with standard train data is :", best_reg_logreg.score(tfidf_train_df, y_train))`

Which returns:

`Accuracy of Logistic Regression on LSA train data is : 0.45Accuracy of Logistic Regression with standard train data is : 0.52`

The drop in performance is significant, but you can work this into an optimisation pipeline and tweak the number of latent components. How does this perform on our test data (7532 documents) though?

`Accuracy of Logistic Regression on LSA test data is : 0.35Accuracy of Logistic Regression on standard test data is : 0.37`

Accuracy has dropped greatly for both, but notice how small the gap between the models is! Our LSA model is able to capture about as much information from our test data as our standard model did, with less than half the dimensions! Since this is a multi-label classification it would be best to visualise this with a confusion matrix (Figure 14). Our results look significantly better when you consider the random classification probability given 20 news categories. If you’re not familiar with a confusion matrix, as a rule of thumb, we want to maximise the numbers down the diagonal and minimise them everywhere else.

And that concludes our implementation of LSA in Scikit-Learn. We’ve covered the intuition, mathematics and coding of this technique.

I hope you’ve enjoyed this post and would appreciate any amount of claps. Feel free to leave any feedback (positive or constructive) in the comments, especially about the math section, since I found that the most challenging to articulate.

## References:

 L. Hobson, H. Cole, H. Hapke, Natural Language Processing in Action (2019), https://www.manning.com/books/natural-language-processing-in-action

 Pedregosa et al., Scikit-learn: Machine Learning in Python (2011), JMLR 12, pp. 2825–2830.

(Video) Latent Semantic Indexing | Explained with Examples

 Hamdaoui Y, TF(Term Frequency)-IDF(Inverse Document Frequency) from scratch in python (2019), Towards Data Science

 Wikipedia contributers, Singular Value Decomposition, https://en.wikipedia.org/wiki/Singular_value_decomposition

## FAQs

### What is the equation for Latent Semantic Analysis? ›

A ≈ Ak = Tk Sk D. Efficient LSI algorithms only compute the first k singular values and term and document vectors as opposed to computing a full SVD and then truncating it.

What is the example of Latent Semantic Analysis? ›

LSA deals with the following kind of issue: Example: mobile, phone, cell phone, telephone are all similar but if we pose a query like “The cell phone has been ringing” then the documents which have “cell phone” are only retrieved whereas the documents containing the mobile, phone, telephone are not retrieved.

Which mathematical technique is used to improve the latent semantic indexing? ›

Latent Semantic Indexing is also known as Latent Semantic Analysis. Latent Semantic Indexing is a method which we use for expanding the correctness of information retrieval.

What is LSA method? ›

Latent semantic analysis (LSA) is a mathematical method for computer modeling and simulation of the meaning of words and passages by analysis of representative corpora of natural text. LSA closely approximates many aspects of human language learning and understanding.

How do you calculate latent? ›

L = Q / M is the equation for latent heat. Here Q denotes the quantity of heat. M is the substance's mass. The quantity of heat (in joules/calories) per moles and unit mass of material experiencing a state change is commonly represented as latent heat.

What is Latent Semantic Analysis simple explanation? ›

Latent Semantic Analysis is a natural language processing method that analyzes relationships between a set of documents and the terms contained within. It uses singular value decomposition, a mathematical technique, to scan unstructured data to find hidden relationships between terms and concepts.

What is the advantage of LSA? ›

LSAs allow employers the opportunity to fund health and wellness costs that traditional group health plans won't offer, such as counselling, corporate gym memberships (or even employee gym memberships), fitness reimbursements and fitness classes.

Why is Latent Semantic Analysis successful? ›

Latent Semantic Analysis is an efficient way of analysing the text and finding the hidden topics by understanding the context of the text. Latent Semantic Analysis(LSA) is used to find the hidden topics represented by the document or text. This hidden topics then are used for clustering the similar documents together.

What are latent semantic keywords? ›

LSI (Latent Semantic Indexing) Keywords are conceptually related terms that search engines use to deeply understand the content on a webpage. The technology was originally patented in 1989.

Which technique is a mathematical technique of determining the best combination of limited resources which can achieve the set objectives? ›

Linear programming is a mathematical technique that determines the best way to use available resources. Managers use the process to help make decisions about the most efficient use of limited resources – like money, time, materials, and machinery.

### What is used in latent semantic analysis to Factorize matrices? ›

Latent Semantic Analysis works on the basis of Singular Value Decomposition. It is a method of factorizing a matrix into three matrices. Let us consider a matrix A which is to be factorized. It is then factorized into three unique matrices U, L and V where U and V are orthonormal matrices and L is a singular matrix.

Which is a broad technique which uses mathematical models to solve management problems? ›

operations research (OR) Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.

What are the problems with Latent Semantic Analysis? ›

LSA ignores the structure of sentences, i.e., it suffers from a syntactic blindness problem. LSA fails to distinguish between sentences that contain semantically similar words but have opposite meanings. Disregarding sentence structure, LSA cannot differentiate between a sentence and a list of keywords.

How LSA is used for evaluation purposes? ›

LSA uses a fully automatic mathematical technique to extract and infer meaning relations from the contextual usage of words in large collections of natural discourse. LSA simulates important practical aspects of human meaning to a very useful level of approximation.

What is LSA in statistics? ›

Latent Semantic Analysis (LSA) is a theory and method for extracting and representing the contextual-usage meaning of words by statistical computations applied to a large corpus of text.

What is the equation for specific latent capacity? ›

The specific latent heat of water is: l f = 3 ⋅ 34 × 10 5 J k g − 1 for fusion (solid→liquid) or freezing (liquid→solid)

What is the formula for calculating delay? ›

To calculate reverb or delay time: Obtain your song's bpm (beats per minute) and time signature. Divide 60,000 by the bpm number. Write down the result.

What is the formula for latent fusion? ›

L = m * L denotes the substance's particular latent heat of fusion. The heat that the material absorbs or releases is represented as Q = mc t as the temperature of the substance varies from t1 (low temperature) to t2 (high temperature). Q = mL + mc Δt is the total quantity of heat absorbed or emitted by the substance.

Why semantic analysis is difficult? ›

However, due to the vast complexity and subjectivity involved in human language, interpreting it is quite a complicated task for machines. Semantic Analysis of Natural Language captures the meaning of the given text while taking into account context, logical structuring of sentences and grammar roles.

What are the examples of semantic analysis? ›

The most important task of semantic analysis is to get the proper meaning of the sentence. For example, analyze the sentence “Ram is great.” In this sentence, the speaker is talking either about Lord Ram or about a person whose name is Ram.

### What does semantics mean for dummies? ›

Semantics is the study of meaning in language. It can be applied to entire texts or to single words. For example, "destination" and "last stop" technically mean the same thing, but students of semantics analyze their subtle shades of meaning.

What does LSA cover? ›

By contrast, an LSA allows you to spend freely on physical, financial and emotional wellness. The employer will decide what is deemed eligible spending. Although the specifics of an LSA will vary, employers may allow you to spend this money on gym memberships, nutritional supplements, daycare, groceries, and more.

Does LSA reduce dimensionality? ›

Latent Semantic Analysis (LSA) is a popular, dimensionality-reduction techniques that follows the same method as Singular Value Decomposition. LSA ultimately reformulates text data in terms of r latent (i.e. hidden) features, where r is less than m, the number of terms in the data.

What is natural LSA? ›

LSA is the abbreviation for linseed, sunflower and almond, a commonly used mixture with great nutritional properties. Tips for eating or cooking.

Why is LSA better than LDA? ›

Both LSA and LDA have same input which is Bag of words in matrix format. LSA focus on reducing matrix dimension while LDA solves topic modeling problems.

Does LSI still work? ›

LSI is a very old method of understanding what a document is about. It was patented in 1988, well before the internet as we know it existed. The nature of LSI makes it unsuitable for applying across the entire internet for purposes of information retrieval.

What are the advantages of LSI? ›

The utility of LSI stems from its ability to address multiple problems associated with other information retrieval methods: sparseness, noise, term independence, synonymy, and polysemy. Synonymy is defined as two terms conveying the same semantic meaning.

What is latent semantic similarity? ›

Latent semantic analysis (LSA) is a statistical model of word usage that permits comparisons of semantic similarity between pieces of textual information. This paper summarizes three experiments that illustrate how LSA may be used in text-based research.

What is Latent Semantic scaling? ›

Latent Semantic Scaling (LSS) is a flexible and cost-efficient semi-supervised document scaling technique. The technique relies on word embeddings and users only need to provide a small set of “seed words” to locate documents on a specific dimension.

How do I find my LSI keywords? ›

You can also type your main keyword into Google and then scroll down to the bottom of the page to find the “Related Searches” section. Check out the listed terms to get more ideas for LSI keywords for your content.

### Which technique in mathematics is best suited for the development of skills in mathematics? ›

One of the best strategies to help you learn math better is to create visual representations and diagrams for abstract concepts. By doing this, you are making abstract concepts more concrete, which makes them easily recognizable while solving problems.

Which of the following is the most relevant method technique of teaching mathematics? ›

Hence, it could be concluded that 'Problem-solving method' is most suitable for teaching mathematics at the upper primary level.

What is the mathematical technique used to select best choice? ›

LINEAR PROGRAMMING

It is the mathematical technique used to select the best choice among several alternatives.

How does ALS matrix factorization work? ›

Alternating Least Squares (ALS) matrix factorisation attempts to estimate the ratings matrix R as the product of two lower-rank matrices, X and Y, i.e. X * Yt = R. Typically these approximations are called 'factor' matrices. The general approach is iterative.

What is the basic intuition behind matrix factorization? ›

The intuition behind matrix factorization is fairly simple, given some user-item matrix, you want to decompose that matrix such that you have a user matrix and an item matrix independently. This allows us to apply different regularization to each latent factor of the original matrix.

What is LSA for text classification? ›

LSA is an information retrieval technique which analyzes and identifies the pattern in unstructured collection of text and the relationship between them. LSA itself is an unsupervised way of uncovering synonyms in a collection of documents.

What are the examples of mathematical Modelling in real life? ›

Mathematical models are used to solve many real-life situations like: • launching a satellite. predicting the arrival of the monsoon. controlling pollution due to vehicles. reducing traffic jams in big cities.

What are the three types of mathematical models? ›

Three types of mathematical models
• Insilications. In physics, we are used to mathematical models that correspond closely to reality. ...
• Heuristics. In reality, though, most theorists outside of engineering and the hard physical sciences (and even some in them, like cosmologists) work on heuristic models. ...
• Abstractions.
Sep 8, 2013

What are the three challenges in doing semantics? ›

These three issues: circularity; the question of whether linguistic know- ledge is different from general knowledge; and the problem of the contribu- tion of context to meaning, show that our definitions theory is too simple to do the job we want.

What is the full form of LSA? ›

Directory of LSA Heads. As for as the Telecommunication services are concerned the Country is divided into 22 Licensed Service Areas (LSA). These LSAs are headed by Advisor or Sr. DDG level officers. The setup at LSAs has been divided into five functional verticals.

### What is the purpose of teaching and learning evaluation? ›

Evaluation of teaching can have many purposes, including collecting feedback for teaching improvement, developing a portfolio for job applications, or gathering data as part of personnel decisions, such as reappointment or promotion and tenure. Most of the methods described below can be used for all of these functions.

When we analyze a document using latent semantic analysis LSA What are we trying to find? ›

Latent Semantic Analysis(LSA) is used to find the hidden topics represented by the document or text. This hidden topics then are used for clustering the similar documents together. LSA is an unsupervised algorithm and hence we don't know the actual topic of the document.

What is the difference between LSA and SVD? ›

lsa gives a way of comparing documents at a higher level than the terms by introducting a concept called the feature. the singular value decomposition (svd) is a way of extracting features from documents.

Why is Semantic Analysis important? ›

Semantic analysis allows organizations to interpret the meaning of the text and extract critical information from unstructured data. Semantic-enhanced machine learning tools are vital natural language processing components that boost decision-making and improve the overall customer experience.

What is the word equation for specific latent heat? ›

Calculating Specific Latent Heat

E = thermal energy required for a change in state, in joules (J) m = mass, in kilograms (kg) L = specific latent heat, in joules per kilogram (J/kg)

How do you calculate latent temperature? ›

Latent heat is also released into the environment when a liquid freezes, and can be calculated from Q = m L f Q = m L f .

What is latent semantic keyword? ›

LSI (Latent Semantic Indexing) keywords are words that are related to a main keyword and are seen as semantically relevant. If your page's primary keyword is 'credit cards,' then LSI keywords would be things like “money,” “credit score,” “credit limit,” or “interest rate.”

What is latent semantic scaling? ›

Latent Semantic Scaling (LSS) is a flexible and cost-efficient semi-supervised document scaling technique. The technique relies on word embeddings and users only need to provide a small set of “seed words” to locate documents on a specific dimension.

How do you calculate latent and sensible heat? ›

Sensible and Latent Heat Transfer Equation for Air
1. q = m ∆h.
2. q = CFM x 4.5 x ∆h.
3. Step one is to plot the entering and leaving air conditions on a psychrometric chart to determine the enthalpy. ...
4. Step two is to put all the known values into our formula and make the calculation.
5. q = 2,000 x 4.5 x 11.7 = 105,300 Btu/hour.
Apr 25, 2022

What are the three types of latent heat? ›

What are the types of latent heat transfer? The two forms of latent heat are latent heat of fusion (melting) and latent heat of vapourisation (boiling).

### What is the formula for latent heat loss? ›

Thus the latent heat loss of evaporation: ΔHev = HV − HL = 2461 kJ/kg. This translates to an energy release from the ocean of 2461 × 398 × 1015 kJ/year = 9.80 × 1020 kJ/year.

What is the formula for calculating temperature? ›

The Temperature Conversion Formula

The conversion formulas we use are the standard ones that are used in most textbooks. To convert temperatures in degrees Fahrenheit to Celsius, subtract 32 and multiply by .5556 (or 5/9). To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.

What is latent heat and how is it calculated? ›

Specific latent heat can be calculated by dividing the amount of heat energy added or removed from the substance by the mass of the substance. The formula is: Specific latent heat = (Heat energy) / (mass of substance)

What is the rule for latent heat? ›

Definition of Latent Heat

Normally, when heat energy is added to or removed from an object, the temperature of the object changes; however, during phase changes, the temperature of an object stays constant. The temperature remains the same because energy is required for an object to change phases.

How does latent semantic indexing work? ›

Latent semantic indexing (also referred to as Latent Semantic Analysis) is a method of analyzing a set of documents in order to discover statistical co-occurrences of words that appear together which then give insights into the topics of those words and documents.

What is the difference between LSA and LDA? ›

Both LSA and LDA have same input which is Bag of words in matrix format. LSA focus on reducing matrix dimension while LDA solves topic modeling problems.

What is PCA vs LSA? ›

Whereas PCA performs decomposition on the correlation matrix of a dataset, SVD/LSA performs decomposition directly on the dataset as it is.

Why is LSA used in social media analytics? ›

An LSA model can be viewed as an improvement over a model based solely on n-grams because it has a more precise measure of similarity. LSA also captures contextual use of words, synonymy, etc. To demonstrate this fact, we tested a baseline model based on unigrams and bigrams combined with multiple linear regressions.

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