# Questions tagged [non-negative-matrix-factorization]

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### Transfer factors information from one matrix to another in the non-negative matrix factorization

I have two dataset X= [r1 x f1] and Y = [r2 x f2] Here f1 and f2 are the features such that f1>>f2 and the common features between f1 and f2 is around ~200. I am interested to know a common or ...
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1 vote
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### What are the modes of a dictionary / transform basis?

So, I'm reading Steven Brunton's book, "Data Driven Science & Engineering", and I'm trying to understand what he means by mode in this following excerpt: Most natural signals, such as ...
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### Correct NMF usage in context of recommender systems

I am trying to teach myself about the NMF models (in the context of recommender systems), and I have come across different suggestions on how to set up such a workflow, but I'm not sure if both are ...
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### Gensim NMF interpretation and output

In these days I am studying and applying Gensim NMF. Looking at the documentation I would like to understand how it works, in their example here they have the following matrices: W is a word-topic ...
• 111
1 vote
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### Relaxed non-negative least squares

I am reconstructing a probability vector from data using non-negative least squares: $$\sum_\alpha \left(\pi_\alpha - \sum_i W_{\alpha i}p_i\right)^2\rightarrow \min,\\ p_i\geq 0,\sum_i p_i=1$$ ...
• 3,354
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### Examples of when PCA would be preferred over NMF

What are some specific examples of when PCA should be used instead of NMF? PCA is a widely used method for dimension reduction in data science, machine learning, and bioinformatics. NMF is also a ...
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### How does LDA (Latent Dirichlet Allocation) assign a topic-distribution to a new document?

I am new to topic modeling and read about LDA and NMF (Non-negative Matrix Factorization). I understand the training process work. Let's say I have 100 documents and I want to train an LDA for these ...
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### Why does NMF perform better than LDA on shorter textual inputs

For the reading that I have done, I found that Dirichlet priors typically don't perform well when they aren't given significant amounts of data. I'm not quite sure why that is. What is it about NMF ...
• 121
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### Geometric Interpretation of Non Negative Matrix Factorization

I'm trying to learn about the geometric interpretation of NMF. I have found the paper by Slim Essid to be very useful. I would like to make a plot like the one in Figure 1 just for a k=2 Topics (i.e. ...
• 121
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### Derive a constant in Kullback-Liebler divergence proof

From Kullback-Liebler divergence of matrix factorization; \begin{equation*} \mathrm{X}\approx\mathbf{WH} \tag{1} \end{equation*} How equation $(2)$ is derived to constant equality in equation $(3)$? ...
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### Non negative matrix factorization initial values and final values

I am planning to use initial values that are {0, 1}. How do we ensure or how does NMF ensure that the final values are also in the [0,1] range. What if we want to model a matrix of frequencies of ...
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### Deep Learning Variation of NNMF

I'm aware that there are different variations of non negative matrix factorization based on the optimization function and I have read about graph regularized NMF. Is there any method to use deep ...
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### What conclusions I can draw from matrix result after non-negative matrix factorization?

I was introduced to NMF for data analysis. I implemented some code and obtained the result of basis matrix $W$ and feature matrix $H$. From $V$ ~ $WH$, my $V$ dimension is 5100*1201. I inputted $W$ ...
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### what is the likelihood of a levy process?

While interpreting NMF in Statistical perspective, we assume a Poisson process and to solve for the factors the using EM algorithm, the likelihood of a Poisson process is assumed to be Multinomial, I ...
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