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

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### Recommend similar users (instead of items) with collaborative filtering

I'm learning about collaborative filtering, and all the resources I've found so far describes how to find items a user might like. However, how would I find the most similar users to a specific user, ...
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### Why is non-negative matrix factorization better than ICA in neuronal analysis

I've recently joined a neuroscience lab and am currently reading up on their pipeline to analyze 2-photon calcium imaging with single neuron resolution. The data consist of a movie where the pixel ...
• 1
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### Why does Non-negative Matrix Factorization not give me 100% R^2 at full rank?

IMPORTANT: Please read the question carefully before labeling it a "code question" & sending it to stack overflow. The question is in fact a theoretical stats question (barring the ...
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### Non-negative Matrix Factorization applied to PET images

for my master thesis work I have to analyze some brain PETs of patients affected by gliomas. Basically the problem is: I have a 3D scale of gray image of the brain. The tumor zone is an high-intensity ...
• 101
34 views

### Interprete Multinomial Naive Bayes when working with real non-negative values

I am currently working on an algorithm that aims to reduce dimensions and map data within the non-negative orthant. Subsequently, the mapped data is utilized as input for a classifier. The classifiers ...
• 123
130 views

### Difference between PCA and NMF in terms of explaining variability?

I want to understand the difference between PCA (principal component analysis) and NMF (non-negative matrix factorization) in terms of the explained variability. When we apply PCA into high-dimensinal ...
• 171
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### Understanding diagonal rescaling in multiplicative update rules for NMF

SUMMARY How does the diagonal rescaling fit into the derivation of a multiplicative update rule for non-negative matrix factorization (NMF)? DESCRIPTION The NMF problem aims to find non-negative ...
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1 vote
36 views

### 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 ...
1 vote
57 views

### Relaxed non-negative least squares

I am reconstructing a probability vector from data using non-negative least squares: $$\sum_\alpha \left(\pi_\alpha - \sum_i W_{\alpha i}p_i\right)^2\rightarrow \min,\\ p_i\geq 0,\sum_i p_i=1$$ ...
• 4,276
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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 ...
• 81
463 views

### 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
546 views

### 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
96 views

### 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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