# Questions tagged [nnmf]

Non-negative matrix factorization (NNMF) is a non-unique matrix factorization of a non-negative matrix $A$ into the non-negative matrices $W$ and $H$ such that they minimise the functional $\frac{1}{2} || A - WH||_{F}^2$.

50 questions
Filter by
Sorted by
Tagged with
13 views

### Apply normalization to error or inverse variance?

I am prepping some data to run through a nonnegative matrix factorization code, and would like to apply a normalization or standardization method. I am interested in trying min-max normalization: <...
31 views

### Why NNMF (non-negative matrix factorization) is a method for linear dimensionality reduction?

Some sources (for example this) say that NNMF is a method for linear dimensionality reduction. How to prove this statement? I see two different explanations of this and I want to know which of them (...
459 views

### What is The Main Difference between PCA and NMF and why to choose one rather than the other?

I have to develop some analyses to study cancer data. I want to use NMF and PCA. Basically these tools choose the best factorization rank and the number of components that is meaningful to your ...
7 views

### Physical significance of non-negative factors of a matrix?

I was trying to make a recommender system using matrix factorization techniques on rating data. I came across 2 algorithms - SVD and NMF. While the basic difference is very clear , I was wondering ...
11 views

### How to choose the best model for Non Negative Matrix Factorization?

I am applying NMF with NMF R package. In the early stages, I'm comparing three algorithms (Lee, Brunet,nsNMF) visualizing how fast they converge and how much they reduce residues as in the image down ...
90 views

### Why does NMF of a symmetric matrix yield orthogonal matrices which are not transpose identical?

Consider the non-negative factorization of a positive, real symmetric matrix A. Non-negative factorization of this matrix yields ...
29 views

### Am I interpreting correctly this NMF analysis?

I have to analyse a set of biological data and I am applying a Non-Negative Matrix Factorization (NMF) Approach. Given a 366 x 144 dataset, I am reasoning about overfitting and the correct rank r to ...
594 views

### What is the difference between Non-Negative Matrix Factorization (NMF) and Factor Analysis (FA)?

I am performing an Exploratory Factor Analysis (EFA) for a multivariate dataset, where variables are all measurements of the same physical measure, only in different locations in space. My purpose is ...
140 views

### Is there a version of NMF that normalizes the sum of scores of each sample?

I want to decompose a nonnegative data matrix $A \in \mathbb{R}^{n\times m}$ into nonnegative basis vectors $U \in \mathbb{R}^{n \times k}$ and a score matrix $V \in \mathbb{R}^{m \times k}$ such that ...
16 views

### How to approximate a Hermitian matrix with a transposed cross product of a single matrix?

I have a complex square matrix, and wish to learn latent factors (equally weighted latent factors, so not SVD) from this matrix. Given a Hermitian matrix A of ...
54 views

### Can NMF assign probabilities to the topics it outputs?

It's my understanding that only LDA can assign probabilities to words within each topic that it discovers since it's a probabilistic graphical model politicians 0.05 united states 0.10 obama 0.20 ...
123 views

### Deriving Multiplicative Update Rules for Regularized NMF

After reading the following CrossValidated post, I cannot derived the correct multiplicative rules for regularized NMF from this paper. They obtain the coefficients $|I_u|$ and $|U_i|$ in the ...
39 views

### Implementation of Proximal alternating linearized minimization

The updates of the gradients are somehow wrong. I have implemented the below given algorithm. I have done something wrong ...
83 views

### Using complex number in non-negative matrix factorization (NMF)

In short, I wonder which kind of data can use complex number for NMF. And could an imaginary part possibly be a vector? For detail, as I saw some papers used complex number in NMF (1), I think it ...
792 views

### Non-negative matrix factorization (NMF) on mixed data using 1-hot encoding

From a standpoint of interpretation, can I use NMF on one-hot encoded categorical data for dimension reduction? I have mixed data and was thinking about one-hot encoding the categorical features and ...
645 views

### Can I use word2vec vectors as input features to NMF or LDA?

I'm trying to do some topic modelling on my corpus and I want to use Word2Vec vectors as an input to my NMF and LDA models. How do I do this? Is it even possible?
280 views

### nmf in scipy returns components with all zero weights

I'm trying to understand whether this behavior is a bug or a feature. Essentially, I have a dataset of ten thousand short pieces of text. I have used the CountVectorizer function to turn this into a ...
96 views

### matrix factorization with non-negative constraint only on one of the factors

I have a 2D spectral data time series with a wavelength dimension and a time dimension, and I'd like to decompose it to the time evolution ($SV^T$ for SVD and $H$ for NNMF) of several spectral ...
275 views

### Distributed PCA or an equivalent

We normally have fairly large datasets to model on, just to give you an idea: over 1M features (sparse, average population of features is around 12%); over 60M rows. A lot of modeling algorithms ...
962 views

### Pattern of out-of-sample reconstruction error in NMF cross-validation: why is it monotonically decreasing? [duplicate]

I am using nonnegative matrix factorization, NMF (in its variant OPNMF, which is subject to additional orthogonality and $H = W^TV$ constraints) to factorize a dataset. To find the optimal number of ...
272 views