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

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### Non-negative matrix factorization clusters

NMF can be used for clustering i.e., $V=WH$ where $W$ represents cluster centers and $H$ represents the membership of samples. But can NMF alone cluster the samples? Can we get better clusters in NMF ...
18 views

### Values overshooting for sparse matrix factorization (recommendation system)

Using this article as reference for ease of replicability, I noticed that when expanding the pivot matrix R with many missing values, the final recommendation matrix tends to have values overshooting ...
29 views

### Is Nonnegative matrix factorization a clustering method or a dimensionality reduction method?

In the matrix factorization we have the problem of decomposing a nonnegative matrix $X$ into two lower-rank matrices $W$ and $H$. I would like to know whether this method is considered as a dimension ...
11 views

### Why does Non-Negative Matrix Factorization reconstructs exactly the same matrix?

I'm trying recently to get into recommender systems and almost all tutorials I find mention collaborative filtering done with matrix factorization. I found this tutorial that describes how to build ...
13 views

### can we use a hybrid optimization schem for NMF

The NMF problem of the form $$X \simeq WH$$ is a constrained biconvex optimization problem, and is often solved by alternating updates schemes. For example, the multiplicative update rules use ...
22 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: <...
42 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 (...
2k 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 ...
8 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 ...
15 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 ...
128 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 ...
93 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 ...
919 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 ...
38 views

### Negative Latent Factors in Factorization Machines

I'm studing a specific implementation of a recommendation system leveraging on a factorization machine algorithm. For each person_id and item_id combination, I have an implicit rating of 1 or 0 ...
211 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 ...
18 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 ...
23 views

### What are the limitations of non-negative matrix factorisation when reducing the dimensions of a data set?

From what I understand NFM (non-negative matrix factorisation) is constrained by the factor that it only supports data sets with non-negative values when reducing the dimensions of a data set. ...
128 views

### Enforcing constraints on weight matrices using ReLU activation

In the paper 'A Deep Non-Negative Matrix Factorization Neural Network' by Flunner and Hunter, proof of Theorem 1 says that "The ReLu Activation function is a standard approximation of a non-negative ...
75 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 ...
141 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 ...
40 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 ...
182 views

### Factorized matrix for recommendations, what then?

I have a dataset that looks like this: Image taken from this blog Let's assume that I have applied Matrix factorization and have learned the zero values for the items missing for every user. I now ...
89 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 ...
198 views

### Normalizing sparse matrix by mean, should the mean be calculated excluding zero?

I have very sparse matrix (70% sparsity) which I want to normalize by mean. I tried using mean both include and exclude zero. The histogram between count (y-axis) and value (x-axis) shows The value ...
961 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 ...
722 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?
322 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 ...
114 views

### Obtaining hard, overlapping clusters using non-negative matrix factorization

From my understanding non-negative matrix factorization (NMF) provides a natural way to obtain soft clusters from a non-negative $n$x$m$ data matrix $X$. NMF decomposes $X$ into two non-negative ...
99 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 ...
319 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 ...
1k 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 ...
314 views

### Nonnegative Matrix Factorization as Maximum Likelihood

Elements of Statistical Learning has this on such NMF loss function (section 14.6 Non-negative Matrix Factorization): The matrices $\mathbf{W}$ and $\mathbf{H}$ are found by maximizing  L(\mathbf{...
5k views

### Deriving Multiplicative Update Rules for NMF

How to derive the multiplicative update rules for the non-negative matrix factorization problem given by Lee and Seung. Minimize $\left \| V - WH \right \|^2$ with respect to $W$ and $H$, subject ...
371 views

### Why do increasing regularization weights make objective function not monotonically decrease?

I run modified non-negative matrix factorization (NMF) and tune the regularization weight from 1e5 to 1e13. The table below ...
83 views

### The reason why NMF has become so popular [duplicate]

Why do we use Non-negative matrix factorization?What is the advantage and superiority of other matrix decomposition methods?
177 views