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 $\frac{1}{2} || A - WH||_{F}^2$.

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15 views

Investigator efficiency computation

I need a little help with inferring ground truth and investigation capabilities from data. I have an incomplete matrix consisting of binary decisions taken by investigators on documents i.e. for every ...
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Are there python implementations of OPNMF (orthonormal projective NMF) or comparable methods to implement it?

I'm looking to implement this specific version of NMF (OPNMF or orthonormal projective NMF), and I don't exactly understand the additional benefits of the OPNMF over regular NMF. I'm hoping to take a ...
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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 ...
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27 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 ...
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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 ...
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32 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 ...
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64 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 ...
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2answers
471 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 ...
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1answer
389 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?
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193 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 ...
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76 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 ...
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199 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 ...
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1answer
455 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 ...
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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{...
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2k 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 ...
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1answer
258 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 ...
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75 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?
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355 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 ...
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335 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. ...
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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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104 views

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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1answer
849 views

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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41 views

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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1answer
476 views

Calculate Frobenius Norm using Non-Negative Matrix Factorization

After performing Non-Negative Matrix Factorization (using R's rnmf() function), I'm left with W, H, and the fitted matrix (W%*%H). The Frobenius norm (squared ...
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624 views

Nonnegative Matrix Factorization - Interpreting clustering indicator matrix

In non-negative matrix factorization (NMF), the problem is to minimize $A - WH$. Dimensions are $A$ (m x n), $W$ (m, k) and $H$ (k, n). The matrix $H$ reveals soft clustering assignments of $n$ items ...
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265 views

Explanation of the decomposition in the Non Negative Matrix Factorization

I perform matrix factorizaition in my data using the sklearn implementation of Non Negative Matrix Factorization. In the evaluation process I am removing some values from my initial dataset and I am ...
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81 views

How to determine mixture coefficient nonparametrically?

Problem: Given a sample $X_m$ from each of $M$ distributions $f_m$ which are all mixtures of the same $C$ unknown distributions $g_c$ but with differing mixture coefficients $\alpha_{mc}$, (when and) ...
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932 views

Non Negative Matrix Factorization and Projection onto other Data

Is there an equivalent in NMF to PCA projection? For example lets say you have 2 datasets of data which are generated by a highly similar process, one which is noisy (dataset 2) and one which is not (...
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Why is non-negativity important for collaborative filtering/recommender systems?

In all modern recommender systems that I have seen that rely on matrix factorization, a non-negative matrix factorization is performed on the user-movie matrix. I can understand why non-negativity is ...
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960 views

Why do we need the regularization term for NMF but not for SVD?

In non-negative matrix factorization (NMF) one minimizes the Frobenius norm plus a regularization term. However SVD simply minimizes the Frobenius norm. Why do we need the regularization term for NMF ...
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173 views

If I multiply two non-negative matrices together and then do NMF, will the result be close to the matrices I started with?

I've been playing around with non-negative matrix factorization (NMF), just doing some example computation, and arrived at the following question: Suppose I pick two non-negative matrices $\textbf{W}$...
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174 views

What is the most efficient algorithm for online Non- negative Matrix Factorization (NMF)?

What is the most efficient algorithm for online Non- negative Matrix Factorization (NMF) in recent study? Thanks.
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1answer
274 views

Factor rotations in non-negative matrix factorization?

My understanding is that solutions from Non-Negative Matrix Factorization (NMF) are not necessarily unique, and rotations can be imposed during the optimization process or after the solutions have ...
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1answer
2k views

Evaluate performance of non-negative matrix factorization (NMF)

I have a complex pipeline for predictive modeling of text, where the non-negative matrix factorization (NMF) is one part. I would like to evaluate the performance of the NMF independently of the ...
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647 views

Non-negative matrix factorization in recommender systems

As I understand, in NMF we should have our three matrices elements non-negative. But I can't understand how to do it so far. Shouldn't we just initialize our factor matrices at the start with random ...
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1answer
831 views

What is the advantage of non-negativity in matrix factorization?

I am wondering why matrix factorization techniques in the machine learning domain almost always expect the provided matrix to be non-negative. What is the advantage of this constraint? Background: I ...
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10k views

How to choose an optimal number of latent factors in non-negative matrix factorization?

Given a matrix $\mathbf V^{m \times n}$, Non-negative Matrix Factorization (NMF) finds two non-negative matrices $\mathbf W^{m \times k}$ and $\mathbf H^{k \times n}$ (i.e. with all elements $\ge 0$) ...
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1answer
2k views

Trying to understand non-negative matrix factorization (NMF)

I'm trying to understand how NMF is derived, and I got the basic idea of NMF, that is, it tries to approximate the original matrix $V$ with $WH$, where $V$ are non-negative, and $W,H$ are constrained ...
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1answer
714 views

In non-negative matrix tri-factorization, initialization not possible because matrix is singular

I have implemented the non-negative matrix tri-factorization algorithm (link to paper). If is similar to the more widely known NMF (non-negative matrix factorization), but incorporates prior knowledge ...
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1answer
3k views

In non-negative matrix factorization, are the coefficients of features comparable?

I'm using Alternating Nonnegative Least Squares Matrix Factorization Using Projected Gradient. The result (I use 2 as rank) is like this: ...
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245 views

Rank-one nonnegative matrix factorization

For non-negative matrix factorization with Frobenius norm: $$\min\limits_{U\in\mathbb{R}_+^{m\times r}, V\in\mathbb{R}_+^{r\times n}}||A-UV||_F^2, A\in\mathbb{R}_+^{m\times n}$$ $r=1$ is a very ...
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3answers
680 views

How to bootstrap non-negative matrix factorization results?

I have RNA-seq data from 9 samples and around 15,000 genes. I know that these 9 samples consist of varying proportions of two cell types, each with their own expression profile. I am using non-...
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1answer
761 views

Method to find 'principal components' of EMG recordings of reflexes

I have a series of electromyographic (EMG) reflex recordings, of which I would like to find out the principal components. My thoughts are that there are multiple processes that added together result ...