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 ...
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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 ...
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1answer
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 ...
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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 ...
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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 ...
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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: <...
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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 (...
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1answer
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 ...
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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 ...
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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 ...
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1answer
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 ...
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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 ...
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1answer
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 ...
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1answer
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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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1answer
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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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2answers
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 ...
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1answer
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?
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1answer
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 ...
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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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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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{...
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2answers
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 ...
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1answer
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 ...
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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?
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177 views

What can be the reasons that L1-regularized NMF gets worse result than standard NMF in sparse matrix computation?

I apply L1-norm as a group sparsity constraint [1,2] into non-negative matrix factorization $V \approx WH$ for source separation. Objective functions: Standard NMF (Kullback-Leibler divergence): $...
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1answer
5k views

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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409 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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1answer
453 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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79 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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138 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
1k 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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1answer
342 views

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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43 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
834 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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1answer
830 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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287 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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96 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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1answer
1k 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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2k views

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 ...