Questions tagged [matrix-factorisation]

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices.

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What is the scikit learn Non-negative Matrix Factorisation Coordinate Descent algorithm?

What is the scikit-learn Coordinate Descent (CD) algorithm for Non-negative Matrix Factorization (NMF)? The sklearn implementation of NMF has two different solvers, Coordinate Descent and ...
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Differences and similarities between nonnegative PCA and nonnegative matrix factorization

I have seen references in the literature to nonnegative principal component analysis (nPCA) and nonnegative matrix factorization (NMF). I have tried reading the papers on both of them but it is not ...
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Vector de-factorization

Suppose one has a data set with a column/vector which consists of factor-like character strings: ["a level", "b value", "c bound", "a level", ...] For conversion ...
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Binary Matrix Factorization: Regularizer to encourage 1-0 matrices

I have the following problem: Given a (user, access rights) binary matrix, I need to find the best (user, role) x (role, access right) binary matrices to reconstruct the original matrix. The current ...
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Same topics appearing multiple times in a NMF model

I am using NMF (Non-negative Matrix factorization) module from Scikit learn to extract 100 topics from a corpus. In contrast to LDA, the output of NMF modeling includes some of the topics multiple ...
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Testing Setup in Temporal Tensor Factorization for Recommendation

I am trying to wrap my head around Temporal Tensor Factorization for Collaborative Filtering, as described in the paper: Temporal Collaborative Filtering with Bayesian Probabilistic Tensor ...
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SVD++ in matrix form

I have been recently reading the following presentation and papers preceding it: http://staff.ustc.edu.cn/~ynyang/group-meeting/2014/matrix-factorization/Matrix-factorization-recommendation-system-...
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Mobile App Recommendation: How to get the rate of a specific user submit for a specific application

I have a mobile app recommendation project, so I need data set which has user-app matrix-rate. Actually, I want to know what rate does a specific user submit for a specific application. in other words,...
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In learning latent factors in matrix factorization, are weights learned based on similarity between e.g. users?

I implemented a recommendation system using user-user interaction data, learning missing ratings through alternating least squares and matrix factorization, which as I understand it, adjusts and ...
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How does recommendation by matrix factorization deal with new movies / users for which there are ratings?

Assume you have the ratings of $n$ users for $m$ movies in a matrix $R \in \mathbb{R}^{n \times m}$. You compute a representation $$R = U \times \Sigma \times V$$ by initializing $u_i, v_j \forall i ...
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Nice examples/illustrations of CPD/Tucker or other tensor decompositions for a presentation?

I'm giving a presentation on tensor decompositions (especially CPD and TKD) and I'm looking for some nice examples or illustrations to demonstrate usefulness and intuition, most likely on three-way ...
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Extension of NMF to 3D

AFAIK, Non-Negative Matrix Factorization (NMF) is the procedure of looking for matrices $A$ and $B$ such that $$Data_{ik} = \sum_j A_{ij} B_{jk}$$ My data matrix is in fact 3D. I would like to fit ...
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How does on test regression for a subspace or matrix factorization?

I've recently been reading a lot of papers and watching a lot of videos on both subspace learning, and matrix factorization. One thing is particularly eluding me though - how does any of this get ...
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How do I recommend items to out of training users based on its recent views?

I used Spark's ALS implementation of matrix factorization (Collaborative Filtering for Implicit Feedback) to train user and item embeddings. Since we have a lot of users in system, I had to sample ...
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Does cardinality of ratings column affect performance of matrix factorization based collaborative filtering?

I am using mllib's implicit preference based implementation of collaborative filtering for generating grocery product recommendations in e-commerce, based on this Netflix Prize winning algorithm. I ...
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Finding unobserved ratings using matrix factorization

Suppose that the utility matrix contains ratings of user on movies. How does matrix factorization find ratings for unobserved (user, movie) pair. Even though the purpose of the algorithm is to find ...
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Neighbourhood based approach on implicit feedback datasets

Is it possible to use a neighbourhood-based approach on implicit feedback dataset? I have a dataset with information about how many times a certain item was viewed by a particular user. I know that MF ...
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How dot product limits expressiveness and leads to sub-optimal solutions in Matrix Factorization?

I am reading one paper on Metric Factorization an it says: "The dot product adopted in matrix factorization based recommender models does not satisfy the inequality property, which may limit their ...
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Loss and Regularization inference

I'm building a Matrix Factorization model for MovieLens dataset with batch-wise training. Loss function for the batch: $$ L_{batch} = 1/|B|\sum_{(u,i)\in{B}}(r_{ui} - \mu - b_u - b_i - p_u^Tq_i)^2 + \...
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Regularization in Embedding models?

What is the best way to regularize latent embeddings, I have two solution in my mind but I'm not sure which one to use over other. In batch-wise training regularize over the whole embedding matrix, ...
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Matrix Factorization for Recommender Systems

Referring to the paper Matrix Factorization Techniques for Recommender Systems, Loss function for Matrix Factorization using bias terms is given as: $$ \min_{p, q, b}\sum_{(u,i)\in\kappa}(r_{ui} - \mu ...
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Regularization term in Matrix Factorization

I'm trying to build a naive recommender system using latent factor model for MovieLens dataset. From the observed set of ratings I'm trying to build a model which will decompose the sparse matrix to N ...
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Reciprocal rescaling of product of two matrices

I read in many papers about product of two matrices being invariant to reciprocal rescalings. What exactly does this means ?
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Does a matrix factorization recommendation engine use user/item related features?

All the tutorials I can find about matrix factorization recommendation systems start with importing users, items, and user-item-ratings, but then only use the rating matrix to train the recommender (...
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Building Recommender for book paragraphs

I have some application which are offering a book to read. Users normally read some paragraphs of it only (it contains +6000 paragraphs). Looking at scatter for ...
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SVD++ vs wALS: Which is the more effective for implicit feedback in Recommendation system

As SVD++ can be used for implicit feedback, I would like to know whether SVD++ can gives better results than the wALS algorithm (paper: Collaborative Filtering for Implicit Feedback Datasets ). I can'...
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Kernelized Probabilistic Matrix Factorization - Implementation?

I am trying to implement a kernelized probabilistic matrix factorization which is mentioned in this paper. KPMF Paper. I have coded two update functions as two separate methods. I don't know if this ...
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Topic Segmentation - should it be done in Raw, TfIdf or Semantic Space?

Let's assume we have a collection of documents and wish to perform some unsupervised topic segmentation. As always, we will perform some preprocessing (including tokenization, accent-removal, ...
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R codes for “Matrix estimation by Universal Singular Value Thresholding”

Consider a real demand estimation problem of a retailer where matrix Y is the real demand need to be estimated by using sales data (matrix) X which is bounded by stock (matrix) C. The estimation ...
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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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How to factorize the Matrix in TensorFlow? (Recommender System)

Given a user ratings matrix which is $n \times p$, where $n$ users rate $p$ movies, I already have a row matrix $n \times 10$ which characterises the user. I ideally wanted to use the TF was method ...
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On minimizing matrix norm (AB-C)

Given A, B and C are matrices with dim(A) = m x n, dim(B) = n x p and dim (C) = m x p, the problem asks to evaluate I need to learn $$\tilde{A}$$ such that $$\min_{\tilde{A}}||\tilde{A}^TB-C||$$ and ...
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Matrix Factorisation Improvement

I am using SGD matrix factorisation (python) using the movielens dataset to make recommendations. I have a website which allows users to give feedback which is positive or negative to whether an item ...
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Can't understand this simple matrix multiplication in python [closed]

Ok guys, I might be very tired here, but I can't figure out why this matrix multiplication by a scalar gives the following result (python) Matrix named 'dx' [ 1.6, 3.6, 0.4, 14.4, 25.6], ...
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Why do we need 2 matrices for word2vec or GloVe

Word2vec and GloVe are the two most known words embedding methods. Many works pointed that these two models are actually very close to each other and that under some assumptions, they perform a matrix ...
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How does SVD actually provide the recommendations? I seem to get conflicting answers

I am reading a text book that basically says the following: Given a matrix A where A is USERS x ITEMS we can use SVD to decompose the matrix into: $$A = U \times \Sigma \times V^T$$ Then we can take ...
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572 views

How exactly does matrix factorization help with collaborative filtering

We start with a matrix of user ratings for different movies with some elements unknow i.e the rating of a yet to be seen movie by an user. We need to fill in this gap. So How can you decompose or ...
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113 views

What is local-NMF? How is it better than original NMF?

I am reading this paper, but don't really understand. Do the words "part-based" or "local" for non-negative matrix factorization (NMF) mean that the algorithm aims to factorize some specific parts ...
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747 views

Prediction with multiple features (attributes) [closed]

I recently used a prediction algorithm to try to predict how much an user is willing to interact with an item using ALS (Matrix Factorisation) but I had to "condense" multiple attributes into one, ...
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Text generation using Tensor Factorization

Text generation is well studied using Markov chains or NNs, but I am not aware of any works to word sequence prediction in terms of subspace learning. Treating phrases or sentences as temporal data ...
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Factorization Machine - prevent over fitting

I was recently asked this question in an interview and wondered what the answer would be - "How do Factorization Machines get around the overfitting problem when using second-order interactions?"
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Tensor Decomposition for Higher-Order Context-Aware Recommender Systems

Let me motivate my problem with an example. Let's assume our observations concern ratings a user give to different items, while navigating through item catalog. The user begins rating item1 (may be ...
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ALS in Spark: what loss function is it minimizing?

I’ve playing with the MovieLens ratings dataset under Spark’s ALS and a manual implementation of ALS and comparing results with the same hyperparameters. I’d like to know this exactly in order to make ...
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308 views

matrix factorization?

I have sparsely populated matrix of users as rows with columns being categorical answers to various questions ( question are of various domain about preferences / behaviors of the users ) . answers ...
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Matrix factorisation of vote share data

Consider a matrix, $\mathbf{V}$, where each row corresponds to one of $m$ electoral district and each column corresponds to one of $n$ candidates or political parties. Each element, $V_{ij}$, is the ...