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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Matrix factorization how to initialize weights and biases?

I have a matrix factorization and I'm wondering how I should initialize its weights and biases. When getting prediction (recommendation), after computing a dot product and adding bias I want to use ...
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What is the best model for a recommendation system using implicit ratings?

I have a similariy matrix that looks like this: I have a bunch of user vectors with 1s and 0s, with a 1 indicating that someone has clicked on an email (as part of a campaign) and zero to indicate ...
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Why is this equation converted to matrix form in this way? Is it possible to multiply an inverse matrix with a vector?

I have been banging my head on wall for days trying to decode this equation. please help me out with this... Below is the equation (consider $x$ as $\Delta x$, and $y$ as $\Delta y$): $x = - \eta(Id-\...
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Can Nonnegative Matrix Factorization be used for extracting the most important features from a dataset with high dimensionality (1000+ variables)?

I would like to extract and identify the most important variables from a biological dataset containing mutational and gene expression data in R. Previous supervised techniques showed that these ...
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1answer
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How to filter Items in Recommender Systems?

I have a Recommender System which recommends Articles based on Similarity from 3 Features, "Page-Title, Article Content, Tags". But some of the Articles are NSFW(Related to Adult Topics). I ...
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35 views

Human intuition behind SVD in case of recommendation system

I checked the SVD for recommendation engine thread but it does not answer my question. I struggled very hard to understand the SVD from a linear-algebra point of view. But in some cases I failed to ...
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1answer
17 views

Negative Latent Factors in Factorized Machines

I'm studing a specific implementation of a recommendation system leveraging on a factorization machine algorithm. For each person_id and ...
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2answers
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what is the meaning of $\mathbb{R}^{768\times (768 * 2)}$?

Hi I'm an undergraduate student interested in Machine Learning. I was reading a paper from ICLR 2020 and came a cross a weird looking vector dimensions. Can anyone tell me what this means?? $\mathbb{R}...
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132 views

What types of matrix multiplication are used in Machine Learning? When are they used?

I'm looking at equations for neural networks and backpropagation and I see this symbol in the equations, ⊙. I thought matrix multiplication of neural networks always involved matrices that matched ...
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What is the generalization of binary/boolean matrix factorization to fuzzy logics called?

Given a matrix of boolean values $\mathbf{X} \in \mathbb{B}^{M \times N} = \{\top, \bot\}^{M \times N}$, the binary/boolean matrix factorization (BMF) problem is to find $\mathbf{U} \in \mathbb{B}^{M \...
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How do I approach this problem?

Let's say I have a dataset with multiple types of multiple ingredients ($salt_1$,$ salt_2$, etc). Each $n\text{-th}$ variation of each ingredient vs flavor may be represented by an $n \times k$ matrix ...
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1answer
224 views

How do I perform K-Means clustering of the Olivetti Dataset

This Question pertains to Matrix Factorization and the full question is given below. Provide for k-means clustering of the Olivetti dataset the following visualizations: A scatter plot of the r = 2-...
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312 views

How to create a model and make predictions with LightFM?

I've been researching on how to develop a hybrid recommender system for a simple book dataset, the main goal is to use both explicit data (purchases) and latent factors (features) to make the ...
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Training a cosine similarity matrix for similar text recommendation

I'm working on similar movie names recommender system. I have a dataset of only movie_titles that I converted into matrix using tfidf and then computed the cosine ...
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1answer
157 views

Intuitive explanation of difference between PCA and SVD [closed]

Can someone explain the difference between SVD and PCA with real life example?
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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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126 views

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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Mobile App Recommendation: How to get the rate of a specific user submit for a specific application [closed]

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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1answer
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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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166 views

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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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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168 views

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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887 views

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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1answer
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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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227 views

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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51 views

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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1answer
62 views

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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430 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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316 views

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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1answer
56 views

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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2answers
108 views

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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1answer
373 views

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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1answer
694 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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1answer
137 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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1answer
895 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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1answer
107 views

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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397 views

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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148 views

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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734 views

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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1answer
322 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 ...