A sparse matrix is a matrix where many of the elements are zeros.

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The name data sparsity in different applications

I am recently surveying the techniques or algorithms which handle the data sparsity problems in various fields. And I find quite similar name "data sparsity" or "sparse data" is used including the ...
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How to do if the most training data is sparse

Consider a problem like this You have a customer profiling application(say classic telecoms data) You have customer transactions(lots of them) you want to find rules There is a data element which is ...
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Using an odds ratio when data is sparse

Suppose I have around 20 exposures that potentially affect an outcome and I want to see which exposures have bigger impacts on the outcome. So I want to calculate each exposures' odds ratios by ...
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17 views

Utilizing A Correlation Matrix Derived from a Sparse Matrix

I have large correlation matrix in Excel that I'd like to use to inform my choice of explanatory variables in a multiple linear regression model. One problem is that the initial data was very sparse, ...
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25 views

LibFM sparse data format

Does the order of columns in the the sparse format matters in case of libfm ? Can I list the non zero components of X in libfm in any order in a row.
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27 views

Sparse ELM vs SVM

What's the difference between SVM and Sparse Extreme Learning Machine with Gaussian kernel proposed in the following paper:http://www.ntu.edu.sg/home/egbhuang/pdf/Sparse-ELM-IEEE-T-Cybernetics.pdf As ...
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22 views

Literature for Cross Validation on Sparse Data?

I've read a lot about Cross Validation to estimate prediction error, specifically for selecting the number of components in a PCA model (I'm not doing SVD/PCA, but it's very similar), but I can't find ...
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85 views

Clustering algorithms for extremely sparse data

I am trying to cluster an extremely sparse text corpus, and I know the number of clusters (my data is the title and author list of scientific publications, for which I already know the number of ...
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52 views

regression algorithms which work with sparse categorical predictors

I am working with a very sparse problem with a large number of categories per feature and I am currently looking for existing machine learning regression algorithm implementations which can either ...
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89 views

Sparse principal component analysis

Does anyone know where I can find an algorithm (as well as an R implementation of it) to carry out sparse principal component analysis?
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Heavy tailed distribution results in sparse random variable?

I often come across that, in Bayesian inference, to encourage sparseness, we should choose a heavy-tailed probability distribution as prior. AFAIK, in heavy-tailed distribution, it's more likely for ...
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1answer
38 views

Statistical Practices Using Sparse Data: Methods for Approximating Standard Deviation

Suppose I know that for a discrete, non-negative r.v. $X$ that $X | X \geq 1$ has $\mu = 3.3$ while when $X \geq 0$ has $\mu = 2.1$. That is, the subset of the population that already has a value ...
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134 views

Compute Shannon entropy between every row of a large, sparse matrix

I have a sparse, binary matrix of user (rows) and items (columns). Each element of this matrix is either 0 or 1: ...
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165 views

Machine learning techniques for spam detection, and in general for text classification

I am going to configure a system for spam detection. What I have is a dataset of labeled (spam/not-spam) strings containing, mostly, sentences. I have a background in machine learning techniques, but ...
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97 views

Selection of sparse principal components

Does anyone have experience with approaches for selecting the number of sparse principal components to include in a regression model?
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Clustering time-shifted sales time-series

I need to perform clustering and classification of time series of weekly sales of different products. My data are weekly sales of different products in differest areas (stores). The challenges on this ...
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39 views

Active set methods for group lasso?

When the solution is extremely sparse, probably the fastest method for solving LASSO regression is least angle regression, which starts from an all-zero solution and adds nonzero elements to the ...
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Random classification forests for extremely sparse response variables

I have a response variable that can be $A,B,C$. It is very sparse, meaning 99% of the sample is $B$ and the rest is approximately evenly divided between $A$ and $C$. How do I predict this variable in ...
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1answer
78 views

Sparse PCA/Dictionary learning when the features are extremely sparse?

I am trying to do sparse PCA/dictionary learning, that is decompose a matrix $X\approx UV$ where the loading matrix $V$ is sparse, usually enforced with an $\ell_1$ penalty (the difference between ...
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36 views

Optimal to sub-optimal sampling patterns

In the compressed sensing (CS) framework an incoherence property $\mu$ is used to quantify the correlation between a sensing matrix $\Phi$ and a representation matrix $\Psi$. This incoherence ...
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1answer
806 views

Clustering algorithms that operate on sparse data matricies [closed]

I'm trying to compile a list of clustering algorithms that are: Implemented in R Operate on sparse data matrices (not (dis)similarity matrices), such as those created by the sparseMatrix function. ...
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162 views

How exactly is sparse PCA better than PCA?

I learnt about PCA a few lectures ago in class and by digging more about this fascinating concept, I got to know about sparse PCA. I wanted to ask, if I'm not wrong this is what sparse PCA is: In ...
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137 views

R or python implementation of sparse PCA for p>n

According to this paper, there are 2 algorithms to perform sparse PCA. One is better if $p>n$. I need to run SPCA on a $2000\times12000$ matrix so I am looking for an implementation of this ...
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1answer
62 views

Interpretation of lasso recovery results

When people say that lasso regression can under certain assumptions recover "the support", i.e. non-zero regression weights, what does this mean? This cannot mean causal recovery, because Pearl has ...
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Sparse variable selection algorithms that account for parameter changes

I am variable selecting for a time-series forecasting model that has parameters sampled from a high variance sampling distribution centred near zero and that undergo changes over time. Each predictor ...
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1answer
128 views

How Can I use some variables selected by LASSO?

I am very new about statistics. So, please understand if my question is somewhat awkward, and please give me related any advice. I have some data set. X = 500 x 100 (500 observations x 100 ...
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1answer
100 views

Limitations of Cohen's kappa for sparse data?

Are there any limitations for using Cohen's kappa with sparse data? I need inter-rater agreement between 2 raters for ~15 items, and the data in the contingency table is quite sparse (0 in some cells, ...
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39 views

Apply double non-negative constrain on Sparse PCA

In Non-negative Sparse PCA, we apply a non-negative constrain in the coordinate matrix. Here I'm up to apply non-negative constrains on both the basis matrix and the coordinate matrix. I'm wondering ...
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485 views

Why such a poor result from sparse PCA R package?

I'm preparing to use R to perform sparse analysis on my data. I tried to get started with an ad hoc example, but the reconstruction result turned out really poor. I'm wondering if I was making any ...
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187 views

What's the tractable data size for Sparse PCA or LASSO?

I'm up to perform certain kinds of sparse decomposition methods on my dataset. However, I'm not sure: what's the tractable data size for the Sparse Decomposition methods? The dataset is a ...
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613 views

Validate cluster analysis in R

I am trying to validate hierarchical cluster analysis result following a paper by Guy Brock, et al. clValid: An R Package for Cluster Validation (pdf). Do I have to use all these methods? What are the ...
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Sparsity regularization for eigenvectors

One way to think about finding the eigenvectors of a matrix $A$ is that they are the critical points of the functional $\vec x^\top A \vec x$ subject to $\|\vec x\|_2=1$. To regularize this problem, ...
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Methodology of modelling sparse events

Let us say that we have a process that generates sequences of the following form: ...
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457 views

Cosine similarity on sparse matrix

I'm trying to implement item based filtering, with a large feature space representing consumers who bought (1) or did not buy (0) a particular product. I have a long tail distribution, so the matrix ...
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68 views

Issues with solving large sparse linear equations

I have some issues solving sparse linear equations $Ax = b$ My matrix $A$ is sparse with dimension of 5 million by 5 million. Actually, it is a combination of two matrices. One is tridiagonal and the ...
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Sparse PCA adjusted variance explained

In the original Sparse PCA paper Sparse Principal Component Analysis ZOU, HASTIE, TIBSHIRANI they describe a way to compute the adjusted variance explained by computing QR decomposition of the Z ...
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Getting rid of a huge categorical factor in multiple regression

I have a large regression problem with a lot of cases, but relatively few independent variables. One of them is a categorical factor with thousands of levels. Robust regression runs forever. In some ...
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What's the convergence rate when solving L1 regularized optimization via coordinate descent with tiny step? [closed]

Wondering if there is an established result for the convergence rate when solving L1 regularized optimization via coordinate descent with tiny step? By "tiny step" I mean the step is always set to a ...
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62 views

Why do Bayesian methods achieve sparsity via normal likelihood and Gamma hyperprior?

In the view of $\ell_1$ regularization, a natural way to incorporate sparsity into a Bayesian model is to add a Laplacian prior in my opinion. But instead of this, a usual fashion to handle sparsity ...
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126 views

Sparse hyperspace clustering

I have a dataset of M elements where every item is represented by a feature vector of length N where N is very large and only a small subset of N is bigger then zero for every item. So I have a sparse ...
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Automatic outlier detection in R

Our model processes millions of multivariate observations; manual outlier detection is impractical. I am looking for a method of automatic outlier detection. I have been trying to use R package ...
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59 views

Confusion related to convexity and non convexity of a problem

I was reading this paper related to sparse PCA enter link description here I didn't understand how they said that the function was convex or non convex I wanted to know how in the screenshot ...
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1answer
271 views

Sparse representations for denoising problems

I have read in a huge number of papers that sparse models (sparse coding, dictionary learning, sparse matrix factorization, ...) are good solutions for image denoising problems. I know that ...
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432 views

Using sparse inverse covariance matrix in estimating least squares coefficients

I am reading the paper introducing the graphical lasso, which is a way to estimate a sparse inverse covariance matrix. http://www-stat.stanford.edu/~tibs/ftp/graph.pdf Finding a sparse inverse ...
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468 views

Dimension reduction for sparse matrix for clustering

I'm looking for a Sparse matrix dimension reduction. I already used some feature selection methods like PCA but it doesn't give me good results. I want to apply mixture models for clustering my data. ...
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1answer
67 views

What is a sparse estimator?

Can anyone point me to a reference, either book or paper, where I can find the precise definition of sparse estimator? Thanks
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Enforcing sparsity on probability

I am trying to induce a probability distribution $Q$ by optimizing an objective function and am wondering how can one encourage sparsity for $Q$ while keeping the optimization convex. In particular, ...
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74 views

Sparse estimated data recommender system

Premise: For a product and a user, the system has to recommend him/her other non-users related with him/her that are most likely to be interested in that same product. Available data includes: ...
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213 views

Sparse matrix representation of a spline interpolation

I use spline interpolation within a statistical model, and the transpose of the operator turns up in the gradient of the log-likelihood. Let me set up some notation first. If $x_1 \ldots x_n$ are a ...
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1answer
276 views

Advice for a sparse high-dimensional regression strategy

I have a regression problem where I would like to predict values given several thousand sparse features. The general data set is an $n \times m$ matrix where each row contains a sample with a value I ...