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

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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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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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81 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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10 views

Dictionary matrix for online sparse coding doesn't learn [migrated]

Following Online Dictionary Learning for Sparse Coding and using an inference function I've found on the Stanford's website, I'm trying to online learn a Dictionary matrix. Tested both on resized ...
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59 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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31 views

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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20 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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23 views

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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33 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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28 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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175 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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144 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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91 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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52 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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10 views

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
92 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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61 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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35 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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42 views

Classifying a sparse and big dataset

I have a large dataset of sparse data. I want to build a model (preferably one that takes a quite small amount of time to respond) that - for any given input - it returns the record(s) from the ...
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325 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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155 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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381 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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41 views

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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66 views

Methodology of modelling sparse events

Let us say that we have a process that generates sequences of the following form: ...
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307 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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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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271 views

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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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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118 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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55 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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229 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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397 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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335 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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65 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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44 views

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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66 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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196 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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225 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 ...
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217 views

Sparsity-inducing regularization for stochastic matrices

It is well-known (e.g. in the field of compressive sensing) that the $L_1$ norm is "sparsity-inducing," in the sense that if we minimize the functional (for fixed matrix $A$ and vector $\vec{b}$) ...
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490 views

Hybrid (K-means + Hierarchical ) clustering

I have a huge dataset (50,000 2000-dimensional sparse feature vectors). I want to cluster them in to k (unknown)clusters. As hierarchical clustering is very expensive in terms of time complexity ...
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158 views

What are $\ell_p$ norms and how are they relevant to regularization?

I have been seeing a lot of papers on sparse representations lately, and most of them use the $\ell_p$ norm and do some minimization. My question is, what is the $\ell_p$ norm, and the $\ell_{p, q}$ ...
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Is there a (parametric) distribution over sparse symmetric, binary matrix-valued random variables?

The title says it all, really. I'm aware of the Wishart distribution for symmetric, nonnegative-definite matrix-valued random variables, and am looking for something along these lines, but for sparse ...
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Inducing sparsity in a Bayesian model

Can someone explain or point me to an introductory reference that deals with the notion of sparsity in Bayesian modeling? What does the idea of sparsity really mean? What does it mean to 'induce ...
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Euclidean distance is usually not good for sparse data?

I have seen somewhere that classical distances (like Euclidean distance) become weakly discriminant when we have multidimensional and sparse data. Why? Do you have an example of two sparse data ...
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1k views

Random forest implementation for sparse data

Is there an R random forest implementation that works well with very sparse data? I have thousands or millions of boolean input variables, but only hundreds or so will be TRUE for any given example. ...
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1answer
890 views

Using SparseM/Matrix Sparse Matrix in training SVM from e1071 returning different results from same data in standard matrix

Using sparse matrix objects in svm training in e1071 returns different results than running on the same data represented as standard matrix: ...
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Confused by MATLAB's implementation of ridge

I have two different implementations of ridge in MATLAB. One is simply $\mathbf x = (\mathbf{A}'\mathbf{A}+\mathbf{I}\lambda)^{-1}\mathbf{A}'\mathbf b$ (as seen ...