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

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How to implement density-based clustering?

I’m looking to implement density-based clustering with R or Mathematica on a giant file (600,000 points on a 3 billion x 3 billion plane). Is DBSCAN the right method for data that is this sparse? I am ...
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20 views

What is the advantage of sparsity?

In many problems the solution is sparse and the authors of methods usually present it as an advantage. How could one leverage the sparsity in general? Why is an advantage?
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81 views

Random forest and LASSO regression both give different variable importances

I have a dataset with 163 observations (all countries in the world with population > 1000000) and 290 variables related to their disease burden and performance. Because there are more variables than ...
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22 views

Torch - SparseLinear nn to handle large inputs and large output for a prediction problem

I'm pretty new to the magic of torch7 and seek your help/advice for a problem of mine. Context: I am working on a prediction problem. We observed a certain pattern in our values and would like to ...
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56 views

Problem in bootstrap analyses (boot package)

I am trying to understand why a subset of 2-parameter binary logistic IRT models I am bootstrapping estimates for (i.e., the discrimination and difficulty parameter estimates) give rise to the same ...
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1answer
94 views

Plausbility of parameter estimates in a 2PLM IRT model: A case of inherently sparse data

This question relates to my previous query regarding differences in IRT parameter estimates (2PLM model) between the ltm package in R and the Mplus latent variable program which is linked here: 2PLM ...
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25 views

Extension to SAFE screening rule for Lasso

In El Ghaoui et al. (2010), "Safe feature elimination in sparse learning" and following works, screening rules are derived for Lasso (as well as other L1-penalized problems): $ \min_w \|y-X w\|^2 + \...
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1answer
182 views

How To Deal With Large Numbers Of Categorical Predictors

I have three data sets that, when joined, have O(320) independent variables for a classification problem. Principal component analysis (PCA) seems out of the question because the data is mostly ...
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2answers
45 views

Linear regression on large sparse feature set

I have a sparse feature matrix with 50K observations and 150K features. All features are binary. On this I have to run a linear regression. I want just a decent fit. Data: Let us consider training ...
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7 views

Tunable sparsity parameter in sparse matrix approximation

I'm mostly casting around for what terms I should be looking for in the literature, but specific recommendations are also welcome. I have a sparse binary matrix in a collaborative filtering scenario. ...
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6 views

What does a structurally spare model mean especially with reference to random forests?

The other day I heard someone say that the model of Random Forest is a spare? I tried doing some digging but didn't come up with anything that I could immediately relate to. Would appreciate any ...
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20 views

Regularized cox survival model with time varying covariates and sparce matrix in R

I was wondering if there is a survival framework in R (or any other language for that matter) for doing the following: Fitting an extended (i.e., time-varying covariates) cox survival model ...
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1answer
11 views

what is sparse solution?

This graph is about panelty least square method, and it is said that once a parameter hits zero, it remains zero for larger garmma, and this results in a sparse solution. I am wondering what it means ...
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67 views

Autoencoders & Predictive sparse decomposition (PSD) & Alternating Direction Multiplier Method (ADMM)

I am studying Deep Learning by Ian Goodfellow, Yoshua Bengio and Aaron Courville. In Chapter #14 Autoencoders the authors write Internally, it has a hidden layer $h$ that describes a code used to ...
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9 views

Are there kernel-based one-class sparse kernel-based outlier detection methods, e.g. one-class Relevance Vector Machine?

I have a commercial outlier detection problem in moderate dimension (8-25). We have a limited number of true positive tags and can roughly evaluate performance of various methods. So far, the 1-...
4
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3answers
130 views

Goodness of fit test on sparse contigency tables with high dimensionality

I have a vector of size 1x3500, which can be viewed as the 'known distribution'. It is simply a table of counts across 3500 groups (i.e. a contingency table). I also have $N$ other vectors of the same ...
3
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60 views

Compressed Sensing: Missing Fourier Coefficients?

This question is regarding the problem of reconstructing a signal given only a subset of the Fourier coefficients are observed: $$\min_x \|x\|_1 \text{ subject to } y = Ax$$ where $x = (x_1,x_2,\...
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15 views

Technical Question about V2 Sparse Regularisation RBM

I am implementing my own RBM in matlab, such that I can adapted them such that I can include as much as I can for my PhD. I am validating my code with several other implementations I am finding on the ...
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23 views

Showing a bound on the $L_2$ error in the N-sparse approximation of a vector

This is a supposedly 'trivial bound' from Donoho's Compressed Sensing paper - trying to figure out where it comes from. Assume that $\theta$ is a vector that obeys the following constraint for some $...
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3answers
251 views

Invert a sparse covariance matrix

I have a postive definite symmetric covariance matrix which looks like this: Note that all A,B,C,D,E,F,G are also poitive definite symmetric covariance matrices I want to find an easy way were I can ...
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1answer
123 views

User segmentation by clustering with sparse data

Imagine that I have 100k users and 1k categories. For each user, up to 5 categories, I know how much money they have spent. Obviously my data is very sparse. Now I want to group users by the money ...
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1answer
94 views

Dimensionality reduction for high dimensional sparse data before clustering or spherical k-means?

I am trying to build my first recommender system where i create a user feature space and then cluster them into different groups. Then for the recommendation to work for a particular user , first i ...
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36 views

Sparse markov chain

I have an instance (path) of discrete time Markov chain of length 10 millions observation with about 1.3 million of states. I am almost sure that the transition probability matrix will be very sparse. ...
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18 views

Markov process with only $n$ most significant transition probabilities known

Suppose I want to simulate a Markov process with a discrete state space. Normally, I need to have all the transition probabilities known. However, in my situation, I can only measure the top $n$ most ...
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2answers
87 views

Theoretical justification for bag of words

Bag of words and visual bag of words are successful machine learning approaches. Does anyone know of a theoretical justification for why / when they work? What I am trying to explain is the good ...
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26 views

Regression - one input variable is mostly 0

Background: I have data obtained by sampling real-world, physical quantities. Say there are $10$ features. One of them, call it $x_1$, due to the nature of the sampling, is 0 most of the time. But ...
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17 views

what is the method in dictionary learning which does not have a overcomplete dictionary?

what is the method in dictionary learning which does not have a overcomplete dictionary? and what is the difference in minimization between these two methods (one using overcompelte dictionary and ...
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27 views

Using Proc distance with a very sparse matrix

I have a large sparse data set and I would like to apply segmentation of my customers. To give you an idea, I have more than 100 variables and 2.2 mln rows. Breakdown of my variables are as follows: <...
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55 views

Entropy weighted KMeans finishes after 1 Iteration. No Entropy in Data?

I want to cluster high dimensional sparse data (100k rows and 2k columns, 10-20 non-zero values per row). Each row represents a person and each column an attribute this person does or does not posess ...
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1answer
66 views

Best way to handle sparse + non-sparse data to create a model

I'm wondering what is the best way to handle sparse+non-sparse data in e.g. a Ridge regression using scikit learn. Ridge can handle both sparse and nonsparse data. Imagine something simple as a ...
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1answer
180 views

efficient “dot” product of two sparse vectors with uncertainty

I'm interested in extensions or analogs of the vector dot product that apply to sparse vectors in the case of uncertainty in the abscissa. The vectors I deal with are often of large (100,000 or 1,...
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1answer
769 views

Gradient boosting decision tree implementation

I am willing to implement my own GBM. I have been looking - unsuccessfully - for a clear article describing the implementation of gradient boosting machine for decision trees. Sources like this are ...
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62 views

Clustering algorithm advice for extracting key features in sparse data

I have the following dataset: consider a dataset $X$ of $1400 \times 600$. The rows represent households at time $1 \leq t \leq 14$. So I have $100$ households. The columns represent the programs that ...
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124 views

Miss Forest & Iterative PCA : How to handle very sparse matrix imputation?

I am currently benchmarking matrix completion methods (k-NN, RandomForest and iterative PCA) on multivariate normal data in which I introduce a certain proportion of NA (5 to 95%). My performance ...
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241 views

Typical range of values for TFIDF

I am working on a text corpus. Each line contains between 10 and 50 words. There are around 25 000 words in the whole text and 1 000 000 lines. I turned this corpus into its tf-idf representation. I ...
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1answer
316 views

Is large scale PCA even possible?

The principal component analysis (PCA) algorithm assumes that columns of an input matrix have zero mean. This can be achieved easily, but when the input matrix is sparse, the centered matrix will now ...
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2answers
196 views

Finding pattern from sparse matrix

I have a large sparse matrix which represents whether the action is happened or not. Each columns represent each action. Each row represents time. The data is collected for every 15min. Zero in the ...
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127 views

How to go from sparse matrix to linear regression model (using SVD)?

I am trying to replicate the Kosinski, Stillwell, & Graepel (2013) study about predicting private traits and attributes from Facebook like data for study purposes. First I have admit, however, ...
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77 views

Kernel K nearest neighbours with sparse data

I have a big sparse matrix (around 5 million of lines, 20 000 predictors), and I would like to run a kernelized k-NN on it. However, I don't know how to scale the data properly. So far, I have scaled ...
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142 views

Feature scaling for non-negative sparse data

Imagine you have many observations on which you want to run a classification algorithm. Each observation is characterized by a matrix of non-negative values. For all observations 90-98% of the values ...
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1answer
326 views

What's the best (Google chart) visualisation for displaying sparse timeline data across thousands of “columns”

I am trying to visualise a sparse dataset but am finding it hard to fit it into the standard categories of charts. I'm a developer building with Google Charts and I really want to stick with that ...
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1answer
131 views

Does the opposite of nested cross-validation make sense?

I'm asking the question from a machine learning point of view. I have a dataset with relatively high sparsity, so if I use nested cross-validation for my feature tuning and evaluation, that is tune ...
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39 views

Instances of sparse covariance matrices

I am trying to find large datasets with inherently sparse covariance matrices, to be tested with our algorithm. Basically, we will take the sample covariance matrix and enforce some structured ...
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42 views

Sparsity of the matrix

We got a matrix of 500 users and 30 tracks. This matrix is complete full (it means every user rated explicit all 30 tracks). Every row is a combination of user id, music id and rating. Every user + ...
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112 views

sparse covariance/correlation thresholding

In our project, we would like to do some optimization on sparse matrices. The idea is to scrape massive amounts of data, form a covariance/correlation matrix, and form a sparsity pattern basically by ...
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1answer
51 views

What are the techniques to deal with classifying sparse categorical features?

Suppose I have a group of features each one is sparse with a few number of values (1-10) what are the required preprocessing steps required to avoid degradation of the performance of the classifier ...
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172 views

Problems using pcr (from pls library) in R with large number of qualitative variables

I'm trying to classify a variable into either 0 or 1, using 50 factors, with a sample size of 2000. 25% of the dependent variables are 0 and the rest are 1. Of these factors, 30 are categorical. I've ...
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146 views

Handling sparse document term matrix

I am working with a corpus of several thousand documents (41,732) however the documents tend to be short (the median number of terms per document is 3) resulting in a sparse document term matrix. ...
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1answer
35 views

Spectral norm of a sparse Gaussian matrix

Suppose $G$ is an $m \times n$ matrix such that each entry of $G$ is a standard normal variable. We know that the spectral norm of $G$ scales as $\sqrt m + \sqrt n$. Now, given a set of indices $S$ ...
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Individual factor significance in multilevel sPLS-DA

I recently was asked by reviewers to "include p-values" with my multilevel sparse partial least squares analysis. In brief, I have a nested design with two factors, say treatment and sampling region. ...