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

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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 ...
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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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5 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 ...
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121 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 ...
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52 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 = ...
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10 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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21 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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242 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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107 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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51 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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30 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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16 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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82 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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24 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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12 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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23 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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44 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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30 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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161 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 ...
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581 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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48 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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104 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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178 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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274 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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162 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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19 views

Quantile or distribution estimation for continuous variable from sparse matrix

I'm not sure where to start and desperatley need help. I've got a somewhat sparse data set and I'm trying to do either a quantile estimation or a distribution estimation for one continuous variable. ...
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111 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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72 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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19 views

Can I run an SVM on sparse temporal data without a regular time interval?

I have data of occurrences with timestamps that could be days or months apart. I'd like to enter the values natively as follows. Are there any SVM algorithms that can support such an input? day 1: ...
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36 views

Robust Sparse K Means clusters and valid index

I used the robust sparse k-means for clustering my dataset and I would like to calculate some distance-based statistics for evaluating my results. Should I compute them on the dissimilarity matrix ...
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11 views

Valid values for nvecs sparseDecom2

I hope this is the right place to ask, and that someone would know the answer I am searching for the optimal sparseness value to solve a sparse regression problem (using MRI data) that involve ...
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120 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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289 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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127 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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33 views

commonalities and differences among groups in a matrix (based on features)

I have a (rather sparse) matrix with 7 columns and 66 rows. Each column represents a user group, each row represents a feature, and each cell represents a weighted value (see note below). I'd like to ...
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143 views

How to input sparse feature

In theano everything is symbolic, so how to input sparse feature in , for example, neural network? The setting is: the task is text application. the input is a mini-batch. Since theano sparse module ...
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38 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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37 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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106 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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45 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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147 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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141 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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32 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. ...
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64 views

How to convert the objective function to canonic form of sparse coding?

As we know the conventional sparse coding problem (LASSO) is: $\min_{\alpha} \| X-D\alpha\|_F^2 + \lambda \|\alpha\|_{1} \tag{1}$ where $X$ , $D$, and $\alpha$ are data, dictionary and coefficients ...
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108 views

Generate Symmetric Positive Definite Matrix with a pre-specified Sparsity

I am trying to generate a correlation matrix $p\times p$ (symmetric p.s.d) with a pre-specified sparsity structure (specified by a graph on $p$ nodes). The nodes that are connected in the graph have ...
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125 views

Calculating means and confidence intervals when most data points are 0

I am looking at data set that has four groups. In each group, the data is mostly, 99+% of time, composed of zeros, but, when it is not zero it can be any float number (e.g., 0.01 to 921.2, with most ...
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426 views

How to build a predictive model with a billion of sparse features?

I am making a model to learn a dataset which has a big feature number and sparse samples (I am planning to use logistic regression). The feature number can be as big as 1,000,000,000. It is sparse ...
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492 views

Kernel SVM on sparse data

I have a sparse dataset where a lot of the columns (features) contain mostly zero values. Class labels are multiple discrete categories (10 classes to be precise). I'm wondering if this should trouble ...
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306 views

Logistic regression with sparse predictor variables

I am currently modeling some data using a binary logistic regression. The dependent variable has a good number of positive cases and negative cases - it is not sparse. I also have a large training set ...