Dimensionality reduction refers to techniques for reducing many variables into a smaller number while keeping as much information as possible. One prominent method is [tag pca]

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Is large scale PCA even possible?

The PCA algorithm assumes that the input matrix columns are with mean zero. This can be achieved easily, but when the input matrix is sparse, the centered matrix will now longer be sparse, and will ...
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Embedding in machine learning

What does word 'embedding' mean in machine learning? As I understand it is finding intrinsic dimensionality of the data. But how it works practically? Specifically, how does Gradient Boosted ...
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Evaluate output of different dimensionality reduction methods

I used PCA, ICA, and FA to perform dimensionality reduction on my data. How can I measure which method performed best? If I reduce my data to 3 dimensions and plot it, what type of trends would ...
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How to quantify performance of Linear Discriminant Analysis (LDA)?

I have implemented Linear Discriminant Analysis (LDA) for dimensionality reduction in C. But I don't know how to quantify performance of the LDA. Could someone help me?
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Techniques for plotting PCA projections in more than three dimensions

After running PCA on my data set, I noticed that using the three first eigenvectors, a separation between two different classes is still achievable (doing PCA on data from two classes). Unfortunately, ...
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Principant Component Analysis being too slow (MLPY Python) [migrated]

I am using the PCAFast method from the MLPY API in python (http://mlpy.sourceforge.net/docs/3.2/dim_red.html) The method is executed pretty fast when it learns a feature matrix generated as follows: ...
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Uniformly sampling principal component scores to explore response surface

New simpler version of the question Consider a sample $\mathbf{X} \in \mathbb{R}^{n\times p}$ of $n$ points in $\mathbb{R}^p$ with $p$ small, say $p=5$, and $n$ large, say $n=3000$. Because they are ...
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Supervised dimensionality reduction

I have a data set consisting of 15K labeled samples (of 10 groups). I want to apply dimensionality reduction into 2 dimensions, that would take into consideration the knowledge of the labels. When I ...
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Would PCA work for boolean (binary) data types?

I want to reduce the dimensionality of higher order systems and capture most of the covariance on a preferably 2 dimensional or 1 dimensional field. I understand this can be done via principal ...
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How to deal with different sizes of sentences when giving them as input to a Neural Network?

I am giving a sentence as input to a tree structured Neural Network, where the leaf nodes will be the word vectors of the words in the sentence. That tree will be a binarized constituency(see the ...
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For a low-rank regularized PCA, what is the limit of dimension reduction for a given p and n of data?

Here p is the dimension of data, and n is the number of data rows, so the data matrix is a $n∗p$, and if we use PCA for dimension reduction, and in this case it is a low-rank regularized PCA, what ...
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“Balancing” principal components

I apologize in advance for the poorness of my statistics and mathematics. I am doing PCA on data (emission spectra) that I know a priori should have two strong components (there are two fluorescent ...
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Dimensionality Reduction on a single Character Vector

I have a dataset I'm using to predict a binary outcome variable with 6 columns. Five of them are 10-30 level categorical variables with information about the user, e.g. job function, industry, ...
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Looking for methods to compare two knowledge bases

I'm working on a model for communication between two computer agents to generate collaborative narratives. These agents have different knowledge bases (KB) and I'm interested on determining how ...
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How does t-SNE slow down with increasing number of dimensions?

I'm trying to understand the computational bounds of t-SNE. It's learned with SGD, so it'll have to go through some number of gradient-descent iterations. We can ignore that here, and focus on the ...
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Sparse features and dimension reduction

Let sparse feature be a feature which values are subsets of some set. For example, the set of countries from which user logged to server is a sparse feature, because for each user we've got the set of ...
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Nonlinear dimensionality reduction (sample size is smaller than number of features)

One question for the nonlinear dimensionality reduction. I have 800 samples and 4900 features for a regression problem, 80% for training and 20% for testing. I have tried linear PCA to reduce it to ...
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What are the differences between autoencoder and t-SNE?

As far as I know, both autoencoder and t-SNE are used for nonlinear dimension reduction. What are the differences between them and why should I use one versus another? thanks!
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Does rank of observation matrix tell anything useful when applying machine learning?

Suppose I have an observation matrix of size $N \times M$ where $N$ is the number of samples and $M$ is the number of variables. If the rank of the observation matrix is $R<M$, does it tell ...
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What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top ...
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Using k-means for reducing the size of the training set of a Kernel SVM

I have a classification problem with the following characteristics: a few million data points around one hundred features non-linearly separable Training a SVM with an RBF Kernel is not feasible ...
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Doubt with a distance based Redundancy analysis

I conducted a distance based redundancy analysis (dbRDA) to explore the relevance of some environmental variables in explaining the patterns of the distribution (i.e., spatial and temporal) of two ...
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154 views

Why is the curse of dimensionality also called the empty space phenomenon?

The curse of dimensionality refers to the fact that the huge number of correlated features tends to increase the complexity of the treatment that has to be applied to the data set. This is also called ...
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How to add a third variable to a bar plot?

I'm trying to find the best way to show the following data: ...
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Practical applications of dimensionality reduction methods: Filtering, Wrapper, Embedded models

Filtering is basically sorting some features and picking top performing ones. Where wrapper in wrapper we go through unused/used features add/remove some of them and test performance over validation. ...
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How to measure loss of performance of clustering by applying dimensionality reduction

Let's suppose I have a given dataset with $n$ features. Having a data-centric approach, I would like to measure the loss of performance of applying a given dimensionnality reduction technique, for a ...
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Isomap and Local MDS- embedding to linear spaces or not?

In Section 14.9 [1], it is said that Isomap and LocalMDS are embeddings into non-linear manifolds. The embedding is clearly a non linear operation, thus worthy of being NLDR. But As both Isomap and ...
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Similarities and dissimilarities in classical multidimensional scaling

I am having trouble reconciling between several terms in MDS. According to [1], Section 14.8, Classical MDS takes similarities as inputs. In [2], also cited in Wikipedia, Classical MDS takes ...
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Reducing number of variables for Independent Component Analysis

Say I have a dataset with $n$ observations of $p$ random variables. Since $p$ is "large" (mine is 72), I would like to perform a fastICA only on a subset of $k$ variables, maintaining the same number ...
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45 views

Naive Bayes Binary Classification with Binary Features

I have a dataset with two classes $C_0$ and $C_1$. I have around $10$ to $20$ features that take binary values (either $0$ or $1$). My dataset has around $10000$ instances, with only a hundred of ...
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Structure of semantic relationships using Latent Semantic Analysis [closed]

I am struggling to answer the below question: How would you describe the structure of semantic relationships among the terms from a document collection using principles of Latest Semantic Analysis? ...
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Principled way of collapsing categorical variables with many categories

What techniques could I use to optimize the collapsing of many categories to a few, for the purpose of using them as an input to a statistical model? Consider a variable like college student major. ...
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238 views

What's wrong with my derivation on stochastic neighbor embedding?

I've been reading the well-known stochastic neighbor embedding [https://www.cs.nyu.edu/~roweis/papers/sne_final.pdf] for a long time. And I've been trying to derive the gradient of its optimization ...
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Classifier with variable number of features

I am trying to make a classifier when each sample has a variable number of features. An example of how this could occur is, for example, if the features are the purchases (type, dollar amount, etc) ...
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PCA/MFA for (graphical) dimension reduction: what to do with very small explained variance?

I ran a Multiple Factor Analysis on a data set with 3,924 rows and 96 columns, of which six are (unordered) categorical, with 12-14 categories in each, and the rest are numeric, mean-centered and ...
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How To Determine The Number Of Dimensions To A Machine Learning Problem

I have a bit to learn about machine learning, so please pardon me if I am asking the wrong type of question. I have read some about neural networks and SVMs, so I'm not completely in the dark. I am ...
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Interpreting standard deviation for PCA

I'm running PCA on my dataset using r and need some help interpreting the standard deviation results. Here are the results ...
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How to interpret PCA plots made using R [duplicate]

I'm using PCA for the first time and just experimenting with it. I used PCA on my dataset that can be found here ...
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Is there a known relationship between the Intrinsic Dimensionality of a dataset and the VC dimension of a model?

We know that the Intrinsic Dimension of a dataset gives the low dimensional sub manifold in which the real data distribution lies. On the other hand, the VC dimension of a model gives the bounds for ...
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Why is feature normalization important in PCA? [duplicate]

If feature normalization is not performed, does the algorithm give incorrect results or is it it inefficient or both?
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Forward sequential feature selection improving classifier performance?

I was in a bit of a conversation with a co-worker about using forward selection. My training data is on order of ~6,000 w/ dimensionality of 1,200, and testing data on order of ~3,000. Currently, I'm ...
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Manifold learning: does an embedding function need to be well behaving?

I am trying to learn about manifold learning techniques; a family of methods in machine learning. According to this idea, there is a low ($d$) dimensional, hidden space where the real data generation ...
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Two broad categories of dimensionality reduction

As a starter in dimensionality reduction (DR), I recently acquired the following understanding. There are two very broad categories of DR techniques: We can compute an analytic form of mapping from ...
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What is the heuristic to decide number of components for LDA dimensionality reduction?

In the PCA case, I prefer to plot the variance and choose number of components regarding that plot's breaking point. In the LDA (linear disriminant analysis) case, what can be used for such an ...
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How to determine which variables need to be trimmed in PCA or Factor analysis?

Background: I'm working with log returns for about 400 tech stocks. I want to use PCA to reduce these into principal components (Internet companies, software developers, circuit board manufacturers, ...
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How can top $k$ principal components retain the predictive power on a dependent variable?

Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from ...
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Standardizing dimension reduction output

I understand that data is (typically) standardized (i.e. zero mean and unit variance) before dimension reduction technique such as PCA/LDA is applied. In addition to this, would it ever make sense to ...
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What is best practise for dimensionality reduction in rows of data

I was wondering what was best practise for dimensionality reduction in observations (as opposed to features) in a data-set? I often have data comprising of a multiple, random number of observations ...
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Can I apply factor analysis on multiple choice questions?

I am looking to validate a questionnaire and would like to know if I can use factor analysis on the multiple-choice questions (MCQ). Also, I have another section where I am asking about participants ...
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When should I use feature selection and when should I use dimensionality reduction techniques?

When should I use feature selection and dimensionality reduction? I know that feature selection is different from dimensionality reduction. But I don't know under what circumstances should I use ...