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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Dimension Reduction to a Relative Single Value After PCA in R?
After reducing the dimensions of a matrix using PCA, I want to transform the "big" components (i.e. they cumulatively account for 90% of the variance) of each row into a single value. The value does ...
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35 views
What kind of attribute selection methods exist for high-dimensional regression data?
I have a 10,000 dimensioned dataset where all attributes are numeric values. I would like to select the best e.g. 50 attributes out of 10,000 so that I can run regression algorithms on it.
I've tried ...
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58 views
Mapping data points to a circle
I have some $d$-dimensional data points ($d \ge 2$). I want map them to a circle such that locality is preserved as much as possible.
I know that PCA only maps points to a line ($d'=1$) or a plane ...
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16 views
seeking advice on dimension reduction for spacial and time-series data
I have 200 data sets, each of them has roughly 600 rows with some exceptions (some have about 2000). Each data set represents data collected from a test subject, and the data in each one of the 200 ...
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2answers
98 views
Basic question re PCA and dimensionality reduction
OK, I get that PCA can be used for dimensionality reduction but there's something basic escaping me.
Let's say I have a feature set $F$ of $N$ features. After I run PCA which of the following are ...
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84 views
Is there a principled approach to dimensionality reduction?
Background
I have walked around my office environment with a video camera. From these image sequences, I wish to determine whether or not there is a 2D embedding that approximates the camera's ...
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32 views
High Dimensional Data, Multicollinearity, and Skewed Dependent Variable - a good approach?
I have a regression problem that has three key issues I am trying to tackle. The first is the data is a p >> n problem, e.g. I have about 1500 features but only about 150 examples. The second is that ...
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29 views
Noise in clustering of high dimensional sparse data
Questions:
1) How to detect noise variables in high dimensional data?
2) Does the method that is presented below make sense?
3) What clustering methods are most insensitive to random variables in ...
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42 views
Dimensionality reduction with locality-sensitive hashing
I have a conceptual understanding of locality-sensitive hashing (LSH) in relation to near-neighbour search. However, the articles that I have read so far seem to gloss over the details of how LSH can ...
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40 views
Reducing the dimension of an embedding
Let $O \in \mathbb R^{p\times m}$ be a data matrix of observations.
Suppose we are given a model $\mu : \mathbb R^n \rightarrow \mathbb R^m$ which is able to approximately fit the observations. Fix ...
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1answer
37 views
Nonlinear manifold learning and distances between projected points
If I use a manifold learning method to project some data points into a low dimensional space, what will be the distances between the projected points? Can I use Euclidean distance? If the distances ...
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1answer
62 views
Plotting high dimensional data
I want to plot high dimensional data on x y plane. For that I know three methods: Principal component analysis (PCA), multidimensional scaling (MDS) and a method from spectral graph theory (using the ...
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304 views
Visualizing high dimensional data
I have samples of two classes which are vectors in high dimensional space and I want to plot them in 2D or 3D.
I know about dimensionality reduction techniques, but I need a really simple and easy to ...
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3answers
81 views
soft question - Why and when is classification useful
From What I understand about classification is that it is used to distinguish unlabeled data points in a collection. So if we have data which is labeled(age, height, weight,...) then we don't need ...
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58 views
How to reduce dimensionality of vector?
I have a set of vectors. I'm working on ways to reduce a n-dimensional vector to a unary value (one-dimensional), say
(x1,x2,....,xn) ------> y
This single value needs to be the characteristic value ...
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1answer
80 views
feature selection vs feature extraction
As per my understanding in dimensionality reduction, Feature selection chooses a subset from a list of available variables and, Feature extraction transforms available variables into lower dimension. ...
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106 views
Dimensionality Reduction Algorithm for Large Dataset?
I have a reasonably large (5k variables x 120k cases) that I'd like to run a dimensionality reduction algorithm on. I tried doing a simple Factor Analysis on it in SPSS, but it (predictably) barfed on ...
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1answer
72 views
What is the dimension (k) of these regression models?
I am attempting to use Akaike's Information Criterion to select the most appropriate model for some data. This means I need to find the likelihood of my data under various models, compute the AIC ...
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65 views
Interpretation of Scree plots and Boruta Outcomes
I have 37 features in my dataset. I used Boruta package in R and according to its analysis, all the features are "important" and should be retained. I examined this result of Boruta and found that if ...
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70 views
Variation explained by single variable
I’m trying to find a way to measure how much a single variable ‘summarizes’ a full set of continuous variables. For instance, in a PCA the first principal component will explain a certain percentage ...
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2answers
98 views
curse of dimensionality & nonparametric techniques
I have seen it many times in a number of articles that nonparametric techniques are subject to the curse of dimensionality, which may lead to the failure of these methods. Why does this happen? Could ...
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60 views
Reduce matrix size for hierachical clustering
I have 500.000 measurements (rows) for 20 samples (columns) and I want to do hierarchical clustering to see of I can detect samples groups in the data. Clustering on the columns works fine in R:
...
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3answers
108 views
Series dimensionality reduction for classification Input
I am looking to construct a predictive model where the outcome variable is binary and the input is time series. To make it more concrete, the model will predict if a customer churns (left the company; ...
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64 views
Finding the projection used in multidimensional scaling
Background
I have a set of data points in high-dimensional (512D) space that I wish to map to 2D for visualisation. I am interested in observing in 2D the (approximate) relative distances between the ...
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3answers
272 views
Does PCA followed by LDA make sense?
This is a question about classification. I am a neuroscience student with little experience of classification methods and I'd be grateful for any advice about the best way to implement a linear ...
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1answer
70 views
Explained variance of non-negative matrix factorisation
How can I calculate R2 or another measure of explained variance for non-negative matrix factorisation. Currently I calculate the total sum of squares (TSS) as the sum of the squared distance of every ...
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87 views
Factor analysis for categorical target variable
I'm doing some research into factor analysis and I've hit that barrier where I don't know what search terms to use.
I'm trying to see if something is possible. Basically I have a data set with ~100 ...
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2answers
126 views
Evaluation of k-means output for >3D
I'm implementing the k-means algorithm (in R Map-Reduce) and I wanted to verify if the output I'm getting is close enough to the true centroids of the cluster. This is how I'm verifying with a 2D ...
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55 views
Dealing with non-flat, unbounded data on a single observation
I'm currently trying to generate a number of (rudimentary) models to perform classifications (or get probability distributions through classifications).
Let's say that I have a particular video from ...
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1answer
437 views
PCA and SVD, R prcomp
I am trying to replicate Shalizi's NY Times PCA example found in his Advanced Data Analysis with an Elementary Point of View book. I found sample code and data here
...
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1answer
60 views
ISOMAP for classification
I implemented ISOMAP and I plan to use it as a feature extraction technique for a classification task.
My problem is that although I can map the training data into a lower dimensional space, how can ...
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1answer
40 views
Does isomap give possible new bases with respect to importance order as PCA?
I am running isomap for feature reduction and I want to see what number of features are best for classification with experiments at different number of features. Do I need to run isomap for each try ...
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1answer
105 views
In non-negative matrix factorization, are the coefficients of features comparable?
I'm using Alternating Nonnegative Least Squares Matrix Factorization Using Projected Gradient. The result (I use 2 as rank) is like this:
...
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1answer
54 views
Why are eigenvalues so significant in DR techniques?
I've read PCA and few more dimension reduction algorithms and all of them talk about using eigen values and matrix operations. How are they so significant in discovering geometrical significance of ...
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43 views
Orthogonalization for dimensionality reduction
There are some methods like singular value decomposition (SVD), principal component analysis (PCA), factorial analysis and many more that are used to reduce a high-dimensional dataset into fewer ...
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76 views
How to interpret this output in Dimension Reduction?
I'm running Linear Discriminant Analysis on a dataset and then performing clustering on it. I'm reducing it to dimensions 2,6,10. On comparing metrics like Accuracy and Normalized Mutual Information, ...
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2answers
169 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
2k views
How to interpret factor scores saved as Reg variables in SPSS?
How do I interpret the factor scores that I save as Regression variables with SPSS? I have 30 attribute variables with reponses such as extremely important, very important, important, not that ...
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37 views
Error analysis and measurement of uncertainty of the dimension reduction methods
I have got a problem of dimension reduction methods: how to do an error analysis and uncertainty measurement for the dimension reduction results?
For example, the Laplacian Eigenmaps method solves a ...
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1answer
193 views
Deciding about dimensionality reduction with PCA
I have 2D data (I have a zero mean normalized data). I know the covariance matrix, eigenvalues and eigenvectors of it. I want to decide whether to reduce the dimension to 1 or not (I use principal ...
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2answers
97 views
How to evaluate dimension reduction from n-space to d-space?
I'm performing dimension reduction on some data sets and would like to evaluate how has a particular dimension reduction algorithm performed in terms of how much data is lost. If we are given 1000 ...
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1answer
442 views
Dimensionality Reduction using PCA, with SVD of correlation matrix
I have computed a correlation matrix from certain data set of dimension 6
The correlation matrix is:
...
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2answers
152 views
How can you make linear discriminant analysis reduce dimensions to the number of dimensions you are looking for?
Let's say I have a $m \times n$ matrix where $m$ is the number of points and $n$ is the number of dimensions. I would like to give a target dimension parameter which is let's say d. d can be a set of ...
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1answer
307 views
Assumptions of factor analysis
I want to check if I really understood factor analysis (FA), especially assumptions that are made before (and possibly after) FA.
Some of the data should be initially correlated and there is a ...
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2answers
115 views
In non-negative matrix factorization, does the first N eigenvector have N greatest variance?
I know for PCA, it's true that the first N eigenvectors have N greatest variance.
But I'm not sure whether that's also true for NMF(Non-negative Matrix Factorization). For example, this ...
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1answer
70 views
What alternatives are there for dataset reduction beside the random sampling?
I have 3 millions instances with 30 features each and I am trying to reduce it in a sensible size for my computer for a classification problem. What are possible methods I can use to reduce the data ...
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35 views
Interpreting “elliptic” shape in visualization of high-dimensional dataset, e.g. COIL-20?
There exist an image dataset referred to as COIL-20. There are several paper that describes different dimensionality reduction methods and apply them to produce a 2d plot of this dataset. These ...
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3answers
101 views
How can I separate each of 100 observations into groups as determined by the data?
I have 3 covariates for 100 observations. How can I separate each of my 100 observations into groups as determined by the data. I was thinking clustering. However, apparently, I need more than 3 ...
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186 views
Clear description of PCA using SVD
After reading thousands of articles on PCA and SVD, using them in a number of programming frameworks and even implementing similar techniques (like Random Indexing) I found out that I still have ...
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108 views
What are features that distinguish clustering, blind signal separation and dimensionality reduction?
In terms of input -> [process] -> output what are features that distinguish clustering, blind signal separation and dimensionality reduction?
From this ...
