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Refers to techniques for reducing a large number of variables or dimensions spanned by data to a smaller number of dimensions while preserving as much information about the data as possible. Prominent methods include PCA, MDS, Isomap, etc. The two main subclasses of techniques: feature extraction ...

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Doubt regarding PCA

I have 5 different independent variables, lets name 1 to 5. The 3rd IV has 10 sub-variables under it and 4th IV has 11 sub-variables in it. Whereas other 3 IV's have just two sub-variables (...
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Principal components: Can I interpret PCA as essentially a change of basis

I was hoping that someone could simply validate or correct my interpretation of Principal Components Analysis. There are a lot of questions on this site about Principal Components analysis--some ...
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How to cluster and reduce dimensionality of Barthel scale data

I 'd like to cluster subjects with their Barthel scale. It looks like below: Since the Barthel scale data is an ordinal scale and a likert-type rating data (given number of points assigned to each ...
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44 views

How to find the minimum set of vectors?

I have a set of vectors. For simplicity, suppose there are $n=20$ vectors and each has $p=5$ elements. These vectors are generated from some experiments, and so it is not very apparent how they are ...
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28 views

Example for Principal Component Analysis

Where principal component analysis can potentially be used ? some examples with some explanation would be great
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26 views

What does ICA return?

I am confused with ICA. With PCA I understood that it always gives the components with maximum variance. What does ICA return? Does it return components with maximum independence? How to find best ...
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1answer
12 views

Self-organizing map dimension

I just have a question on the chosen dimension of Self-organizing map. Typically, an SOM has a dimension of 2 or 3 but rarely larger than that. Is there a particular reason why this is the case?
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11 views

Gaussianity and Whitening in ICA - The feeling and intuition behind it

I understand what ICA does at a high level but in the cocktail party problem context. All the examples, articles I have read take a similar problem to explain ICA where the aim is to derive the ...
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6 views

optimality of LDA dimensionality reduction

typically when you do dimensionality reduction using LDA, you select $n_{class}-1$ vectors with largest eigenvalues as discriminants given the fact that you only need $n-1$ dimensions to classify $n$ ...
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98 views

How do I get the density of a region in a vector space?

I have a simple problem, which I think must have an easy solution. I have a vector space say with a 1000 dimensions for each vector. Now, I have a large number of sample vectors from this vector ...
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21 views

Dimensionality reduction for multivariate time series data?

I'm trying to perform dimensionality reduction on a multivariate time-series data set which gives information on the medical history of a group of 12000 patients. The data contains 19 different ...
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25 views

Linear Discriminant Analysis as Dimensionality Reduction very sensitive to Training Set size

I'm working with supervised classification of object-based satellite imageryand currently investigate different dimensionality reduction methods on their suitability to this application. As part of my ...
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26 views

What kind of PCA is best for my data?

I'm using sklearn to reduce the dimensionality of an object.This scan is 3D, with shape [15,15,15] and contains mostly zeros, altough the non-zero values are usally clustered together in some groups. ...
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27 views

PCA Dimension Reduction for Cox Proportional Hazard Model

I am trying to figure out if it is possible and appropriate to use PCA to reduce the dimensions of my dataset? A little background - I have survival data with 8 covariates. I have run a Pearson's ...
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19 views

Variability in categorical variables while reducing dimensionality

If a dataset has a variable with categorical values (A, B, C, D, E, F), would converting them to numeric and breaking them down into separate columns (for example, column A that will have 1s for all ...
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24 views

PCA: mean of marginal distribution of high-dimensional vector

Consider the following probabilistic model: $$p(x) = \mathcal{N}(0, I_d), \ x \in \mathbb{R}^d$$ $$p(y|x) = \mathcal{N}(Wx + \mu, \sigma^2I_D), \ y, \mu \in \mathbb{R}^D, W \in \mathbb{R}^{D\times d}...
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15 views

Performing PCA on properly scaled data [duplicate]

I would like to perform PCA on a dataset, however, not all of the data is in the same scale. Some variables are Height, Weight, Age, while others are Dribbles per Game, Shots per Game, Blocks per Game....
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23 views

Non-negative matrix factorization (NMF) on mixed data using 1-hot encoding

From a standpoint of interpretation, can I use NMF on one-hot encoded categorical data for dimension reduction? I have mixed data and was thinking about one-hot encoding the categorical features and ...
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11 views

How do I decide number of hidden layers and neurons for Auto-encoder for dimension reduction?

Supposed I have a 30-dimensional problem and would like to reduce it into 3-dimensional latent space. How do I decide which architecture will be better for my problem? This might be a silly question ...
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218 views

Why with two classes, LDA gives only one dimension?

I am working with dimensionality reduction algorithms. Linear Discriminant Analysis (LDA) is a supervised algorithm that takes into account the class label (which is not the case of PCA for example). ...
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35 views

Comparing PCA representations between low-pass and high-pass filtered time-series data

I am currently trying to reduce the number of variables I input into a vector autoregressive (VAR) model. For those that don't already know, VAR models are used on time-series data. My primary concern ...
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Bag of Visual Words: is feature extraction even needed?

I'm currently implementing a BoVW as part of my lab project. The steps the algorithm used are as follows: spliting all photos into patches cluster these pathces using K-means based on pixel values of ...
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1answer
35 views

Regression with multidimensional output variable Y

Say we have an $N \times q$ matrix $Y$ with $N>q$. Also, we have an $N \times p$ data matrix $X$. We are interested in a model of $Y = X \times W + \epsilon$, where $W$ is a $p \times q$ matrix ...
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20 views

Clustering by same random projection

I have $N$, $1024$-dimensional vectors. I want to cluster them by some similarity. Given the high dimensionality, standard metrics won't work. I tried a few Approximate Nearest Neighbor ...
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72 views

Can I reconstruct the original data from a dimensionality reduced data using t-SNE?

I have implemented dimensionality reduction using PCA, AE, and t-SNE! I am trying to compare the output of the three methods by finding the reconstruction error. I have managed to reconstruct the data ...
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57 views

Dimensionality reduction: Feature Selection or Feature Extraction?

Case: I have a dataset with a large number of features, which I want to reduce. Should I look for a method that identifies the most important ones and throw away the rest, or should I look for a ...
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38 views

What exactly is called “embedding” in dimensionality reduction?

In the following slide I do not understand the definition of the term embedding. In the third paragraph, it says it is a mapping from low-dim. to high-dim, but in the last paragraph it suggests that ...
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Dimensionality Reduction/Clustering - Unordered Attribute Groupings

I'm looking to do some dimensionality reduction on data where each record describes a common set of $k$ attributes on $n_i$ different subjects (in my case, members of a household - think age, gender, ...
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25 views

images in the paper “Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs”

I have some confusion about this image in the paper "Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs" I am wondering what kind of technique they use to lower the dimension of the ...
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80 views

Using a single principle component (PC) space to describe how a dataset changes across conditions

Given a design matrix that consists of N (>100) variables and J (>100) observations (the data, itself, is actual time-series): ...
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153 views

Is MCA equivalent to PCA when all variables are binary?

I am looking to apply principal component analysis on binary (true/false) data, and I have come across the "equivalence between PCA and MCA" (Multiple Correspondense Analysis) for binary data, but ...
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48 views

Dimension reduction [closed]

Can i apply dimension reduction method such as random forest, lasso, factor anaysis or principle compoenet analysis on data which was extracted from two stage stratfied survey
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Recognition accuracy decreases as the number of LDA features increase?

Helloy guys. I'm currently using KALDI building an HMM-GMM system and I added LDA transform to the original 12-dim features, wondering if I can get a better performance of the system. The input dim ...
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62 views

LDA vs PCA 2d plot

PCA (Principal Component Analysis) is often used to represent 2d or 3d plot of the data, where y=PC2 and x=PC1 (eventually z=PC3). Given that there is an 'order' between components, it makes sense to ...
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48 views

PCA on layers of deep neural network in time series prediction (or linear regression in general) for explainability

Are there any references on applying PCA or some other dimensionality reduction to the intermediate layers of deep neural networks in the context of time series or regression? I was thinking that ...
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MCA and K-Means simultaneously

I was reading the article Multiple Correspondence K-means: Simultaneous versus sequential approach for dimension reduction https://link.springer.com/chapter/10.1007/978-3-319-55477-8_8 I have this ...
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How to plot High Dimensional supervised K-means on a 2D plot chart

I'm Having a ML problem where my data set contains 80 features labelled into 3 groups (0, 1, -1). I want to plot the data on a 2D surface to see how "close" (similar) data with ...
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Framework for reducing the dimension of the features of multiple correlated Time Series with a notable amount of memory

I have a dataset that I am trying to analyse that consists of multiple (~500) time series each with around 25 observations. For each observation I have a large number of covariates, some of which will ...
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46 views

Dimensionality Reduction on VGG Image Vector

I have a random forest model which I am using to make retail demand predictions. I am looking at trying to leverage product image data to improve the predictions and have put the images through VGG-...
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158 views

Principal component analysis and DBScan

My data has 30 dimensions and 150 observations. I want to cluster the data with DBScan. Is there a difference between: 1. Performing a PCA and clustering all 30 principal components or 2. Just ...
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38 views

Autoencoders and/or PCA for highly sparse float vectors and a dataset of more than 2 million examples

I have a highly dimensional sparse dataset composed of 2.5 million of examples as follow : dataset_dimension=[2500000,360,280,18] Each example of this dataset ...
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Obtaining hard, overlapping clusters using non-negative matrix factorization

From my understanding non-negative matrix factorization (NMF) provides a natural way to obtain soft clusters from a non-negative $n$x$m$ data matrix $X$. NMF decomposes $X$ into two non-negative ...
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18 views

Flag redundant categorical variables in a big dataset

I have a dataset with ~150 categorical variables and ~150k rows. It is expected beforehand that a number of the categorical variables will be either identical, or nearly so. I would like to code ...
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354 views

Issue with the results of PCA component values

I am performing PCA on a dataset of (28 features + 1 class label) and 11M rows (samples) using the following simple code: ...
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1answer
53 views

Data reduction with nominal variable data

I have a bunch of factor variables. I believe the data comes from only a few clusters. I'd like to analyze the data and perform data reduction. I want to know the ...
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24 views

PCA and data normalization

I have a database where the number of features is about 60 times greater than the number of samples (60000 to 1000). I want to use some dimensional reduction techniques, including PCA. Data are all ...
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281 views

Are dimensionality reduction techniques useful in deep learning

I have been working on Machine learning and noticed that most of the time, dimensionality reduction techniques like PCA and t-SNE are used in machine learning. But, i rarely noticed anyone doing it ...
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39 views

H2O PCA number of components

I wonder why number of components in H2o PCA algorithm is limited to 9. It is not sure sometimes to be enough. k: Specify the rank of matrix approximation. This can be a value from 1 to 9 and ...
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Interpreting PCA, comparing genetic structure within mice population from two continents

I'm interested in comparing the intra-regional genetic relatedness between two populations of mice. One population is native to Europe, while the other is native to North America. I ran PCA to find ...
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36 views

PCA: Are the first two components enough to find which two data sets are more tightly clustered?

I will create an example to explain my question. Say I have two independent data clusters in a 3D space (x,y,z). The two data clusters, Cluster A and B, are very distant to each other, such that ...