Questions tagged [optimal-scaling]

Optimal scaling or optimal quantification is an algorithmic approach to transform categorical variables into scale (interval) ones which would be "optimal" in some statistical sense (for example, their linear correlations will be maximized). There exist nonlinear "optimal scaling versions" of many classic linear kinds of analysis, including regression, PCA, etc.

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K-means to cluster texts, scaling

I want to cluster a folder of texts. I created a data file where for each text, I write whether a certain word appears in it or not. I want to cluster according to this. So my matrix is globally only ...
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Is it possible to scale the mean and std of estimated rate/period, to another period?

Hello, all. When it comes to calculating the average from some time-spanning date, let's say the average of 20 weekly sales records from a specific store - while also calculating the standard ...
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Minimizer of $\int\mu({\rm d}x)\int\kappa(x,{\rm d}y)|g(x)-g(y)|^2$ for a jump kernel $\kappa$ of the Metropolis-Hastings algorithm

Let $\kappa$ be a sub-Markov kernel on a measurable space $(E,\mathcal E)$ and $\mu$ be a probability measure on $(E,\mathcal E)$ reversible with respect to $\kappa$. Assume $\kappa$ and $\mu$ admit a ...
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Scaling into a range causes unsymmetrical error

I need to scale up sine and cosine values to fit to two-compliment vector. By using the general formula I am getting an approximation error only near the maxima of the function (near -1 and 1). I ...
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Is it compulsary to normalize the dataset if doing so can negatively impact a Binary Logistic regression performance?

I am using raw data set with 4 feature variables (Total Cholesterol, Systolic Blood Pressure, Diastolic Blood Pressure, and Cigraeette count) to do a Binominal Classification (find stroke likelihood) ...
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Optimal Scaling HMC proof

I'm reading the paper https://arxiv.org/pdf/1001.4460.pdf I get very confused when reading the author proof of the theorem (4.2) Here are few points. (1) The expected squared jump distance is ...
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Is this scaling algorithm viable?

I just came up with my own random number scaling algorithm (and I'm sure someone else has come up with it before me), and I wanted to see if any of you can find holes in it. The idea is to take a ...
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65 views

proper way to scale and plot data points on top of each other

I hope this is the right place that I am posting this question. If not please feel free to comment so that I find the right place. I have 4 sets of points that represent points on hexagons. My data ...
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Estimate the asymptotic efficiency of a Markov chain sampling by the method of batching

In the paper Efficient Metropolis Jumping Rules, the author is writing that he used "the method of batching" for the estimation of $\operatorname{eff}_{\overline\theta_i}$ in Table 1 (on page 605). ...
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How can we verify the intuition that in the RW-Metropolis-Hastings algorithm with Gaussian proposal too small and too large variances are bad choices

Let $d\in\mathbb N$ and consider the Random Walk Metropolis-Hastings algorithm with a Gaussian proposal kernel $Q$ such that $Q(x,\;\cdot\;)=\mathcal N_d(x,\sigma^2_dI_d)$ for all $x\in\mathbb R^d$. ...
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How does the celebrated result about the diffusion limit of the Random Walk Metroplis-Hastings algorithm help us to find the optimal scaling

Let $d\in\mathbb N$ with $d>1$ $\ell>0$ $\sigma_d^2:=\frac{\ell^2}{d-1}$ $f\in C^2(\mathbb R)$ be positive with $$\int f(x)\:{\rm d}x=1$$ and $g:=\ln f$ $Q_d$ be a Markov kernel on $(\mathbb R^...
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categorical predictors in partial least squares

I am interested in running a partial least squares analysis using PROC PLS in SAS 9.4. I understand that, by default, the predictors and response variables in PLS are centered to a mean 0 and scaled ...
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74 views

How to find the optimal convergence rate?

Suppose there is some data $X_{1},X_{2},\ldots,X_{n}$. We further suppose that there is some parameter $\theta$, for which we want to do statistical inference. Assume that there is a asymptotical (...
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Scaling regression coefficients Take 2: Gelman (2008) approach

I am asking a follow-up question about interpreting regression coefficients that have been scaled following Gelman's (2008, 2009) recommendations. Original recommendation to divide continuous ...
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Dealing with data with high variance

I've a scaling problem. Let's say my target variable is a net revenue column and it has some range of (-34624455, 298878399). So the max-min value is 333502854. Now in the test set, I have a record ...
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829 views

Pros and Cons of MinMax Normalization vs. Standardization

I have a large dataset with 800 columns and 6,000,000 rows with many dummy variables (70%+). I want to Normalize it. Given that so many variables are binary, taking values 0 or 1, I am tending ...
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Using Boruta and Scaling with neural network

When using Boruta for variable selection and also scaling your complete data set to values between 0 and 1 is it typical to select variables using Boruta based on the scaled values or the raw values?
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Scaling step in Baum-Welch algorithm

I am implementing the Baum-Welch Algorithm for training a Hidden Markov Process, to basically better understand the training process. I have implemented the iterative procedures described in Rabiner'...
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How to compare stock time-series with different holidays

Many researches just assume 252 trading days, means 21 days per month, which is helpful. But when you need to compare stock returns from different countries, it happens that each stock is not traded (...
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256 views

Does SVM prediction accuracy depend on a positive scaling of the kernel function?

Support vector machine (SVM) is a supervised learning algorithm. It draws hyperplanes to separate data points of different classes. The objective function involves inner products of pairs of feature ...
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463 views

Standardising these datasets so that they are comparable

Context: Let's say I have two datasets from 2000 and 2010. Each dataset consists of an example for each area of a city along with variables A, B and C, which are all numerical variables which ...
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Categorical Principal Component Analysis [duplicate]

I am planning to perform a Categorical Principal Component Analysis, I have 14 variables with categorical ordinal data (from a 5 point likert scale) and one variable with categorical nominal data. ...
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110 views

Scaling data, keeping relative numerical dispersion

I have values two vectors that are spread across ranges of [-5, -1] and [1, 5] respectively. They can be decimals. Here is a toy example: ...
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Normalization by decimal scaling

I came to this normalization technique Normalization by decimal scaling normalizes by moving the decimal point of values of attribute A. The number of decimal points moved depends on the maximum ...
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scaling for SVM destroys my results [duplicate]

I'm applying standard 0-1 scaling of features before SVM classification for financial data but the results are worse. This is the results before scaling ...
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Scaling and Rounding

x y 0.4 0 11.43 11 0.45 0 0.44 0 Total 12.72 11 I have a very large dataset of x values and rounded off values of x as y. Y cannot take ...
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What does R do with negative values in log() scale?

Some context of the problem: I am working on an analysis of some hypothetical donation data: I would like to investigate the differences between 'major donors' (those whose largest single donation is ...
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244 views

Likert Scale 3 2 1 0 1 2 3 possible?

In my questionnaire I want to ask people to score on a dimensional Likert-type scale their attitude toward a specific target group. E.g. People with .... are stupid.... intelligent. I want to use ...
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Which type of feature scaling to use [duplicate]

I've been writing some simple machine learning algorithms and looking at time-series data. In doing so, I have come across the use of feature scaling: rescaling and standardizing as they are referred ...
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Mathematics of simple performance testing [duplicate]

I have a set of sorted tables T that have known but different dimensions. There are two types of functions in this system: f(T) g(T, n), where n is an integer parameter. ... and two types of costs ...
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716 views

Similarities and dissimilarities between optimal scaling procedures in CATPCA and MCA

I have seen that multiple correspondence analysis (MCA) can also be seen as a generalization of principal component analysis when the variables to be analyzed are categorical instead of quantitative. ...
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33 views

should weights be scaled too?

I am using supervised learning algorithms (specificly SVM) on my data. I know that scaling was needed for my input data. however as I am also adding weights (using pairwise comparison), I am not sure ...
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Scaling in SVM (why and how to , plus references)

Hi I know why feature scaling is preferred in SVM, I have two questions: 1-does anyone know of legit articles of books explaining it. I am writing my thesis and I need references. It doesnt have to be ...
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Optimal scaling / CATREG (categorical regression) for imputed data

I have a data set with 5 different kinds of nutrient statuses and I want to see whether they are associated with categorical / ordinal grades at school. I have multiple covariates which I will ...
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717 views

Scaling data: why not standardize response variable to unit variance (in addition to zero mean)?

I have been reading Elements of Statistical Learning. And I saw some example R codes written online. I realise that very often the explanatory variables $X$ (the data of the predictors) are ...
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1answer
454 views

Can I categorize the factor scores to use them as predictors of an ordinal logistic regression?

I was wondering if I can categorize the factor saved scores by taking their quartiles (or some other measures, I am not sure what should I use!) as cut points and use them as predictors in an ordinal ...
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613 views

Optimal scaling level for variables categorized from continuous data

A variable was categorized into 10 equally spaced intervals from a continuous variable which was originally in proportion. Now, we have to use this variable in CATREG procedure. If we choose the ...
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Can I use optimally scaled variables for a factor analysis to account for rotation? If I can then how?

I have discussed this issue several times in this site, but I am asking it again for a final justification from the experts of our community. I wanted to extract four factors (I should call dimensions ...
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975 views

How to obtain optimally scaled data from homals in R?

I am using the homals-package in R to optimally quantify my data that contains categorical (nominal and ordinal) as well as numerical variables. My goal is to ...
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What is the advantage of transforming variables from nominal to ordinal/numerical when it reduces variance explained in CatPCA?

Context I have a dataset of 8 categorical variables. And I want to apply Categorical Principal Component Analysis (CatPCA). Before doing that, I have been advised to look at the transformation plots ...
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How to calculate Rousseeuw’s and Croux’ (1993) Qn scale estimator for large samples?

Let $Q_n = C_n.\{|X_i-X_j|;i < j\}_{(k)}$ so for a very short sample like $\{1,3,6,2,7,5\}$ it can be calculated from finding the $k$th order static of pairwise differences: ...
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1answer
143 views

Parametric Surface Reconstruction from Contours with Quick Rescaling

I'm looking to construct a 3-D surface of a part of the brain based on 2-D contours from cross-sectional slices from multiple angles. Once I get this shape, I want to "fit" it to another set of ...
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How can I use optimal scaling to scale an ordinal categorical variable?

In an answer to this question about treating categorical data as continuous, optimal scaling was mentioned. How does this method work and how is it applied?