I'm using PCA from sckit-learn and I'm getting some results which I'm trying to interpret, so I ran into question - should I subtract the mean (or perform standardization) before using PCA, or is this somehow embedded into sklearn implementation?
Moreover, which of the two should I perform, if so, and why is this step needed?
I will try to explain it with an example. Suppose you have a dataset that includes a lot features about housing and your goal is to classify if a purchase is good or bad (a binary classification). The dataset includes some categorical variables (e.g. location of the house, condition, access to public transportation, etc.) and some float or integer numbers (e.g. market price, number of bedrooms etc). The first thing that you may do is to encode the categorical variables. For instance, if you have 100 locations in your dataset, the common way is to encode them from 0 to 99. You may even end up encoding these variables in one-hot encoding fashion (i.e. a column of 1 and 0 for each location) depending on the classifier that you are planning to use. Now if you use the price in million dollars, the price feature would have a much higher variance and thus higher standard deviation. Remember that we use square value of the difference from mean to calculate the variance. A bigger scale would create bigger values and square of a big value grow faster. But it does not mean that the price carry significantly more information compared to for instance location. In this example, however, PCA would give a very high weight to the price feature and perhaps the weights of categorical features would almost drop to 0. If you normalize your features, it provides a fair comparison between the explained variance in the dataset. So, it is good practice to normalize the mean and scale the features before using PCA.
Before PCA, you should,
Mean normalize (ALWAYS)
Scale the features (if required)
Note: Please remember that step 1 and 2 are not the same technically.
This is a really non-technical answer but my method is to try both and then see which one accounts for more variation on PC1 and PC2. However, if the attributes are on different scales (e.g. cm vs. feet vs. inch) then you should definitely scale to unit variance. In every case, you should center the data.
Here's the iris dataset w/ center and w/ center + scaling. In this case, centering lead to higher explained variance so I would go with that one. Got this from sklearn.datasets import load_iris data. Then again, PC1 has most of the weight on center so patterns I find in PC2 I wouldn't think are significant. On the other hand, on center | scaled the weight is split up between PC1 and PC2 so both axis should be considered.
Related
I'm working on the heart attack analysis on Kaggle in python.
I am a beginner and I'm trying to figure whether it's still necessary to one-hot-encode or LableEncode these features. I see so many people encoding the values for this project, but I'm confused because everything already looks scaled (apart from age, thalach, oldpeak and slope).
age: age in years
sex: (1 = male; 0 = female)
cp: ordinal values 1-4
thalach: maximum heart rate achieved
exang: (1 = yes; 0 = no)
oldpeak: depression induced by exercise
slope: the slope of the peak exercise
ca: values (0-3)
thal: ordinal values 0-3
target: 0= less chance, 1= more chance
Would you say it's still necessary to one-hot-encode, or should I just use a StandardScaler straight away?
I've seen many people encode the whole dataset for this project, but it makes no sense to me to do so. Please confirm if only using StandardScaler would be enough?
When you apply StandardScaler, the columns would have values in the same range. That helps models to keep weights under bound and gradient descent will not shoot off when converging. This will help the model converge faster.
Independently, in order to decide between Ordinal values and One hot encoding, consider if the column values are similar or different based on the distance between them. If yes, then choose ordinal values. If you know the hierarchy of the category, then you can manually assign the ordinal values. Otherwise, you should use LabelEncoder. It seems like the heart attack data is already given with ordinal values manually assigned. For example, higher chest pain = 4.
Also, it is important to refer to notebooks that perform better. Take a look at the one below for reference.
95% Accuracy - https://www.kaggle.com/code/abhinavgargacb/heart-attack-eda-predictor-95-accuracy-score
I am trying to assess the infuence of sex (nominal), altitude (nominal) and latitude (nominal) on corrected wing size (continuous; residual of wing size by body mass) of an animal species. I considered altitude as a nominal factor given the fact that this particular species is mainly distributed at the extremes (low and high) of steep elevational gradients in my study area. I also considered latitude as a nominal fixed factor given the fact that I have sampled individuals only at three main latitudinal levels (north, center and south).
I have been suggested to use Linear Mixed Model for this analysis. Specifically, considering sex, altitude, latitude, sex:latitude, sex:altitude, and altitude:latitude as fixed factors, and collection site (nominal) as the random effect. The latter given the clustered distribution of the collection sites.
However, I noticed that despite the corrected wing size follow a normal distribution, it violates the assumption of homoscedasticity among some altitudinal/latitudinal groups. I tried to use a non-parametric equivalent of factorial ANOVA (ARTool) but I cannot make it run because it does not allow cases of missing data and it requires to asses all possible fixed factor and their interactions. I will appreciate any advice on what type of model I can use given the design of my data and what software/package can I use to perform the analysis.
Thanks in advance for your kind attention.
Regards,
I am trying to generate a model that uses several physico-chemical properties of a molecule (incl. number of atoms, number of rings, volume, etc.) to predict a numeric value Y. I would like to use PLS Regression, and I understand that standardization is very important here. I am programming in Python, using scikit-learn. The type and range for the features varies. Some are int64 while other are float. Some features generally have small (positive or negative) values, while other have very large value. I have tried using various scalers (e.g. standard scaler, normalize, minmax scaler, etc.). Yet, the R2/Q2 are still low. I have a few questions:
Is it possible that by scaling, some of the very important features lose their significance, and thus contribute less to explaining the variance of the response variable?
If yes, if I identify some important features (by expert knowledge), is it OK to scale other features but those? Or scale the important features only?
Some of the features, although not always correlated, have values that are in a similar range (e.g. 100-400), compared to others (e.g. -1 to 10). Is it possible to scale only a specific group of features that are within the same range?
The whole idea of scaling is to make models more robust to analysis on features space. For example, if you have 2 features as 5 Kg and 5000 gm, we know both are same, but for some algorithm, which are sensitive to metric space such as KNN, PCA etc, they will be more weighted towards second features, so scaling must be done for these algos.
Now coming to your question,
Scaling doesn't effect the significance of features. As i explained above, it helps in better analysis of data.
No, you should not do, reason explained above.
If you want to include domain knowledge in your model, you can use it as prior information. In short, for linear model, this is same as regularization. It has very good features. if you think, you have many useless-features, you can use L1 regularization, which creates sparse effect on features space, which is nothing but assign 0 weight to useless features. Here is the link for more-info.
One more point, some method such as tree based model doesn't need scaling, In last, it mostly depend on the model, you choose.
Lose significance? Yes. Contribute less? No.
No, it's not OK. It's either all or nothing.
No. The idea of scaling is not to decrease / increase significance / effect of a variable. It's to transform all variables to a common scale that can be interpreted.
For big datasets with 2bil+ samples and approximately 100+ features per sample. Among these, 10% features you have are numerical/continuous variables and the rest of it are categorical variables (position, languages, url etc...).
Let's use some examples:
e.g: dummy categorical feature
feature: Position
real values: SUD | CENTRE | NORTH
encoded values: 1 | 2 | 3
...would have sense use reduction like SVD because distance beetween sud:north > sud:centre and, moreover, it's possible to encode (e.g OneHotEncoder, StringIndexer) this variable because of the small cardinality of it values-set.
e.g: real categorical feature
feature: url
real values: very high cardinality
encoded values: ?????
1) In MLlibthe 90% of the model works just with numerical values (a part of Frequent Itemset and DecisionTree techniques)
2) Features transformers/reductor/extractor as PCA or SVD are not good for these kind of data, and there is no implementation of (e.g) MCA
a) Which could be your approach to engage with this kind of data in spark, or using Mllib?
b) Do you have any suggestions to cope with this much categorical values?
c) After reading a lot in literature, and counting the implemented model in spark, my idea, about make inference on one of that features using the others (categorical), the models at point 1 could be the best coiche. What do you think about it?
(to standardize a classical use case you can imagine the problem of infer the gender of a person using visited url and other categorical features).
Given that I am a newbie in regards to MLlib, may I ask you to provide a concrete example?
Thanks in advance
Well, first I would say stackoverflow works in a different way, you should be the one providing a working example with the problem you are facing and we help you out using this example.
Anyways I got intrigued with the use of the categorical values like the one you show as position. If this is a categorical value as you mention with 3 levels SUD,CENTRE, NORTH, there is no distance between them if they are truly categorical. In this sense I would create dummy variables like:
SUD_Cat CENTRE_Cat NORTH_Cat
SUD 1 0 0
CENTRE 0 1 0
NORTH 0 0 1
This is a truly dummy representation of a categorical variable.
On the other hand if you want to take that distance into account then you have to create another feature which takes this distance into account explicitly, but that is not a dummy representation.
If the problem you are facing is that after you wrote your categorical features as dummy variables (note that now all of them are numerical) you have very many features and you want to reduce your feature's space, then is a different problem.
As a rule of thumbs I try to utilize the entire feature space first, now a plus since in spark computing power allows you to run modelling tasks with big datasets, if it is too big then I would go for dimensionality reduction techniques, PCA etc...
I'm trying to find confidence intervals for the means of various variables in a database using SPSS, and I've run into a spot of trouble.
The data is weighted, because each of the people who was surveyed represents a different portion of the overall population. For example, one young man in our sample might represent 28000 young men in the general population. The problem is that SPSS seems to think that the young man's database entries each represent 28000 measurements when they actually just represent one, and this makes SPSS think we have much more data than we actually do. As a result SPSS is giving very very low standard error estimates and very very narrow confidence intervals.
I've tried fixing this by dividing every weight value by the mean weight. This gives plausible figures and an average weight of 1, but I'm not sure the resulting numbers are actually correct.
Is my approach sound? If not, what should I try?
I've been using the Explore command to find mean and standard error (among other things), in case it matters.
You do need to scale weights to the actual sample size, but only the procedures in the Complex Samples option are designed to account for sampling weights properly. The regular weight variable in Statistics is treated as a frequency weight.