# How to visualize data of a multidimensional dataset (TIMIT)

I've built a neural network for a speech recognition task using the timit dataset. I've extracted features using the perceptual linear prediction (PLP_ method. My features space has 39 dimensions (13 PLP values, 13 about first order derivative and 13 about second order derivative).

I would like to improve my dataset. The only thing I've tried thus far is normalizing the dataset using a standard scaler (standardizing features with mean 0 and variance 1).

My questions are:

• Since my dataset has high dimensionality, is there a way to visualize? For now, I've just plotted the dataset values using a heat map.
• Are there any methods for separating my sample even more, making it easier to differentiate between the classes?

My heat map is below, representing 20 samples. In this heatmap there are 5 different phonemes, related to vowels, in particular, uh, oy, aw, ix, and ey. As you can see, each phoneme is not really distinguishable from the others. Does anyone know how could I improve it?

• You'll need to perform dimension reduction, otherwise you'll not be able to visualize the R^n vector space. – eliasah Oct 24 '15 at 14:29
• For visual analysis, I would focus on the primitive variables and not worry about the derivatives for the time being since you can infer slopes and inflection points so easily visually. Totally separate from the visualization question: Are the derivatives helping the ANN at all? It should actually have the ability to learn the derivatives on its own since nth order derivatives are just linear adds and subtracts if the abscissa are uniformly spaced. – AN6U5 Oct 24 '15 at 19:08
• "Are the derivatives helping the ANN at all?" - Good question! ... i thought that it could be an extra unuseful information (i mean the derivatives), but in more than 1 scientific paper i've noticed that these are used. Furthermore very often the energy is used, which is nothing more than a squared sum of the values. So even energy should be automatically inferred by ANN, but is used anyway. – giogix Oct 25 '15 at 17:19

Like I said in the comment, you'll need to perform dimension reduction, otherwise you'll not be able to visualize the $\mathbb{R}^n$ vector space and this is why :

Visualization of high-dimensional data sets is one of the traditional applications of dimensionality reduction methods such as PCA (Principal components analysis).

In high-dimensional data, such as experimental data where each dimension corresponds to a different measured variable, dependencies between different dimensions often restrict the data points to a manifold whose dimensionality is much lower than the dimensionality of the data space.

Many methods are designed for manifold learning, that is, to find and unfold the lower-dimensional manifold. There has been a research boom in manifold learning since 2000, and there now exist many methods that are known to unfold at least certain kinds of manifolds successfully.

One of the most used methods for dimension reduction is called PCA or Principal component analysis. PCA is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. You can read more on this topics here.

So once you reduce your high dimensional space into a ${\mathbb{R}^3}$ or ${\mathbb{R}^2}$ space you will able to project it using your adequate visualization method. References :

EDIT: To avoid confusion for some concerning PCA and Dimension Reduction, I add the following details :

PCA will allow you compute the principal components of your vector model, so the information are not lost but "synthesized".

Unfortunately there is no other imaginable way to display 39 dimensions on a 2/3 dimension screen. If you wish to analyze correlations between your 39 features, maybe you should consider another visualization technique.

I would recommend a scatter plot matrix in this case.

• I don't think there will be much salvageable information left after projecting from $R^{39}$ down to $R^{3}$ using PCA. This just isn't realistic nor will it provide any insight. Further, the vast majority of the variance will thrown away and you will have mashed together 39 dimensions into 3 without any insight into which tiny piece comes from which original dimension. I would be interested to see an example of successfully deriving actionable visual insight from $PCA(R^{39})==>R^{3}$ if you have one. – AN6U5 Oct 24 '15 at 18:55
• PCA will allow you compute the principal components of your vector model, so the information are not lost but "synthesized". Unfortunately there is no other imaginable way to display 39 dimensions on a 2/3 dimension screen. If you wish to analyze correlations between your 39 features, maybe you should consider another visualization technique. I would recommend a scatter plot matrix in this case. – eliasah Oct 24 '15 at 19:08
• Its 2019 and i am still reading your comments. Any other ways we got now.? Python profiling is latest out there. – IamTheRealFord Nov 14 '19 at 10:02
• My answer still stands @IamTheRealFord – eliasah Nov 15 '19 at 16:23