Understanding and Comparing Clustering and Dimension Reduction Techniques

Understanding and Comparing Clustering and Dimension Reduction Techniques | CodeSignal Learn

Comparing Dimension Reduction Techniques

Next, let's talk about dimensionality reduction techniques.

Principal Component Analysis (PCA), Independent Component Analysis (ICA), and t-Distributed Stochastic Neighbor Embedding (t-SNE) are all statistical techniques used for dimensionality reduction. They all have strengths and weaknesses and can be best applied based on the specifics of the given dataset.

PCA is an unsupervised method that is most useful in an exploratory scenario where we're not quite sure what we're looking for. PCA aims to find the directions (principal components) that maximize the variance of the data. It assumes that data axes with greater variance are more significant. However, these axes might not be optimal for separating different classes in the data, so it is possible that PCA could end up removing the features that are critical for discrimination.

On the contrary, ICA is also an unsupervised method, but while PCA focuses on maximizing variance, ICA aims to find the statistically independent axes. Essentially, it assumes that the observed data are linear combinations of some unknown independent components. This makes ICA especially useful when you need to separate mixed signals, such as separating out background noise from music. However, ICA assumes non-Gaussian statistics, which may not always be the case.

T-SNE, like PCA, is an unsupervised technique. It computes the probability that pairs of data points in the high-dimensional space are related and then chooses a low-dimensional embedding that produces a similar distribution. Unlike PCA and ICA, t-SNE does not suggest a linear mapping from high- and low-dimensional space. Hence, it can capture complex polynomial relationships between features. It is particularly good at preserving local structure, making it excellent for exploratory data analysis. But this strength is also its weakness. Preserving local structure often comes at the expense of distorting global structure. The degree of distortion increases with increasing number of dimensions. Also, it tends to be computationally expensive, especially with large datasets.

Additionally, t-SNE has a few hyperparameters like perplexity and learning rate that can significantly affect the output, and it's not always clear how to choose these.

In summary, the choice of PCA, ICA, or t-SNE really depends on the specific dataset and the problem you are trying to solve. PCA is good if you think a linear model could describe your data. ICA is good if your data is thought to comprise independent components. Lastly, t-SNE is a great exploratory tool if you're working with high-dimensional data and want to visualize it in a low-dimensional space.