How can you explain dimensionality reduction to a beginner in Machine Learning?

Dimensionality reduction in machine learning is like summarizing a long book into a short story. In a big dataset, you have lots of details (or dimensions) about each item, like a book filled with characters, places, and events. But sometimes, too many details can be overwhelming and make it hard to see the main points. Dimensionality reduction techniques simplify this information, keeping only the most important parts, just like a summary captures the essence of a book without every single detail. This makes it easier to understand the data, spot trends, and make predictions without getting lost in unnecessary information. It's a way of focusing on the 'big picture' rather than every tiny detail.

My introduction to Dimensionality Reduction began with Kaggle projects, initially for feature selection/engineering. But dimensionality reduction methods are used for various purposes, e.g. t-SNE is mainly used for visualization or ICA is used in signal processing. I found their use, in anomaly detection, quite interesting. Here, the idea was to use a dimensionality reduction method such as PCA to learn the underlying structure of the dataset. After that, we will reconstruct the dataset, using the fitted PCA, and then calculate how different the reconstructed data points are from the original. Those data points that PCA does the poorest job of reconstructing are the most anomalous!

The quantity of dimensions or attributes used to represent the data is referred to as dimensionality. For instance, every pixel in an image dataset can represent a dimension, and every word in a text dataset can represent a dimension. Your data is more complex and high-dimensional the more dimensions it contains.

Dimensionalidade se refere ao número de atributos ou características (dimens?es) que est?o presentes em um conjunto de dados. Em termos mais simples, é o número de variáveis que descrevem cada ponto de dados em um espa?o multidimensional. Por exemplo, se você estiver trabalhando com dados sobre carros e estiver considerando apenas duas características, como a velocidade máxima e o consumo de combustível, seus dados teriam duas dimens?es. No entanto, se você também adicionasse características como peso, tamanho, potência do motor e assim por diante, a dimensionalidade aumentaria.

Imagine you have a big collection of pictures of different animals, and each picture has lots of tiny pixels. Now, you want to understand these pictures better, but dealing with so many pixels for each picture can be overwhelming. Dimensionality reduction is a way to take all these pixels (represent a high number of dimensions) and find a simpler way to represent the pictures without losing too much important information. It's like finding smaller set of things that still capture the essence of the pictures. So, instead of working with huge pixels for each image, you might find a way to represent each picture using just a few features that are most significant to differentiate between animals, like shape, size, color distribution, etc.

High-dimensional data often contains complex, non-linear relationships among variables. Traditional linear techniques might fail to capture these intricate relationships effectively. In high-dimensional spaces, there's an increased risk of overfitting models to the training data. Balancing model complexity and generalization becomes challenging, requiring robust regularization techniques to prevent overfitting while still capturing essential information. Identifying relevant features and performing feature engineering becomes more intricate in high-dimensional non-linear spaces. Visualizing high-dimensional data in a non-linear space is challenging.

High dimensional data generally is computationally expensive. Hence it harder to generalize and analyse. Hence we have to carefully choose the features.

A few key challenges of high-dimensional data: 1. Sparsity of information ( makes learning difficult ) 2. Inability of humans to visualize more than 3 dims 3. Larger data storage / processing requirements

There are a couple of ways in which high-dimensional data can be hard to work with. 1. Increased computational complexity, increasing training time faster than linear time 2. Increased risk of overfitting; with too much data, the model might fail to appropriately generalize 3. Reduced interpretability; with a larger model trying to generate a trend for a larger set of data, understanding what your model is doing and trying to explain it becomes a more difficult task 4. Difficulty in visualization; visualizing 2 dimensions is intuitive, and 3 dimensions is a bit harder but still possible. Going beyond that baffles our minds. Because of this, high dimensionality makes us lose full grasp of our data, thus making it harder to work with.

High-dimensional data poses challenges in machine learning, including the curse of dimensionality, which leads to sparsity and difficulties in exploration, visualization, and generalization. Redundancy and noise can harm model quality and efficiency. Complex models like neural networks can reduce interpretability and explainability, hindering communication and validation of results. Effective training may demand more data and computational resources.

A redu??o de dimensionalidade permite que o modelo de ML foque no que é mais importante entre as caracteristicas adquiridas pelos pesos calculados por ele no processo de treinamento. Tambem auxilia na utiliza??o de algoritmos para compara??o de dados desbalanceados, auxiliando em tarefas como detec??o de desvio de dados e de conceito.

Dimensionality reduction is like simplifying information to its most important parts. It helps in making data analysis quicker, more accurate, and easy to understand. By removing unnecessary details, it improves the performance of models, reduces the risk of errors, and saves computational resources.

Dimensionality reduction involves transforming data into a lower-dimensional space, offering various advantages. It can lead to improved performance and accuracy by removing irrelevant or noisy dimensions, reducing overfitting, and enhancing generalization. Additionally, it enhances interpretability, simplifies visualization, and identifies influential features. Furthermore, it reduces storage and transmission costs by compressing data into a more compact representation.

Consider if you have to predict something about a person, and you have a ton of data about them, such as shoe size, hair color, hair length, number of fingers, height, weight, age, and so on. Imagine you are predicting how likely they will get heart disease. Clearly, hair length is not so relevant. Therefore, you would seek to remove that feature, thus "reducing the dimensionality". The reason you'd do this is generallly because more data requires bigger models and more money to store and run. There are various techniques, such as analyzing for entropy reduction per variable (i.e. how much do they affect our accuracy?). This process can be complex and the wrong decision can greatly reduce your performance. Feel free to reach out for advice!

Dimension reduction is beneficial for various reasons, including: Computational Efficiency: High-dimensional datasets can be computationally expensive to process. Reducing dimensionality can lead to faster model training and prediction times. Noise Reduction: Removing irrelevant or redundant features can help reduce noise and improve the model's generalization performance on new, unseen data. Visualization: Dimension reduction facilitates the visualization of data in lower-dimensional spaces, allowing for easier exploration and interpretation.

An common approach to reduce dimensionality is feature selection, where features with low impact on the model's outcome can be removed from the dataset. Some techniques are: Variance: features with little change though the data it is probability not relevant for the outcome Correlation: Selecting only one from a set of highly correlated features can reduce redundant information. Variance Inflation Factor (VIF): multicollinearity in the analysis of regression models, which occurs when two or more variables present a high correlation. Some machine learning models like random forest are able to calculate feature importance, this information can be used to choose the best features to keep and re-train the model.

Two common methods for dimension reduction are: Principal Component Analysis (PCA): PCA is a mathematical technique that transforms the original features into a new set of uncorrelated variables called principal components. These components capture the maximum variance in the data, allowing for a reduction in dimensionality while retaining much of the information. t-Distributed Stochastic Neighbor Embedding (t-SNE): t-SNE is a non-linear dimensionality reduction technique that focuses on preserving the pairwise similarities between data points. It is often used for visualization purposes, helping to reveal the underlying structure and relationships within the data.

We have two categories of dimensionality reduction one is 1. Feature Selection: Here we have three methods that is I) Filter methods which includes Chi-Square test, Mutual Information, Correlation based feature selection. II) Wrapper Method which includes Recursive Feature Elimination, Forward Selection, Backward Selection III) Embedded method which includes Lasso and Tree based like Random Forest to extract features. 2. Feature Extraction: Here we have five methods Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), t-distributed Stochastic Neighbor Embedding (t-SNE), Autoencoders, Factor Analysis.

Similar to model selection, some techniques have a higher propensity to work well for any given situation. That said, the best way to select a dim reduction technique is set up a validation framework, evaluate several techniques, then pick the best one. The key is to know how to quantify what "best" is. To do this, ask yourself, why are you using dimensionality reduction in the first place? What do you want to do? That should initiate an inner monologue that leads to the right conclusion.

One of my most popular YouTube videos is a PCA with Taylor Swift images demo. (Look up Principal Component Analysis Taylor Swift to find it) I used principal component analysis on an image of Taylor Swift and retained 90 to 99% of the variance. We then looked at how blurry the images looked at each level of variance. The grayscale images looked blurry at 90%, but got pretty decent by 97%. Now, it's important to remember that PCA creates linear combinations of the existing dimensions. This means that the most effective use of PCA is on datasets which are highly skewed along certain dimensions - because we can then highly reduce the dimensionality without losing much variance.

Dimensionality reduction simplifies complex data by reducing the number of features or variables. Imagine a dataset as a multi-dimensional space; dimensionality reduction aims to project this space into a lower-dimensional form while preserving important relationships. Picture it like taking a photo of a 3D object from different angles—though you lose some details, the essence remains. Techniques like Principal Component Analysis (PCA) or t-SNE help identify essential patterns and structures in data, making it more manageable for machine learning models. In simpler terms, it's like distilling a recipe: keep the essential flavors while simplifying the ingredients.