¿Cuáles son las técnicas de reducción de dimensionalidad más comunes y cómo se pueden evitar sus trampas?

The PCA method is highly effective for linear correlations of features. The method has particular disadvantages when it comes to complex and non-linear datasets (e.g. circular or donut-shaped clusters). If PCA is applied to this dataset, the data points overlap when projected onto the first principal component. The Kernel PCA method helps to map the original dataset into a higher-dimensional space and perform PCA in this new dimension. As a result, the features can now be successfully separated from each other.

PCA identifies linear combinations of original features that capture the most variance in the data. These combinations, known as principal components, are orthogonal to each other. PCA reduces dimensionality by projecting data onto the subspace defined by the principal components, discarding those with the least variance. To effectively use PCA, it is necessary to standardize the data, choose the number of components to retain, and interpret the results. Some pitfalls to avoid include loss of information and interpretability, overlooking non-linear relationships, and assuming normality of the data. Being aware of these limitations is crucial for applying PCA effectively and deriving relevant insights from the data.

Principal Component Analysis (PCA) is a method that identifies linear combinations of original features capturing the highest variance in data, termed principal components. These components are mutually perpendicular. By projecting data onto the subspace defined by principal components and discarding those with lower variance, PCA reduces dimensionality. Implementation involves data standardization, selecting the number of components to retain, and result interpretation. Caution is needed to avoid pitfalls, such as potential information loss and reduced interpretability. Additionally, PCA may not account for non-linear relationships, and assumptions about data normality should be considered.

A PCA plot shows clusters of samples based on their similarity. PCA does not discard any samples or characteristics (variables). Instead, it reduces the overwhelming number of dimensions by constructing principal components (PCs).

Principal Component Analysis (PCA) is a statistical technique that is widely used in various fields, including telecommunications. It is used to reduce the dimensionality of complex data sets by extracting the principal components that contain the most information and rejecting noise or less important data while preserving all the crucial details In the context of telecommunications, PCA has been used to analyze financial performance of companies in the industry and to analyze customer churn data in the telecommunications industry. By computing transformed variables or new dimensions along the direction of major variability in the data, PCA can help identify the most significant factors that contribute to customer churn.

Singular Value Decomposition (SVD) is a dimensionality reduction technique. It decomposes a matrix into three smaller matrices, keeping only the largest singular values. This reduces dimensionality by approximating the original matrix. To use SVD, scale the data, choose the approximation rank, and apply the transformation. Challenges include loss of information, overlooking non-linear relationships, and handling sparse or missing data. Being aware of these is crucial when applying SVD.

Singular Value Decomposition (SVD) is a technique that breaks down a matrix into three smaller matrices: a left singular matrix, a diagonal matrix of singular values, and a right singular matrix. Utilizing SVD for dimensionality reduction involves retaining only the largest singular values and their corresponding columns in the left and right singular matrices. This process allows SVD to approximate the original matrix with a lower-rank version. Implementation requires data scaling, selecting the rank of the approximation, and applying the transformation. However, caution is necessary to avoid pitfalls, such as potential loss of information and interpretability.

Singular Value Decomposition (SVD) is a matrix factorization technique used in linear algebra. It decomposes a matrix into three separate matrices - U, Σ, and V^T. U represents the left singular vectors, which form an orthonormal basis for the column space of the original matrix. Σ is a diagonal matrix containing the singular values of the original matrix. These values convey the importance of each singular vector in describing the data. V^T stands for the transpose of the matrix of right singular vectors, providing an orthonormal basis for the row space of the original matrix.

Singular Value Decomposition (SVD) is a powerful mathematical technique that has been widely used in various fields, including telecommunications. SVD is used to decompose a matrix into three matrices, which can be used to extract the most important features of the data. In the context of telecommunications, SVD has been used to enhance detection of signals in wireless communication systems. SVD has also been used in multiple input multiple output (MIMO) transmission, which provides a very large spectral efficiency. Overall, SVD is an effective technique for extracting the most important features of complex data sets, and its applications in the telecommunications industry include enhancing signal detection and improving spectral efficiency

Linear Discriminant Analysis (LDA) is a technique that identifies linear combinations of original features optimizing the separation between different data classes. These combinations, termed linear discriminants, are mutually orthogonal. LDA reduces dimensionality by projecting data onto the subspace defined by linear discriminants, retaining the most discriminative ones. Implementation involves labeling data, standardizing it, selecting the number of discriminants to keep, and interpreting results. Caution is necessary to avoid pitfalls, including overfitting and neglecting non-linear relationships. Also, adherence to assumptions of normality, homoscedasticity, and independence is essential for accurate LDA application in data analysis.

Linear Discriminant Analysis (LDA) is a technique aimed at identifying linear combinations of original features that optimize the separation between distinct classes within the dataset. These derived combinations, termed linear discriminants, exhibit orthogonality to each other.

LDA is used not only in dimensionality reduction but also in classification models. In text models it converts your dataframe into a special form of optimized matrix which is reducing the dimension of your dataframe

In the context of telecommunications, LDA has been used to classify and predict customer churn. In one study, LDA was used to identify the most significant factors that contribute to customer churn in the telecommunications industry. The study concluded that LDA is an effective technique for identifying the most significant factors that contribute to customer churn. LDA has also been used to analyze the performance of wireless communication systems. By computing transformed variables or new dimensions along the direction of major variability in the data, LDA can help identify the most significant factors that contribute to the performance of a system.

Since this is about as clear as mud, I'd like to try to make it a bit more approachable. NMF is a method where a big matrix (a kind of data table where all numbers are zero or more) is broken down into two smaller ones. Think of it like simplifying a big, complicated puzzle into two easier ones. NMF helps to focus on the most important parts of the data, like finding key themes or hidden patterns. To use NMF, your data needs to be all positive numbers. You also need to adjust your data, decide how much to simplify it, and then apply the technique. However, be careful: you might miss some details, overlook complex patterns, and choosing the right level of simplification can be tricky.

t-SNE (t-Distributed Stochastic Neighbor Embedding) is a technique that transforms high-dimensional data into a lower-dimensional space, preserving local similarities between data points. It achieves dimensionality reduction by establishing a probability distribution over pairs of data points in the high-dimensional space and seeking a comparable distribution in the low-dimensional space. For effective use, normalize your data, determine the desired dimensionality, and fine-tune parameters. However, caution is needed to avoid potential loss of global structure and interpretability. t-SNE is sensitive to parameter choices and can be computationally expensive, requiring thoughtful consideration during implementation.

t-SNE is like a magic trick that turns complicated data into a simpler form, keeping things that are close together still close. It works by making a kind of map in both the original and simpler spaces, focusing on how things are similar. To make it work, you need to get your data ready, decide how many details you want to keep, and adjust some settings. But, be careful—it might lose a bit of the big picture, be tricky with settings, and need a lot of computer power.

Something I've found useful, often not mentioned, is the importance of domain experience and context when applying dimensionality reduction techniques. For instance, in using PCA or SVD, deep understanding of the application field can reveal which components or singular values are truly relevant, beyond their mathematical contribution. I've seen cases where component removal based only on statistical criteria missed valuable aspects for specific analysis. Therefore, it's crucial to combine these techniques with a strong knowledge of the study area, ensuring dimensionality reduction is not only mathematically sound but also relevant and applicable to the specific context.

When discussing the pitfalls of dimensionality reduction, a classic example is the use of PCA in genetic data analysis. In such a scenario, PCA might condense thousands of genetic markers into just a few principal components. While this simplifies the data, crucial genetic variations, potentially critical for understanding disease susceptibility or treatment response, can be lost. This over-condensation risks oversimplifying the complex and nuanced genetic landscape, leading to conclusions that might overlook vital subtleties. Such examples highlight the need for cautious interpretation and application of dimensionality reduction techniques, especially in fields where every data point can carry significant implications.

Often not included is a Contextual marker. Time and again we find that the abstract is only so because there is no Contextual anchor to make finding relevant

Dimensionality reduction techniques, like PCA, Factor Analysis, t-SNE, simplify data by reducing variables. While all these techniques mentioned are useful, the efficacy of these can be significantly compromised by endogeneity - a situation where explanatory variables correlate with the error term due to omitted variables, measurement error, or simultaneity, leading to biased and inconsistent estimates. To mitigate this, consider back-to-basics methods like Instrumental Variables (IV), Panel Data Techniques (fixed and random effects models), Structural Equation Modeling (SEM), Difference-in-Differences (DiD), Sensitivity Analysis, and Advanced Machine Learning Techniques, including regularized regression (LASSO, Ridge) and ensemble methods.