Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data.

Udemy course Feature Engineering and Dimensionality Reduction Feature Selection vs Dimensionality Reduction While both methods are used for reducing the number of features in a dataset, there is an important difference. Feature selection is simply selecting and excluding given features without changing them. Dimensionality reduction transforms features into a lower dimension NED New What you'll learn The importance of Feature Engineering and Dimensionality Reduction in Data Science. Practical explanation and live coding with Python. Description Artificial Intelligence (AI) is indispensable these days.

Principal Component Analysis (PCA) is a powerful and well-established data transformation method that can be used for data visualization, dimensionality reduction, and possibly improved performance with supervised learning tasks. In this use case blog, we examine a dataset consisting of measurements of benign and malignant tumors which are computed from digital images of a fine needle aspirate of breast mass tissue. Specifically, these 30 variables describe specific characteristics of the cell nuclei present in the images, such as texture symmetry and radius. The first step in applying PCA to this process was to see if we can more easily visualize separation between the malignant and benign classes in two dimensions. To do this, we first divide our dataset into train and test sets and perform the PCA using only the training data.

Dimensionality reduction is an unsupervised learning technique. Nevertheless, it can be used as a data transform pre-processing step for machine learning algorithms on classification and regression predictive modeling datasets with supervised learning algorithms. There are many dimensionality reduction algorithms to choose from and no single best algorithm for all cases. Instead, it is a good idea to explore a range of dimensionality reduction algorithms and different configurations for each algorithm. In this tutorial, you will discover how to fit and evaluate top dimensionality reduction algorithms in Python.

Recent work has shown the tremendous vulnerability to adversarial samples that are nearly indistinguishable from benign data but are improperly classified by the deep learning model. Some of the latest findings suggest the existence of adversarial attacks may be an inherent weakness of these models as a direct result of its sensitivity to well-generalizing features in high dimensional data. We hypothesize that data transformations can influence this vulnerability since a change in the data manifold directly determines the adversary's ability to create these adversarial samples. To approach this problem, we study the effect of dimensionality reduction through the lens of adversarial robustness. This study raises awareness of the positive and negative impacts of five commonly used data transformation techniques on adversarial robustness. The evaluation shows how these techniques contribute to an overall increased vulnerability where accuracy is only improved when the dimensionality reduction technique approaches the data's optimal intrinsic dimension. The conclusions drawn from this work contribute to understanding and creating more resistant learning models.

Reducing the number of input variables for a predictive model is referred to as dimensionality reduction. Fewer input variables can result in a simpler predictive model that may have better performance when making predictions on new data. Linear Discriminant Analysis, or LDA for short, is a predictive modeling algorithm for multi-class classification. It can also be used as a dimensionality reduction technique, providing a projection of a training dataset that best separates the examples by their assigned class. The ability to use Linear Discriminant Analysis for dimensionality reduction often surprises most practitioners.

We propose a new concept of rateless auto-encoders (RL-AEs) that enable a flexible latent dimensionality, which can be seamlessly adjusted for varying distortion and dimensionality requirements. In the proposed RL-AEs, instead of a deterministic bottleneck architecture, we use an over-complete representation that is stochastically regularized with weighted dropouts, in a manner analogous to sparse AE (SAE). Unlike SAEs, our RL-AEs employ monotonically increasing dropout rates across the latent representation nodes such that the latent variables become sorted by importance like in principal component analysis (PCA). This is motivated by the rateless property of conventional PCA, where the least important principal components can be discarded to realize variable rate dimensionality reduction that gracefully degrades the distortion. In contrast, since the latent variables of conventional AEs are equally important for data reconstruction, they cannot be simply discarded to further reduce the dimensionality after the AE model is trained. Our proposed stochastic bottleneck framework enables seamless rate adaptation with high reconstruction performance, without requiring predetermined latent dimensionality at training. We experimentally demonstrate that the proposed RL-AEs can achieve variable dimensionality reduction while achieving low distortion compared to conventional AEs.

Summarizing high-dimensional data using a small number of parameters is a ubiquitous first step in the analysis of neuronal population activity. Recently developed methods use "targeted" approaches that work by identifying multiple, distinct low-dimensional subspaces of activity that capture the population response to individual experimental task variables, such as the value of a presented stimulus or the behavior of the animal. These methods have gained attention because they decompose total neural activity into what are ostensibly different parts of a neuronal computation. However, existing targeted methods have been developed outside of the confines of probabilistic modeling, making some aspects of the procedures ad hoc, or limited in flexibility or interpretability. Here we propose a new model-based method for targeted dimensionality reduction based on a probabilistic generative model of the population response data.

In this paper, we propose a dimensionality reduction method applied to tensor-structured data as a hidden layer (we call it TensorProjection Layer) in a convolutional neural network. Our proposed method transforms input tensors into ones with a smaller dimension by projection. The directions of projection are viewed as training parameters associated with our proposed layer and trained via a supervised learning criterion such as minimization of the cross-entropy loss function. We discuss the gradients of the loss function with respect to the parameters associated with our proposed layer. We also implement simple numerical experiments to evaluate the performance of the TensorProjection Layer.

Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the multi-criteria dimensionality reduction problem where we are given multiple objectives that need to be optimized simultaneously. As an application, our model captures several fairness criteria for dimensionality reduction such as the Fair-PCA problem introduced by Samadi et al. [NeurIPS18] and the Nash Social Welfare (NSW) problem. In the Fair-PCA problem, the input data is divided into k groups, and the goal is to find a single d-dimensional representation for all groups for which the maximum reconstruction error of any one group is minimized.