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Dimensionality Reduction


Dimensionality Reduction in Machine Learning

#artificialintelligence

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.


Feature Engineering and Dimensionality Reduction

#artificialintelligence

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.


Applying Dimensionality Reduction with PCA to Cancer Data

#artificialintelligence

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.


6 Dimensionality Reduction Algorithms With Python

#artificialintelligence

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.


Linear Discriminant Analysis for Dimensionality Reduction in Python

#artificialintelligence

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.


Model-based targeted dimensionality reduction for neuronal population data

Neural Information Processing Systems

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.


TensorProjection Layer: A Tensor-Based Dimensionality Reduction Method in CNN

arXiv.org Machine Learning

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.


Multi-Criteria Dimensionality Reduction with Applications to Fairness

Neural Information Processing Systems

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.


Learning nonlinear level sets for dimensionality reduction in function approximation

Neural Information Processing Systems

We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime.


Dimensionality reduction: theoretical perspective on practical measures

Neural Information Processing Systems

Dimensionality reduction plays a central role in real-world applications for Machine Learning, among many fields. In particular, metric dimensionality reduction where data from a general metric is mapped into low dimensional space, is often used as a first step before applying machine learning algorithms. In almost all these applications the quality of the embedding is measured by various average case criteria. Metric dimensionality reduction has also been studied in Math and TCS, within the extremely fruitful and influential field of metric embedding. Yet, the vast majority of theoretical research has been devoted to analyzing the worst case behavior of embeddings and therefore has little relevance to practical settings.