Dimensionality reduction or dimension reduction is the process of reducing the number of random variables under consideration by obtaining a set of principal variables. It can be divided into feature selection (find a subset of the original variables) and feature extraction (transform the data in the high-dimensional space to a space of fewer dimensions). (Wikipedia)
You've just stumbled upon the most complete, in-depth Visualization/Dimensionality Reduction course online. This course is designed to give you the Visualization/Dimensionality Reduction skills you need to become an expert data scientist. By the end of the course, you will understand Visualization/Dimensionality Reduction extremely well and be able to use the techniques on your own projects and be productive as a computer scientist and data analyst. What makes this course a bestseller? Like you, thousands of others were frustrated and fed up with fragmented Youtube tutorials or incomplete or outdated courses which assume you already know a bunch of stuff, as well as thick, college-like textbooks able to send even the most caffeine-fuelled coder to sleep.
Become a Data Scientist expert! Everything you need to get the job you want! "Dimensionality Reduction: Machine Learning with Python" is likely a guide or tutorial that focuses on the topic of dimensionality reduction in the context of machine learning. In machine learning, dimensionality reduction is the process of reducing the number of features in a dataset while preserving as much of the important information as possible. This is often necessary because high-dimensional datasets can be difficult to work with, and can lead to problems such as overfitting and increased computational complexity. This guide likely covers these techniques with some implementation of these techniques using python libraries like numpy, scikit-learn and matplotlib .
Abstract: The weighted Euclidean distance between two vectors is a Euclidean distance where the contribution of each dimension is scaled by a given non-negative weight. The Johnson-Lindenstrauss (JL) lemma can be easily adapted to the weighted Euclidean distance if weights are known at construction time. Given a set of n vectors with dimension d, it suffices to scale each dimension of the input vectors according to the weights, and then apply any standard JL reduction: the weighted Euclidean distance between pairs of vectors is preserved within a multiplicative factor ε with high probability. However, this is not the case when weights are provided after the dimensionality reduction. In this paper, we show that by applying a linear map from real vectors to a complex vector space, it is possible to update the compressed vectors so that the weighted Euclidean distances between pairs of points can be computed within a multiplicative factor ε, even when weights are provided after the dimensionality reduction.
ONLINE TRAINING, with Dr. Mira ABBOUD fees 50$ or 2.000.000 LBP, via OMT 5 days - January 23, 24, 25, 26 & 27 6:00pm - 8:00pm (UCT +2) The training covers the following topics: Python basics (lists/tuples/dictionaries) Numpy Library (slicing, boolean indexing) Data Acquisition with Pandas (Series & Dataframes) Data Manipulation (filter, aggregation & grouping, Cross-tabulation) Data Visualization Introduction to Pre-processing (outliers detection, null values, features selection, dimensionality reduction, standardization) - we will cover one or two techniques of each. Build basic classification model in Python
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. Perhaps the most popular technique for dimensionality reduction in machine learning is Principal Component Analysis, or PCA for short. This is a technique that comes from the field of linear algebra and can be used as a data preparation technique to create a projection of a dataset prior to fitting a model. In this tutorial, you will discover how to use PCA for dimensionality reduction when developing predictive models.
Data forms the foundation of any machine learning algorithm, without it, Data Science can not happen. Sometimes, it can contain a huge number of features, some of which are not even required. Such redundant information makes modeling complicated. Furthermore, interpreting and understanding the data by visualization gets difficult because of the high dimensionality. This is where dimensionality reduction comes into play. Dimensionality reduction is the task of reducing the number of features in a dataset. In machine learning tasks like regression or classification, there are often too many variables to work with. These variables are also called features.
Welcome to the second part of Humans Learning from Machines. In this series, we discuss the philosophical relevance of some interesting concepts in Artificial Intelligence. In part 1: The Curse of Dimensionality; More is not always better!, we explored how more data can affect learnability in terms of Computational Burden, the Volume of Space, Visualisation and Parameter Estimation. In this part, we discuss how to handle the curse of dimensionality and how we can apply these concepts to improve our well-being. As we wrapped up the first part, When we feel overwhelmed by the infinite dimensions of data surrounding us, we change our perspectives and see things from a different angle to separate noise and relevant information.
A dataset is made up of a number of features. As long as these features are related in someway to the target and are optimal in number a machine learning model will be able to produce decent results after learning from the data. But if the number of features are high and most of the features do not contribute towards the model's learning then the performance of the model will go down and the time taken to output predictions also increases. The process of reducing the number of dimensions by transforming the original feature space into a subspace is one method of performing dimensionality reduction and Principal Component Analysis (PCA) does this. So let's take a look into the building concepts of PCA.
Abstract: Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the regression. The method can result in substantial gains in estimation efficiency and prediction accuracy over traditional maximum likelihood and least squares estimates. While predictor envelopes have been developed and studied for independent data, no work has been done adapting predictor envelopes to spatial data. In this work, the predictor envelope is adapted to a popular spatial model to form the spatial predictor envelope (SPE).
In this paper, we consider the problem of non-linear dimensionality reduction under uncertainty, both from a theoretical and algorithmic perspectives. Since real-world data usually contain measurements with uncertainties and artifacts, the input space in the proposed framework consists of probability distributions to model the uncertainties associated with each sample. We propose a new dimensionality reduction framework, called NGEU, which leverages uncertainty information and directly extends several traditional approaches, e.g., KPCA, MDA/KMFA, to receive as inputs the probability distributions instead of the original data. We show that the proposed NGEU formulation exhibits a global closed-form solution, and we analyze, based on the Rademacher complexity, how the underlying uncertainties theoretically affect the generalization ability of the framework. Empirical results on different datasets show the effectiveness of the proposed framework.