Dimensionality

Tame the Curse of Dimensionality! Learn Dimensionality Reduction (PCA) and implement it with Python and Scikit-Learn.Continue reading on Towards Data Science » Tame the Curse of Dimensionality! Learn Dimensionality Reduction (PCA) and implement it with Python and Scikit-Learn.Continue reading on Towards Data Science » FOLLOW US ON GOOGLE NEWS Read original article here Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink to the primary…

Photo by Mathew Schwartz on UnsplashIntroductionIn the previous article, we discussed the surprising behavior of data in higher dimensions. We found that volume tends to accumulate in the corners of spaces in a strange way, and we simulated a hypersphere inscribed inside a hypercube to investigate this, observing an interesting decrease in their volume ratio as the dimensions grew. Examples that demonstrated the advantages of multi-dimensional thinking were the DVD-paper experiment and the kernel trick in support vector…

Learn how to efficiently apply state-of-the-art Dimensionality Reduction methods and boost your Machine Learning models.Continue reading on Towards Data Science » Learn how to efficiently apply state-of-the-art Dimensionality Reduction methods and boost your Machine Learning models.Continue reading on Towards Data Science » FOLLOW US ON GOOGLE NEWS Read original article here Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink to the…

Discussing theory and implementation with Python and Scikit-learnOriginal image by an_photos from Pixabay (Slightly edited by author)I have already discussed different types of dimensionality reduction techniques in detail.Principal Component Analysis (PCA), Factor Analysis (FA), Linear Discriminant Analysis (LDA), Autoencoders (AEs), and Kernel PCA are the most popular ones.Non-Negative Matrix Factorization (NMF or NNMF) is also a linear dimensionality reduction technique that can be used to reduce the dimensionality of…

Comparison of PCA and dynamic factor modelPhoto by Kolleen Gladden on UnsplashMany data scientists are forced to deal with the challenge of dimension. Data sets can contain huge amounts of variables, making them complex to understand and compute. For example an asset manager can be overwhelmed with the many dynamic variables associated with its portfolio, and processing a large amount of data can lead to computational issues. Reducing the dimension is a way to extract the information from a large number of variables into…

Performing PCA using both methods and comparing the resultsImage by Viktor Peschel from PixabaySingular value decomposition (SVD) and eigendecomposition (ED) are both matrix factorization methods that come from linear algebra.In the field of machine learning (ML), both can be used as data reduction methods (i.e. for dimensionality reduction).Previously, we’ve discussed eigendecomposition in detail. Today, we’ll give more emphasis on discussing SVD.Principal component analysis (PCA) can be performed using both methods. PCA…

Neural Networks and Deep Learning Course: Part 45Photo by Robert Katzki on UnsplashCan general machine learning algorithms outperform neural networks with small datasets?In general, deep learning algorithms such as neural networks require a massive amount of data to achieve reasonable performance. So, neural networks like autoencoders can benefit from very large datasets that we use to train the models.Sometimes, general machine learning algorithms can outperform neural network algorithms when they are trained with very…

Linear discriminant analysis (LDA) for dimensionality reduction while maximizing class separabilityPhoto by Will Francis on UnsplashDimensionality reduction can be achieved using various techniques. Eleven such techniques have already been discussed in my popular article, 11 Dimensionality reduction techniques you should know in 2021.There, you will properly learn the meanings behind some technical terms such as dimensionality and dimensionality reduction.In short, dimensionality refers to the number of features…

Non-linear dimensionality reduction using kernel PCAPhoto by Steve Johnson on UnsplashStandard PCA is suitable for linear dimensionality reduction as it does linear transformation when reducing the number of features in the data. In other words, standard PCA works well with linearly separable data in which the different classes can be clearly separated by drawing a straight line (in the case of 2D data) or a hyperplane (in the case of 3D and higher dimensional data).Standard PCA will not work well with linearly…

Using gradient boosting and FDA to classify ECG data in PythonPhoto by Markus Spiske on UnsplashThe curse of dimensionality refers to the challenges and difficulties that arise when dealing with high-dimensional datasets in machine learning. As the number of dimensions (or features) in a dataset increases, the amount of data required to accurately learn the relationships between the features and the target variable grows exponentially. This can make it difficult, to train a high-performing machine learning model on a…