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Dimensionality Reduction


Dimensionality Reduction for Machine Learning - neptune.ai

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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.


t-SNE Machine Learning Algorithm -- A Great Tool for Dimensionality Reduction in Python

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A successful data scientist understands a wide range of Machine Learning algorithms and can explain the results to stakeholders. But, unfortunately, not every stakeholder has a sufficient amount of training to grasp the complexities of ML. Luckily, we can aid our explanations by using dimensionality reduction techniques to create visual representations of high dimensional data. This article will take you through one such technique called t-Distributed Stochastic Neighbor Embedding (t-SNE). Perfect categorization of Machine Learning techniques is not always possible due to the flexibility demonstrated by specific algorithms, making them useful when solving different problems (e.g., one can use k-NN for regression and classification).


Dimensionality Reduction on Face using PCA

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Machine Learning has a wide variety of dimensionality reduction techniques. It is one of the most important aspects in the Data Science field. As a result, in this article, I will present one of the most significant dimensionality reduction techniques used today, known as Principal Component Analysis (PCA). But first, we need to understand what Dimensionality Reduction is and why it is so crucial. Dimensionality reduction, also known as dimension reduction, is the transformation of data from a high-dimensional space to a low-dimensional space in such a way that the low-dimensional representation retains some meaningful properties of the original data, preferably close to its underlying dimension.


TLDR: Twin Learning for Dimensionality Reduction

arXiv.org Artificial Intelligence

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. They are a crucial component of diverse tasks like visualization, compression, indexing, and retrieval. Aiming for a totally different goal, self-supervised visual representation learning has been shown to produce transferable representation functions by learning models that encode invariance to artificially created distortions, e.g. a set of hand-crafted image transformations. Unlike manifold learning methods that usually require propagation on large k-NN graphs or complicated optimization solvers, self-supervised learning approaches rely on simpler and more scalable frameworks for learning. In this paper, we unify these two families of approaches from the angle of manifold learning and propose TLDR, a dimensionality reduction method for generic input spaces that is porting the simple self-supervised learning framework of Barlow Twins to a setting where it is hard or impossible to define an appropriate set of distortions by hand. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss borrowed from the self-supervised literature to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to implement and train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process that does not require mining negative samples to contrast, eigendecompositions, or cumbersome optimization solvers. By replacing PCA with TLDR, we are able to increase the performance of GeM-AP by 4% mAP for 128 dimensions, and to retain its performance with 16x fewer dimensions.


Dimensionality Reduction for Machine Learning

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What is High Demensional Data? How does it affect your Machine Learning models? Have you ever wondered why your model isn't meeting your expectations and you have tried hyper-tuning the parameters until the ends of the earth, with no improvements? Understanding your data and your model may be key. Underneath such an immense and complicated hood, you may be concerned that there are few to no ways of gaining more insight into your data, as well as your model.


Isomap Embedding -- An Awesome Approach to Non-linear Dimensionality Reduction

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As you can see, Isomap is an Unsupervised Machine Learning technique aimed at Dimensionality Reduction. It differs from a few other techniques in the same category by using a non-linear approach to dimensionality reduction instead of linear mappings used by algorithms such as PCA. We will see how linear vs. non-linear approaches differ in the next section. Isomap is a technique that combines several different algorithms, enabling it to use a non-linear way to reduce dimensions while preserving local structures. Before we look at the example of Isomap and compare it to a linear method of Principal Components Analysis (PCA), let's list the high-level steps that Isomap performs: For our example, let's create a 3D object known as a Swiss roll.


Interactive Dimensionality Reduction for Comparative Analysis

arXiv.org Machine Learning

Finding the similarities and differences between groups of datasets is a fundamental analysis task. For high-dimensional data, dimensionality reduction (DR) methods are often used to find the characteristics of each group. However, existing DR methods provide limited capability and flexibility for such comparative analysis as each method is designed only for a narrow analysis target, such as identifying factors that most differentiate groups. This paper presents an interactive DR framework where we integrate our new DR method, called ULCA (unified linear comparative analysis), with an interactive visual interface. ULCA unifies two DR schemes, discriminant analysis and contrastive learning, to support various comparative analysis tasks. To provide flexibility for comparative analysis, we develop an optimization algorithm that enables analysts to interactively refine ULCA results. Additionally, the interactive visualization interface facilitates interpretation and refinement of the ULCA results. We evaluate ULCA and the optimization algorithm to show their efficiency as well as present multiple case studies using real-world datasets to demonstrate the usefulness of this framework.


Dimensionality Reduction using an Autoencoder in Python

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Dimensionality is the number of input variables or features for a dataset and dimensionality reduction is the process through which we reduce the number of input variables in a dataset. A lot of input features makes predictive modeling a more challenging task. When dealing with high dimensional data, it is often useful to reduce the dimensionality by projecting the data to a lower dimensional subspace which captures the "essence" of the data. This is called dimensionality reduction. "dimensionality reduction yields a more compact, more easily interpretable representation of the target concept, focusing the user's attention on the most relevant variables."


Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Survey

arXiv.org Machine Learning

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component Analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel for unfolding the manifold of data to its maximum variance. We first briefly introduce kernel learning by SDP for the transduction task. Then, we explain MVU in detail. Various versions of supervised MVU using nearest neighbors graph, by class-wise unfolding, by Fisher criterion, and by colored MVU are explained. We also explain out-of-sample extension of MVU using eigenfunctions and kernel mapping. Finally, we introduce other variants of MVU including action respecting embedding, relaxed MVU, and landmark MVU for big data.


Guide To Dimensionality Reduction With Recursive Feature Elimination

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Therefore, feature elimination in statistics and machine learning is referred to as choosing a subset of relevant features from the dataset to use in further …