Dimensionality Reduction A Short Tutorial (original) (raw)

Three Novel Approaches to Dimensionality Reduction

2018

In this paper, we propose three novel approaches to dimensionality reduction, each of which reduces the number of dimensions of a dataset Dnxp from p to k. We shall implement two clustering techniques (hierarchical and k-means clustering) and then compare our three novel approaches with six existing approaches (Random Projections (RP), Principal Component Analysis (PCA), the variance approach (Var), the Direct Approach (DA), the combined approach (CA) and the New Random Approach (NRA)) by the extent to which they preserve each of these clustering techniques. We shall use the rand index to measure the extent to which the clustering of the original dataset (using any of the two clustering techniques) is preserved by any dimensionality reduction technique.

Recent methods for dimensionality reduction: A brief comparative analysis

Dimensionality reduction is a key stage for both the design of a pattern recognition system or data visualization. Recently, there has been a increasing interest in those methods aimed at preserving the data topology. Among them, Laplacian eigenmaps (LE) and stochastic neighbour embedding (SNE) are the most representative. In this work, we present a brief comparative among very recent methods being alternatives to LE and SNE. Comparisons are done mainly on two aspects: algorithm implementation, and complexity. Also, relations between methods are depicted. The goal of this work is providing researches on this field with some discussion as well as criteria decision to choose a method according to the user's needs and/or keeping a good trade-off between performance and required processing time.

Investigating the Relative Performances of Assorted Dimensionality Reduction Techniques

ICAI 20, 2018

In this paper, we shall implement ten techniques which can be used to reduce the dimensionality of a data set. These include random projection (RP), principal component analysis (PCA), the variance approach (Var), the combined approach (CA), the direct approach (DA), the new random approach version 1 (NRA v1), the new random approach version 2 (NRA v2), and three novel approaches (Nov App1, Nov App2 and Nov App3 proposed by Baba, Nsang and Adeseye[1]. We shall investigate the relative effective performances of these techniques based on four different criteria: classification preservation, variance preservation, interpoint distance preservation and total run time. We shall then describe hierarchical clustering, and compare the ten dimensionality reduction techniques mentioned above for hierarchical clustering preservation.

Data Dimensionality Reduction Techniques : Review

2020

Data science is the study of data. It involves developing methods of recording, storing, and analyzing data to effectively extract useful information. The goal of data science is to gain insights and knowledge from any type of data — both structured and unstructured. Data science is related to computer science, but is a separate field. Computer science involves creating programs and algorithms to record and process data, while data science covers any type of data analysis, which may or may not use computers. Data science is more closely related to the mathematics field of Statistics, which includes the collection, organization, analysis, and presentation of data. Because of the large amounts of data modern companies and organizations maintain, data science has become an integral part of IT. For example, a company that has petabytes of user data may use data science to develop effective ways to store, manage, and analyze the data. The company may use the scientific method to run test...

Dimensionality reduction methods

Metodološki zvezki, 2005

In case one or more sets of variables are available, the use of dimensional reduction methods could be necessary. In this contest, after a review on the link between the Shrinkage Regression Methods and Dimensional Reduction Methods, authors provide a different multivariate extension of the Garthwaite's PLS approach (1994) where a simple linear regression coefficients framework could be given for several dimensional reduction methods.

Some steps towards a general principle for dimensionality reduction mappings

2010

In the past years, many dimensionality reduction methods have been established which allow to visualize high dimensional data sets. Recently, also formal evaluation schemes have been proposed for data visualization, which allow a quantitative evaluation along general principles. Most techniques provide a mapping of a priorly given finite set of points only, requiring additional steps for out-of-sample extensions. We propose a general view on dimensionality reduction based on the concept of cost functions, and, based on this general principle, extend dimensionality reduction to explicit mappings of the data manifold. This offers the possibility of simple out-of-sample extensions. Further, it opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points. We demonstrate the approach based in a simple example.

Dimensionality Reduction with Image Data

Lecture Notes in Computer Science, 2004

A common objective in image analysis is dimensionality reduction. The most common often used data-exploratory technique with this objective is principal component analysis. We propose a new method based on the projection of the images as matrices after a Procrustes rotation and show that it leads to a better reconstruction of images. Summary. A common objective in image analysis is dimensionality reduction. The most often used data-exploratory technique with this objective is principal component analysis. We propose a new method based on the projection of the images as matrices after a Procrustes rotation and show that it leads to a better reconstruction of images. Ã ÝÛÓÖ × Eigenfaces; Multivariate linear regression; Singular value decomposition; Principal component analysis; Generalized proscrustes analysis.

A Survey on Dimension Reduction Techniques for Classification of Multidimensional Data

Progresses in information collection and storage capabilities amid the previous decades have prompted a data over-burden in many sciences. To translate the data covered up in multidimensional information can be considered as trying and entangled assignment. High-dimensional datasets present numerous numerical difficulties and in addition some opportunities, and will undoubtedly offer ascent to new hypothetical improvements. The statistical methods face challenging tasks when dealing with such high‐dimensional data. In any case, a significant part of the information is profoundly redundant furthermore, can be productively conveyed down to a much littler number of variables without a noteworthy loss of data. The mathematic strategies making conceivable this lessening are called dimensionality reduction; they have generally been produced by fields such as Statistics or Machine Learning. In this survey we order the plenty of dimension reduction systems accessible and give the numerical knowledge behind them., auto associative neural network ________________________________________________________________________________________________________ I. INTRODUCTION To interpret the data covered up in multidimensional data can be considered as trying furthermore, confused assignment. Ordinarily, dimension reduction or data compression is considered as the initial step to data analysis and investigation of multidimensional data. Statically and machine learning strategies confront a considerable issue when managing such high‐ dimensional data, and typically the quantity of data variables is decreased before an data mining algorithm can be effectively applied. The dimensionality reduction can be made in two unique courses: by just keeping the most relevant variables from the original dataset (this procedure is called feature selection) or by abusing the redundancy of the dataset and by finding a more diminutive course of action of new variables, each being a blend of the information variables, containing essentially the same data as the information variables (this system is called dimensionality reduction). A standout amongst the most broadly utilized dimensionality reduction methods, Principal Component Analysis (PCA), goes back to Karl Pearson in 1901 [1]. The key thought is to discover a new arrange framework in which the information can be communicated with numerous less variables without a critical error. This new premise can be global or local and can satisfy altogether different properties. The late explosion of information accessible together with the evermore intense computational assets have pulled in the consideration of numerous specialists in Statistics, Computer Science and Applied Mathematics who have added to an extensive variety of computational procedures managing the dimensionality reduction issue (for surveys see [3,2,4]). In numerical terms, the issue we research can be expressed as takes after: given the p-dimensional arbitrary variable x = (x1,...,xp)T , and a lower dimensional representation of it, s = (s1,...,sk)T with k<p, that catches the content in the original data, as per some basis. The segments of s are infrequently called the hidden components. Different fields use distinctive names for the p multivariate vectors:the term "variable" is mostly used in statistics, while "feature" and "attribute" are options normally utilized as a part of the computer science and machine learning literature. Throughout this paper, we accept that we have n perceptions, each being a realization of the p-dimensional random variable x = (x1,…,xp) T with mean E(x) = µ= (µ1,…, µp) T and covariance matrix E{(x-µ)(x-µ) T }= ∑p×p. We denote such an observation matrix by X={xi,j:1≤i≤p,1≤j≤n}. If µi and σi = ∑(i,i) denote the mean and the standard deviation of the ith random variable, separately, then we will frequently institutionalize the perceptions xi,j by (xi,j-µi)/σi, where ^ µi = xi = 1/n   n j j xi 1 , and σi = 1/n 2) , (1 xi j i x n j   . We recognize two noteworthy sorts of dimension reduction strategies: linear and non-linear. Linear strategies result in each of the k≤p parts of the new variable being a linear mix of the original variables: Si = wi,1 x1+…wi,pxp, for i = 1,…,k, or (1) s = Wx, (2) Where Wk,p is the linear transformation weight matrix. Expressing the same relationship as x = As; (3) with Ap×k, we note that the new variables s are also called the hidden or the latent variables. In terms of an n×p observation matrix X, we have Si,j = wiX1,j + …wi,p Xp,j ; for i = 1,…, k, and j = 1,…,n, (4) where j indicates the jth realization, or, equivalently,

Comparative Analysis of Dimensionality Reduction Methods

Undergraduate Research Project , 2019

The face is the primary focus of attention and plays a major role in identification and establishing the uniqueness of a particular person from the rest of the human society. In most of the face recognition systems around, extraction or selection of facial features and the implementation of recognition are through efficient algorithms, these algorithms are modified for different purposes. The specific objective was to design a model that uses face recognition to compare dimensionality reduction methods. This research work provided a comparative analysis on three methods of dimensionality reduction. The methodology was based on using face recognition to analysis the accuracy and time of recognition of faces (with variations) using principal component analysis (PCA), linear discriminant analysis (LDA) and convolution neural network (CNN). The model used a dataset of 400 facial images (black and white) which combines Olivetti facial dataset and a local facial dataset (extracted from pictures of some students in RCF FUTA). Eigenfaces and fisherfaces were used to train the SVM classifier. The result from LDA and CNN showed better performance than PCA.

A survey of dimensionality reduction techniques

Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for a single experiment and therefore the statistical methods face challenging tasks when dealing with such high-dimensional data. However, much of the data is highly redundant and can be efficiently brought down to a much smaller number of variables without a significant loss of information. The mathematical procedures making possible this reduction are called dimensionality reduction techniques; they have widely been developed by fields like Statistics or Machine Learning, and are currently a hot research topic. In this review we categorize the plethora of dimension reduction techniques available and give the mathematical insight behind them.