A New Learning Algorithm for Classification in the Reduced Space

Studies in Classification, Data Analysis, and Knowledge Organization

In this paper new methodologies for clustering and dimensionality reduction of large data sets are illustrated using both a least-squares and maximum likelihood approach. The methodologies are described by both real applications and Monte Carlo simulations.

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.

2006 9th International Conference on Information Fusion, 2006

Clustering has been known as a popular technique for pattern recognition, image processing, and data mining. Unfortunately, all known clustering algorithms tend to break down in high dimensional spaces; this is due to the inherent sparsity of the points. We investigate, in this paper, the use of linear and nonlinear principal manifolds for learning lowdimensional representations for clustering. Several leading methods: PCA, KPCA, Sammon, and CCA are examined and tested in clustering experiments using synthetic and real datasets from the UCI Databases. We compare the clustering performance of the K-means algorithm on data projected by these projection methods. The experimental results show that K-means clustering on data projected by KPCA outperforms those projected by the three other methods.

Encyclopedia of Analytical Chemistry, 2000

Introduction 1 2 Principal Component Analysis 2 2.1 Variance-based Coordinate System 3 2.2 Information Content of Principal Components 3 2.3 Case Studies 4 3 Cluster Analysis 5 3.1 Hierarchical Clustering 6 3.2 Practical Considerations 8 3.3 Case Studies 8 4 Pattern Recognition 9 4.1 k-Nearest Neighbor 12 4.2 Soft Independent Modeling by Class Analogy 12 4.3 Feature Selection 13 4.4 Case Studies 13 5 Software 19 6 Conclusion 19 Abbreviations and Acronyms 19 Related Articles 19 References 20 Clustering and classification are the major subdivisions of pattern recognition techniques. Using these techniques, samples can be classified according to a specific property by measurements indirectly related to the property of interest (such as the type of fuel responsible for an underground spill). An empirical relationship or classification rule can be developed from a set of samples for which the property of interest and the measurements are known. The classification rule can then be used to predict the property in samples that are not part of the original training set. The set of samples for which the property of interest and measurements is known is called the training set. The set of measurements that describe each sample in the data set is called a pattern. The determination of the property of interest by assigning a sample to its respective category is called recognition, hence the term pattern recognition. For pattern recognition analysis, each sample is represented as a data vector x D (x 1 , x 2 , x 3 , x j ,. .. , x n), where component x j is a measurement, e.g. the area a of the jth peak in a chromatogram. Thus, each sample is considered as a point in an n-dimensional measurement space. The dimensionality of the space corresponds to the number of measurements that are available for each sample. A basic assumption is that the distance between pairs of points in this measurement space is inversely related to the degree of similarity between the corresponding samples. Points representing samples from one class will cluster in a limited region of the measurement space distant from the points corresponding to the other class. Pattern recognition (i.e. clustering and classification) is a set of methods for investigating data represented in this manner, in order to assess its overall structure, which is defined as the overall relationship of each sample to every other in the data set.

2017

Clustering is a method of finding homogeneous classes of the known objects. Clustering plays a major role in various applications in data mining such as, computational biology, medical diagnosis, information recovery, CRM, scientific data investigation, selling, and web analysis. Most of the researchers have a major interest in designing clustering algorithms. “Big data” involves terabytes and petabytes of data. Big data is challenging because of its five important characteristics such as volume, velocity, variety, variability and complexity. Therefore big data is difficult to handle using conventional tools and techniques. There are so many issues in clustering techniques, so some of the issues is how to process the data and big data is clustered in more compact format, Clustering algorithm suffer from stability problem, ensemble of single and multi level clustering. An important issue in clustering is that we do not have earlier knowledge regarding data. Also selection of input pa...

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,

In machine learning and statistics, classification is issue of recognizing to which of an arrangement of classes a new observation belongs, on the basis of training set of information containing perceptions (or cases) whose classification enrollment is known. Progresses in information collection and storage capabilities amid the previous decades have prompted a data burden in many scientific areas. In this paper analysis of the performance of various classification algorithm is done on reduced and compressed data and concluded which data is more effective for classifying the data. Low Rank matrices perform the best among the three and Huffman's coding is preferred when we want to save memory space and AANNs is efficient when it to reduce the dimensionality of the data. For classification Low Rank Matrices produces more accurate result than other two.

Many applications require the clustering of large amounts of high-dimensional data. Most clustering algorithms, however, do not work eeectively and eeciently in high-dimensional space, which is due to the so-called "curse of dimensionality". In addition, the high-dimensional data often contains a signiicant amount of noise which causes additional eeectiveness problems. In this paper, we review and compare the existing algorithms for clustering high-dimensional data and show the impact of the curse of di-mensionality on their eeectiveness and eeciency. T h e c o m-parison reveals that condensation-based approaches (such as BIRCH or STING) are the most promising candidates for achieving the necessary eeciency, but it also shows that basically all condensation-based approaches have s e-vere weaknesses with respect to their eeectiveness in high-dimensional space. To overcome these problems, we develop a new clustering technique called OptiGrid which is based on constructing an optimal grid-partitioning of the data. The optimal grid-partitioning is determined by calculating the best partitioning hyperplanes for each d i-mension (if such a partitioning exists) using certain projections of the data. The advantages of our new approach are (1) it has a rm mathematical basis (2) it is by far more eective than existing clustering algorithms for high-dimensional data (3) it is very eecient e v en for large data sets of high dimensionality. To demonstrate the eective-ness and eciency of our new approach, we perform a series of experiments on a number of diierent data sets including real data sets from CAD and molecular biology. A comparison with one of the best known algorithms (BIRCH) shows the superiority of our new approach. Permission to copy without fee a l l o r part of this material is granted p r ovided that the copies are not made or distributed f o r direct commercial advantage, the VLDB copyright notice a n d the title of the publication and its date appear, and notice is given

IRJET, 2020

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.