Nonlinear Dimensionality Reduction With Missing Data Using Parametric Multiple Imputations

Bodt, Cyril de; Mulders, Dounia; Verleysen, Michel; Lee, John A.

doi:10.1109/tnnls.2018.2861891

Cited by 23 publications

(18 citation statements)

References 57 publications

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“…This feature hinders the ability to analyze whether the neighborhoods are reproduced at different data scales and does not highlight the local and global properties of the mapping. For these reasons, some studies developed dimensionality reduction (DR) quality criteria which measure the high-dimensional neighborhood preservation in the projection [43], becoming generally adopted in several publications [44][45][46]. This neighborhood preservation principle is indeed considered as the driving factor in the DR quality [47].…”

Section: Neighborhood Preservation Assessmentmentioning

confidence: 99%

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

López-Sánchez

Bodt

Lee³

et al. 2021

Appl Intell

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Random Projection is one of the most popular and successful dimensionality reduction algorithms for large volumes of data. However, given its stochastic nature, different initializations of the projection matrix can lead to very different levels of performance. This paper presents a guided random search algorithm to mitigate this problem. The proposed method uses a small number of training data samples to iteratively adjust a projection matrix, improving its performance on similarly distributed data. Experimental results show that projection matrices generated with the proposed method result in a better preservation of distances between data samples. Conveniently, this is achieved while preserving the database-friendliness of the projection matrix, as it remains sparse and comprised exclusively of integers after being tuned with our algorithm. Moreover, running the proposed algorithm on a consumer-grade CPU requires only a few seconds.

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Section: Neighborhood Preservation Assessmentmentioning

confidence: 99%

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

López-Sánchez

Bodt

Lee³

et al. 2021

Appl Intell

Self Cite

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“…It is common for existing kernel-based methods to reveal the underlying structure of data by calculating the pairwise similarity between samples. However, in many successful machine learning algorithms, such as dimensionality reduction [34], [35], clustering [16], [36], and recent feature selection algorithms [32], [37], [38], researchers find that it is beneficial to preserve only the reliable local geometry as a representation of the data structure. There are two main underlying reasons.…”

Section: A Construction Of the Neighbor Kernelmentioning

confidence: 99%

Multiple Kernel Clustering With Neighbor-Kernel Subspace Segmentation

Zhou

Liu

Li³

et al. 2020

IEEE Trans. Neural Netw. Learning Syst.

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Multiple kernel clustering (MKC) has been intensively studied during the last few decades. Even though they demonstrate promising clustering performance in various applications, existing MKC algorithms do not sufficiently consider the intrinsic neighborhood structure among base kernels, which could adversely affect the clustering performance. In this paper, we propose a simple yet effective neighbor-kernel-based MKC algorithm to address this issue. Specifically, we first define a neighbor kernel, which can be utilized to preserve the block diagonal structure and strengthen the robustness against noise and outliers among base kernels. After that, we linearly combine these base neighbor kernels to extract a consensus affinity matrix through an exact-rank-constrained subspace segmentation. The naturally possessed block diagonal structure of neighbor kernels better serves the subsequent subspace segmentation, and in turn, the extracted shared structure is further refined through subspace segmentation based on the combined neighbor kernels. In this manner, the above two learning processes can be seamlessly coupled and negotiate with each other to achieve better clustering. Furthermore, we carefully design an efficient iterative optimization algorithm with proven convergence to address the resultant optimization problem. As a by-product, we reveal an interesting insight into the exact-rank constraint in ridge regression by careful theoretical analysis: it back-projects the solution of the unconstrained counterpart to its principal components. Comprehensive experiments have been conducted on several benchmark data sets, and the results demonstrate the effectiveness of the proposed algorithm.

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“…B. Multiple Imputations: [7]Recently many embedding Dimensionality Reduction methods were developed to arrest the 'Curse of Dimensionality', but these methods cannot directly employ on data sets that are incomplete. The limitations are addressed by developing general methods for non linear dimensionality reduction with missing data.…”

Section: Dimensionality Reduction Techniques Using Deep Learningmentioning

confidence: 99%

Traditional Dimensionality Reduction Techniques using Deep Learning

Monca¹,

Parvathy²

2019

IJRTE

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From the analysis of big data, dimensionality reduction techniques play a significant role in various fields where the data is huge with multiple columns or classes. Data with high dimensions contains thousands of features where many of these features contain useful information. Along with this there contains a lot of redundant or irrelevant features which reduce the quality, performance of data and decrease the efficiency in computation. Procedures which are done mathematically for reducing dimensions are known as dimensionality reduction techniques. The main aim of the Dimensionality Reduction algorithms such as Principal Component Analysis (PCA), Random Projection (RP) and Non Negative Matrix Factorization (NMF) is used to decrease the inappropriate information from the data and moreover the features and attributes taken from these algorithms were not able to characterize data as different divisions. This paper gives a review about the traditional methods used in Machine algorithm for reducing the dimension and proposes a view, how deep learning can be used for dimensionality reduction.

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Nonlinear Dimensionality Reduction With Missing Data Using Parametric Multiple Imputations

Cited by 23 publications

References 57 publications

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

Multiple Kernel Clustering With Neighbor-Kernel Subspace Segmentation

Traditional Dimensionality Reduction Techniques using Deep Learning

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