This document discusses dimension reduction techniques for visualizing large, high-dimensional data. It presents multidimensional scaling (MDS) and generative topographic mapping (GTM) for this task. To address challenges of data size, an interpolation approach is introduced that maps new data points based on a reduced set of sample points. Experimental results show MDS and GTM interpolation can efficiently visualize millions of data points in 2-3 dimensions with reasonable quality compared to processing all points directly.
Spectroscopy or hyperspectral imaging consists in the acquisition, analysis, and extraction of the spectral information measured on a specific region or object using an airborne or satellite device. Hyperspectral imaging has become an active field of research recently. One way of analysing such data is through clustering. However, due to the high dimensionality of the data and the small distance between the different material signatures, clustering such a data is a challenging task.In this paper, we empirically compared five clustering techniques in different hyperspectral data sets. The considered clustering techniques are K-means, K-medoids, fuzzy Cmeans, hierarchical, and density-based spatial clustering of applications with noise. Four data sets are used to achieve this purpose which is Botswana, Kennedy space centre, Pavia, and Pavia University. Beside the accuracy, we adopted four more similarity measures: Rand statistics, Jaccard coefficient, Fowlkes-Mallows index, and Hubert index. According to accuracy, we found that fuzzy C-means clustering is doing better on Botswana and Pavia data sets, K-means and K-medoids are giving better results on Kennedy space centre data set, and for Pavia University the hierarchical clustering is better
The variational Gaussian process (VGP), a Bayesian nonparametric model which adapts its shape to match com- plex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity.
Universal Approximation Property via Quantum Feature Maps
----
The quantum Hilbert space can be used as a quantum-enhanced feature space in machine learning (ML) via the quantum feature map to encode classical data into quantum states. We prove the ability to approximate any continuous function with optimal approximation rate via quantum ML models in typical quantum feature maps.
---
Contributed talk at Quantum Techniques in Machine Learning 2021, Tokyo, November 8-12 2021.
By Quoc Hoan Tran, Takahiro Goto and Kohei Nakajima
A PSO-Based Subtractive Data Clustering AlgorithmIJORCS
There is a tremendous proliferation in the amount of information available on the largest shared information source, the World Wide Web. Fast and high-quality clustering algorithms play an important role in helping users to effectively navigate, summarize, and organize the information. Recent studies have shown that partitional clustering algorithms such as the k-means algorithm are the most popular algorithms for clustering large datasets. The major problem with partitional clustering algorithms is that they are sensitive to the selection of the initial partitions and are prone to premature converge to local optima. Subtractive clustering is a fast, one-pass algorithm for estimating the number of clusters and cluster centers for any given set of data. The cluster estimates can be used to initialize iterative optimization-based clustering methods and model identification methods. In this paper, we present a hybrid Particle Swarm Optimization, Subtractive + (PSO) clustering algorithm that performs fast clustering. For comparison purpose, we applied the Subtractive + (PSO) clustering algorithm, PSO, and the Subtractive clustering algorithms on three different datasets. The results illustrate that the Subtractive + (PSO) clustering algorithm can generate the most compact clustering results as compared to other algorithms.
COMPARATIVE PERFORMANCE ANALYSIS OF RNSC AND MCL ALGORITHMS ON POWER-LAW DIST...acijjournal
Cluster analysis of graph related problems is an important issue now-a-day. Different types of graph
clustering techniques are appeared in the field but most of them are vulnerable in terms of effectiveness
and fragmentation of output in case of real-world applications in diverse systems. In this paper, we will
provide a comparative behavioural analysis of RNSC (Restricted Neighbourhood Search Clustering) and
MCL (Markov Clustering) algorithms on Power-Law Distribution graphs. RNSC is a graph clustering
technique using stochastic local search. RNSC algorithm tries to achieve optimal cost clustering by
assigning some cost functions to the set of clusterings of a graph. This algorithm was implemented by A.
D. King only for undirected and unweighted random graphs. Another popular graph clustering
algorithm MCL is based on stochastic flow simulation model for weighted graphs. There are plentiful
applications of power-law or scale-free graphs in nature and society. Scale-free topology is stochastic i.e.
nodes are connected in a random manner. Complex network topologies like World Wide Web, the web of
human sexual contacts, or the chemical network of a cell etc., are basically following power-law
distribution to represent different real-life systems. This paper uses real large-scale power-law
distribution graphs to conduct the performance analysis of RNSC behaviour compared with Markov
clustering (MCL) algorithm. Extensive experimental results on several synthetic and real power-law
distribution datasets reveal the effectiveness of our approach to comparative performance measure of
these algorithms on the basis of cost of clustering, cluster size, modularity index of clustering results and
normalized mutual information (NMI).
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Spectroscopy or hyperspectral imaging consists in the acquisition, analysis, and extraction of the spectral information measured on a specific region or object using an airborne or satellite device. Hyperspectral imaging has become an active field of research recently. One way of analysing such data is through clustering. However, due to the high dimensionality of the data and the small distance between the different material signatures, clustering such a data is a challenging task.In this paper, we empirically compared five clustering techniques in different hyperspectral data sets. The considered clustering techniques are K-means, K-medoids, fuzzy Cmeans, hierarchical, and density-based spatial clustering of applications with noise. Four data sets are used to achieve this purpose which is Botswana, Kennedy space centre, Pavia, and Pavia University. Beside the accuracy, we adopted four more similarity measures: Rand statistics, Jaccard coefficient, Fowlkes-Mallows index, and Hubert index. According to accuracy, we found that fuzzy C-means clustering is doing better on Botswana and Pavia data sets, K-means and K-medoids are giving better results on Kennedy space centre data set, and for Pavia University the hierarchical clustering is better
The variational Gaussian process (VGP), a Bayesian nonparametric model which adapts its shape to match com- plex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity.
Universal Approximation Property via Quantum Feature Maps
----
The quantum Hilbert space can be used as a quantum-enhanced feature space in machine learning (ML) via the quantum feature map to encode classical data into quantum states. We prove the ability to approximate any continuous function with optimal approximation rate via quantum ML models in typical quantum feature maps.
---
Contributed talk at Quantum Techniques in Machine Learning 2021, Tokyo, November 8-12 2021.
By Quoc Hoan Tran, Takahiro Goto and Kohei Nakajima
A PSO-Based Subtractive Data Clustering AlgorithmIJORCS
There is a tremendous proliferation in the amount of information available on the largest shared information source, the World Wide Web. Fast and high-quality clustering algorithms play an important role in helping users to effectively navigate, summarize, and organize the information. Recent studies have shown that partitional clustering algorithms such as the k-means algorithm are the most popular algorithms for clustering large datasets. The major problem with partitional clustering algorithms is that they are sensitive to the selection of the initial partitions and are prone to premature converge to local optima. Subtractive clustering is a fast, one-pass algorithm for estimating the number of clusters and cluster centers for any given set of data. The cluster estimates can be used to initialize iterative optimization-based clustering methods and model identification methods. In this paper, we present a hybrid Particle Swarm Optimization, Subtractive + (PSO) clustering algorithm that performs fast clustering. For comparison purpose, we applied the Subtractive + (PSO) clustering algorithm, PSO, and the Subtractive clustering algorithms on three different datasets. The results illustrate that the Subtractive + (PSO) clustering algorithm can generate the most compact clustering results as compared to other algorithms.
COMPARATIVE PERFORMANCE ANALYSIS OF RNSC AND MCL ALGORITHMS ON POWER-LAW DIST...acijjournal
Cluster analysis of graph related problems is an important issue now-a-day. Different types of graph
clustering techniques are appeared in the field but most of them are vulnerable in terms of effectiveness
and fragmentation of output in case of real-world applications in diverse systems. In this paper, we will
provide a comparative behavioural analysis of RNSC (Restricted Neighbourhood Search Clustering) and
MCL (Markov Clustering) algorithms on Power-Law Distribution graphs. RNSC is a graph clustering
technique using stochastic local search. RNSC algorithm tries to achieve optimal cost clustering by
assigning some cost functions to the set of clusterings of a graph. This algorithm was implemented by A.
D. King only for undirected and unweighted random graphs. Another popular graph clustering
algorithm MCL is based on stochastic flow simulation model for weighted graphs. There are plentiful
applications of power-law or scale-free graphs in nature and society. Scale-free topology is stochastic i.e.
nodes are connected in a random manner. Complex network topologies like World Wide Web, the web of
human sexual contacts, or the chemical network of a cell etc., are basically following power-law
distribution to represent different real-life systems. This paper uses real large-scale power-law
distribution graphs to conduct the performance analysis of RNSC behaviour compared with Markov
clustering (MCL) algorithm. Extensive experimental results on several synthetic and real power-law
distribution datasets reveal the effectiveness of our approach to comparative performance measure of
these algorithms on the basis of cost of clustering, cluster size, modularity index of clustering results and
normalized mutual information (NMI).
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Web image annotation by diffusion maps manifold learning algorithmijfcstjournal
Automatic image annotation is one of the most challenging problems in machine vision areas. The goal of this task is to predict number of keywords automatically for images captured in real data. Many methods are based on visual features in order to calculate similarities between image samples. But the computation cost of these approaches is very high. These methods require many training samples to be stored in memory. To lessen thisburden, a number of techniques have been developed to reduce the number
of features in a dataset. Manifold learning is a popular approach to nonlinear dimensionality reduction. In
this paper, we investigate Diffusion maps manifold learning method for webimage auto-annotation task.Diffusion maps
manifold learning method isused to reduce the dimension of some visual features. Extensive experiments and analysis onNUS-WIDE-LITE web image dataset with
different visual featuresshow how this manifold learning dimensionality reduction method can be applied effectively to image annotation.
Multimodal Biometrics Recognition by Dimensionality Diminution MethodIJERA Editor
Multimodal biometric system utilizes two or more character modalities, e.g., face, ear, and fingerprint,
Signature, plamprint to improve the recognition accuracy of conventional unimodal methods. We propose a new
dimensionality reduction method called Dimension Diminish Projection (DDP) in this paper. DDP can not only
preserve local information by capturing the intra-modal geometry, but also extract between-class relevant
structures for classification effectively. Experimental results show that our proposed method performs better
than other algorithms including PCA, LDA and MFA.
E XTENDED F AST S EARCH C LUSTERING A LGORITHM : W IDELY D ENSITY C LUSTERS ,...csandit
CFSFDP (clustering by fast search and find of densi
ty peaks) is recently developed density-
based clustering algorithm. Compared to DBSCAN, it
needs less parameters and is
computationally cheap for its non-iteration. Alex.
at al have demonstrated its power by many
applications. However, CFSFDP performs not well whe
n there are more than one density peak
for one cluster, what we name as "no density peaks"
. In this paper, inspired by the idea of a
hierarchical clustering algorithm CHAMELEON, we pro
pose an extension of CFSFDP,
E_CFSFDP, to adapt more applications. In particular
, we take use of original CFSFDP to
generating initial clusters first, then merge the s
ub clusters in the second phase. We have
conducted the algorithm to several data sets, of wh
ich, there are "no density peaks". Experiment
results show that our approach outperforms the orig
inal one due to it breaks through the strict
claim of data sets
Introducing New Parameters to Compare the Accuracy and Reliability of Mean-Sh...sipij
Mean shift algorithms are among the most functional tracking methods which are accurate and have almost simple computation. Different versions of this algorithm are developed which are differ in template updating and their window sizes. To measure the reliability and accuracy of these methods one should normally rely on visual results or number of iteration. In this paper we introduce two new parameters which can be used to compare the algorithms especially when their results are close to each other.
Dimensionality Reduction and feature extraction.pptxSivam Chinna
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.
A simple framework for contrastive learning of visual representationsDevansh16
Link: https://machine-learning-made-simple.medium.com/learnings-from-simclr-a-framework-contrastive-learning-for-visual-representations-6c145a5d8e99
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This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.
Comments: ICML'2020. Code and pretrained models at this https URL
Subjects: Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML)
Cite as: arXiv:2002.05709 [cs.LG]
(or arXiv:2002.05709v3 [cs.LG] for this version)
Submission history
From: Ting Chen [view email]
[v1] Thu, 13 Feb 2020 18:50:45 UTC (5,093 KB)
[v2] Mon, 30 Mar 2020 15:32:51 UTC (5,047 KB)
[v3] Wed, 1 Jul 2020 00:09:08 UTC (5,829 KB)
Adversarial Variational Autoencoders to extend and improve generative model -...Loc Nguyen
Generative artificial intelligence (GenAI) has been developing with many incredible achievements like ChatGPT and Bard. Deep generative model (DGM) is a branch of GenAI, which is preeminent in generating raster data such as image and sound due to strong points of deep neural network (DNN) in inference and recognition. The built-in inference mechanism of DNN, which simulates and aims to synaptic plasticity of human neuron network, fosters generation ability of DGM which produces surprised results with support of statistical flexibility. Two popular approaches in DGM are Variational Autoencoders (VAE) and Generative Adversarial Network (GAN). Both VAE and GAN have their own strong points although they share and imply underline theory of statistics as well as incredible complex via hidden layers of DNN when DNN becomes effective encoding/decoding functions without concrete specifications. In this research, I try to unify VAE and GAN into a consistent and consolidated model called Adversarial Variational Autoencoders (AVA) in which VAE and GAN complement each other, for instance, VAE is a good data generator by encoding data via excellent ideology of Kullback-Leibler divergence and GAN is a significantly important method to assess reliability of data which is realistic or fake. In other words, AVA aims to improve accuracy of generative models, besides AVA extends function of simple generative models. In methodology this research focuses on combination of applied mathematical concepts and skillful techniques of computer programming in order to implement and solve complicated problems as simply as possible.
TOWARDS REDUCTION OF DATA FLOW IN A DISTRIBUTED NETWORK USING PRINCIPAL COMPO...cscpconf
For performing distributed data mining two approaches are possible: First, data from several sources are copied to a data warehouse and mining algorithms are applied in it. Secondly,
mining can performed at the local sites and the results can be aggregated. When the number of
features is high, a lot of bandwidth is consumed in transferring datasets to a centralized location. For this dimensionality reduction can be done at the local sites. In dimensionality reduction a certain encoding is applied on data so as to obtain its compressed form. The
reduced features thus obtained at the local sites are aggregated and data mining algorithms are applied on them. There are several methods of performing dimensionality reduction. Two most important ones are Discrete Wavelet Transforms (DWT) and Principal Component Analysis (PCA). Here a detailed study is done on how PCA could be useful in reducing data flow across a distributed network.
A Novel Algorithm for Design Tree Classification with PCA
Dimension Reduction And Visualization Of Large High Dimensional Data Via Interpolation
1. Dimension Reduction and Visualization of Large High-Dimensional Data via Interpolation Seung-HeeBae, Jong Youl Choi, Judy Qiu, and Geoffrey Fox School of Informatics and Computing Pervasive Technology Institute Indiana University SALSA project http://salsahpc.indiana.edu
2. Outline Introduction to Point Data Visualization Review of Dimension Reduction Algorithms. Multidimensional Scaling (MDS) Generative Topographic Mapping (GTM) Challenges Interpolation MDS Interpolation GTM Interpolation Experimental Results Conclusion 1
3. Point Data Visualization Visualize high-dimensional data as points in 2D or 3D by dimension reduction. Distances in target dimension approximate to the distances in the original HD space. Interactively browse data Easy to recognize clusters or groups An example of chemical data (PubChem) Visualization to display disease-gene relationship, aiming at finding cause-effect relationships between disease and genes. 2
4. Multi-Dimensional Scaling Pairwise dissimilarity matrix N-by-N matrix Each element can be a distance, score, rank, … Given Δ, find a mapping in the target dimension Criteria (or objective function) STRESS SSTRESS SMACOF is one of algorithms to solve MDS problem 3
5. Generative Topographic Mapping K latent points N data points Input is high-dimensional vector points Latent Variable Model (LVM) Define K latent variables (zk) Map K latent points to the data space by using a non-linear function f (by EM approach) Construct maps of data points in the latent space based on Gaussian Mixture Model 4
6.
7. Find an optimal configuration in a lower-dimension
8. Iterative optimization methodPurpose Maximize Log-Likelihood Minimize STRESS or SSTRESS ObjectiveFunction O(KN) (K << N) O(N2) Complexity EM Iterative Majorization (EM-like) Optimization Method Vector representation Pairwise Distance as well as Vector Input Format
9. Challenges Data is getting larger and high-dimensional PubChem : database of 60M chemical compounds Our initial results on 100K sequences need to be extended to millions of sequences Typical dimension 150-1000 MDS Results on 768 (32x24) core cluster with 1.54TB memory 6 Interpolation reduces the computational complexity O(N2) O(n2 + (N-n)n)
10. Interpolation Approach Two-step procedure A dimension reduction alg. constructs a mapping of n sample data (among total N data) in target dimension. Remaining (N-n) out-of-samples are mapped in target dimension w.r.t. the constructed mapping of the n sample data w/o moving sample mappings. MPI nIn-sample Trained data Training N-n Out-of-sample Interpolated map 7 1 Interpolation 2 ...... P-1 p Total N data MapReduce
11. MDS Interpolation Assume it is given the mappings of n sampled data in target dimension (result of normal MDS). Landmark points (do not move during interpolation) Out-of-samples (N-n) are interpolated based on the mappings of n sample points. Find k-NN of the new point among n sample data. Based on the mappings of k-NN, find a position for a new point by the proposed iterative majorizing approach. Computational Complexity – O(Mn), M = N-n 8
12. GTM Interpolation Assume it is given the position of K latent points based on the sample data in the latent space. The most time consuming part of GTM Out-of-samples (N-n) are positioned directly w.r.t. Gaussian Mixture Model between the new point and the given position of K latent points. Computational Complexity – O(M), M = N-n 9
14. Quality Comparison (1) 11 GTM interpolation quality comparison w.r.t. different sample size of N = 100k MDS interpolation quality comparison w.r.t. different sample size of N = 100k
15. Quality Comparison (2) 12 GTM interpolation quality up to 2M MDS interpolation quality up to 2M
16. Parallel Efficiency 13 MDS parallel efficiency on Cluster-II GTM parallel efficiency on Cluster-II
17.
18. DryadLINQ using a 16 core machine with 16 GB, Hadoop 8 core with 48 GB, Azure small instances with 1 core with 1.7 GB.ThilinaGunarathne, Tak-Lon Wu, Judy Qiu, and Geoffrey Fox, “Cloud Computing Paradigms for Pleasingly Parallel Biomedical Applications,” in Proceedings of ECMLS Workshop of ACM HPDC 2010
19. MDS Interpolation via MapReduce 15 DryadLINQ on 32 nodes X 24 Cores cluster with 48 GB per node. Azure using small instances ThilinaGunarathne, Tak-Lon Wu, Judy Qiu, and Geoffrey Fox, “Cloud Computing Paradigms for Pleasingly Parallel Biomedical Applications,” in Proceedings of ECMLS Workshop of ACM HPDC 2010
20. MDS Interpolation Map 16 PubChem data visualization by using MDS (100k) and Interpolation (100k+100k).
21. GTM Interpolation Map 17 PubChem data visualization by using GTM (100k) and Interpolation (2M + 100k).
22. Conclusion Dimension reduction algorithms (e.g. GTM and MDS) are computation and memory intensive applications. Apply interpolation (out-of-sample) approach to GTM and MDS in order to process and visualize large- and high-dimensional dataset. It is possible to process millions data point via interpolation. Could be parallelized by MapReduce fashion as well as MPI fashion. 18
23. Future Works Make available as a Service Hierarchical Interpolation could reduce the computational complexity O(Mn) O(Mlog(n)) 19
24. Acknowledgment Our internal collaborators in School of Informatics and Computing at IUB Prof. David Wild Dr. Qian Zhu 20
26. EM optimization Find K centers for N data K-clustering problem, known as NP-hard Use Expectation-Maximization (EM) method EM algorithm Find local optimal solution iteratively until converge E-step: M-step: 22
27. Parallelization Interpolation is pleasingly parallel application Out-of-sample data are independent each other. We can parallelize interpolation app. by MapReduce fashion as well as MPI fashion. ThilinaGunarathne, Tak-Lon Wu, Judy Qiu, and Geoffrey Fox, “Cloud Computing Paradigms for Pleasingly Parallel Biomedical Applications,” in Proceedings of ECMLS Workshop of ACM HPDC 2010 23 nIn-sample Trained data Training N-n Out-of-sample Interpolated map 1 Interpolation 2 ...... P-1 p Total N data
Editor's Notes
Microarray data
EC2 HM4XL - High memory large instances (8 * 3.25 Ghz cores, 68GB memory)EC2 HCXL – High CPU extra large (8 * 2.4 Ghz, 7GB memory)EC2 Large – 2 * 2.4 Ghz , 7.5 GB memoryGTM interpolation is memory bound. Hence, less cores per memory (less memory & memory bandwidth contention) has the advantage. DryadLINQ efficiency suffers due to 16 core 16 GB machines.
Efficiency drop in MDS DryadLINQ at the last point is due to unbalanced partition (2600 blocks in to 768 cores)