2,485 research outputs found
Data Clustering And Visualization Through Matrix Factorization
Clustering is traditionally an unsupervised task which is to find natural groupings or clusters in multidimensional data based on perceived similarities among the patterns. The purpose of clustering is to extract useful information
from unlabeled data.
In order to present the extracted useful knowledge obtained by clustering in a meaningful way, data visualization becomes a popular and growing area of research field. Visualization can provide a qualitative overview of large and complex data sets, which help us the desired insight in truly understanding the phenomena of interest in data.
The contribution of this dissertation is two-fold: Semi-Supervised Non-negative Matrix Factorization (SS-NMF) for data clustering/co-clustering and Exemplar-based data Visualization (EV) through matrix factorization. Compared to traditional data mining models,
matrix-based methods are fast, easy to understand and implement, especially suitable to solve large-scale challenging problems in text mining, image grouping, medical diagnosis, and bioinformatics.
In this dissertation, we present two effective matrix-based solutions
in the new directions of data clustering and visualization.
First, in many practical learning domains,
there is a large supply of unlabeled data but limited labeled data, and in most cases it might
be expensive to generate large amounts of labeled data. Traditional clustering algorithms completely ignore these valuable labeled data and thus are inapplicable to these problems. Consequently, semi-supervised clustering, which can incorporate the domain knowledge to guide a clustering algorithm, has become a topic of significant recent interest.
Thus, we develop a Non-negative Matrix Factorization
(NMF) based framework to incorporate prior knowledge into data clustering. Moreover, with the fast growth of Internet and computational technologies in the past decade, many data mining applications have advanced swiftly from the simple clustering of one data type to the co-clustering of multiple data types, usually involving high heterogeneity. To this end, we extend SS-NMF to perform heterogeneous data co-clustering. From a theoretical perspective, SS-NMF for data clustering/co-clustering is mathematically rigorous. The convergence and correctness of our algorithms are proved.
In addition, we discuss the relationship between SS-NMF with other well-known clustering and co-clustering models.
Second, most of current clustering models only provide the centroids (e.g., mathematical means of the clusters)
without inferring the representative exemplars from real data, thus they are unable to better summarize or visualize the raw data.
A new method, Exemplar-based Visualization (EV), is proposed to cluster and visualize an extremely large-scale data.
Capitalizing on recent advances in matrix approximation and factorization, EV provides a means
to visualize large scale data with high accuracy (in
retaining neighbor relations), high efficiency (in computation), and
high flexibility (through the use of exemplars).
Empirically, we demonstrate the superior performance of our matrix-based data clustering and visualization models
through extensive experiments performed on the publicly available large scale data sets
Adaptive semi-supervised affinity propagation clustering algorithm based on structural similarity
Uzimajući u obzir nezadovoljavajuće djelovanje grupiranja srodnog širenja algoritma grupiranja, kada se radi o nizovima podataka složenih struktura, u ovom se radu predlaže prilagodljivi nadzirani algoritam grupiranja srodnog širenja utemeljen na strukturnoj sličnosti (SAAP-SS). Najprije se predlaže nova strukturna sličnost rješavanjem nelinearnog problema zastupljenosti niskoga ranga. Zatim slijedi srodno širenje na temelju podešavanja matrice sličnosti primjenom poznatih udvojenih ograničenja. Na kraju se u postupak algoritma uvodi ideja eksplozija kod vatrometa. Prilagodljivo pretražujući preferencijalni prostor u dva smjera, uravnotežuju se globalne i lokalne pretraživačke sposobnosti algoritma u cilju pronalaženja optimalne strukture grupiranja. Rezultati eksperimenata i sa sintetičkim i s realnim nizovima podataka pokazuju poboljšanja u radu predloženog algoritma u usporedbi s AP, FEO-SAP i K-means metodama.In view of the unsatisfying clustering effect of affinity propagation (AP) clustering algorithm when dealing with data sets of complex structures, an adaptive semi-supervised affinity propagation clustering algorithm based on structural similarity (SAAP-SS) is proposed in this paper. First, a novel structural similarity is proposed by solving a non-linear, low-rank representation problem. Then we perform affinity propagation on the basis of adjusting the similarity matrix by utilizing the known pairwise constraints. Finally, the idea of fireworks explosion is introduced into the process of the algorithm. By adaptively searching the preference space bi-directionally, the algorithm’s global and local searching abilities are balanced in order to find the optimal clustering structure. The results of the experiments with both synthetic and real data sets show performance improvements of the proposed algorithm compared with AP, FEO-SAP and K-means methods
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
Exemplar-based Linear Discriminant Analysis for Robust Object Tracking
Tracking-by-detection has become an attractive tracking technique, which
treats tracking as a category detection problem. However, the task in tracking
is to search for a specific object, rather than an object category as in
detection. In this paper, we propose a novel tracking framework based on
exemplar detector rather than category detector. The proposed tracker is an
ensemble of exemplar-based linear discriminant analysis (ELDA) detectors. Each
detector is quite specific and discriminative, because it is trained by a
single object instance and massive negatives. To improve its adaptivity, we
update both object and background models. Experimental results on several
challenging video sequences demonstrate the effectiveness and robustness of our
tracking algorithm.Comment: ICIP201
Optimizing Dynamic Time Warping’s Window Width for Time Series Data Mining Applications
Dynamic Time Warping (DTW) is a highly competitive distance measure for most time series data mining problems. Obtaining the best performance from DTW requires setting its only parameter, the maximum amount of warping (w). In the supervised case with ample data, w is typically set by cross-validation in the training stage. However, this method is likely to yield suboptimal results for small training sets. For the unsupervised case, learning via cross-validation is not possible because we do not have access to labeled data. Many practitioners have thus resorted to assuming that “the larger the better”, and they use the largest value of w permitted by the computational resources. However, as we will show, in most circumstances, this is a naïve approach that produces inferior clusterings. Moreover, the best warping window width is generally non-transferable between the two tasks, i.e., for a single dataset, practitioners cannot simply apply the best w learned for classification on clustering or vice versa. In addition, we will demonstrate that the appropriate amount of warping not only depends on the data structure, but also on the dataset size. Thus, even if a practitioner knows the best setting for a given dataset, they will likely be at a lost if they apply that setting on a bigger size version of that data. All these issues seem largely unknown or at least unappreciated in the community. In this work, we demonstrate the importance of setting DTW’s warping window width correctly, and we also propose novel methods to learn this parameter in both supervised and unsupervised settings. The algorithms we propose to learn w can produce significant improvements in classification accuracy and clustering quality. We demonstrate the correctness of our novel observations and the utility of our ideas by testing them with more than one hundred publicly available datasets. Our forceful results allow us to make a perhaps unexpected claim; an underappreciated “low hanging fruit” in optimizing DTW’s performance can produce improvements that make it an even stronger baseline, closing most or all the improvement gap of the more sophisticated methods proposed in recent years
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