1,184 research outputs found
Robust Path-based Image Segmentation Using Superpixel Denoising
Clustering is the important task of partitioning data into groups with similar characteristics, with one category being spectral clustering where data points are represented as vertices of a graph connected by weighted edges signifying similarity based on distance. The longest leg path distance (LLPD) has shown promise when used in spectral clustering, but is sensitive to noisy data, therefore requiring a data denoising procedure to achieve good performance. Previous denoising techniques have involved identifying and removing noisy data points, however this is not a desirable pre-clustering step for data sets with a specific structure like images. The process of partitioning an image into regions of similar features known as image segmentation can be represented as a clustering problem by defining the vector of intensity and spatial information at each pixel as data point. We therefore propose the method of pre-cluster denoising to formulate a robust LLPD clustering framework. By creating a fine clustering of approximately equal-sized groups and averaging each, a reduced number of data points can be defined that represent the relevant information of the original data set by locally averaging out noise influence. We can then construct a smaller graph representation of the data based on the LLPD between the reduced data points, and identify the spectral embedding coordinates for each reduced point. An out-of-sample extension procedure is then used to compute spectral embedding coordinates at each of the original data points, after which a simple (k-means) clustering is performed to compute the final cluster labels. In the context of image segmentation, computing superpixels provides a nice structure for performing this type of pre-clustering. We show how the above LLPD framework can be carried out in the context of image segmentation, and show that a simple computationally efficient spatial interpolation procedure can be used instead to extend the embedding in a way that yields better segmentation performance with respect to ground truth on a publicly available data set. Similar experiments are also performed using the standard Euclidean distance in place of the LLPD to show the proficiency of the LLPD for image segmentation
Overlapping and Robust Edge-Colored Clustering in Hypergraphs
A recent trend in data mining has explored (hyper)graph clustering algorithms
for data with categorical relationship types. Such algorithms have applications
in the analysis of social, co-authorship, and protein interaction networks, to
name a few. Many such applications naturally have some overlap between
clusters, a nuance which is missing from current combinatorial models.
Additionally, existing models lack a mechanism for handling noise in datasets.
We address these concerns by generalizing Edge-Colored Clustering, a recent
framework for categorical clustering of hypergraphs. Our generalizations allow
for a budgeted number of either (a) overlapping cluster assignments or (b) node
deletions. For each new model we present a greedy algorithm which approximately
minimizes an edge mistake objective, as well as bicriteria approximations where
the second approximation factor is on the budget. Additionally, we address the
parameterized complexity of each problem, providing FPT algorithms and hardness
results
Coresets for Wasserstein Distributionally Robust Optimization Problems
Wasserstein distributionally robust optimization (\textsf{WDRO}) is a popular
model to enhance the robustness of machine learning with ambiguous data.
However, the complexity of \textsf{WDRO} can be prohibitive in practice since
solving its ``minimax'' formulation requires a great amount of computation.
Recently, several fast \textsf{WDRO} training algorithms for some specific
machine learning tasks (e.g., logistic regression) have been developed.
However, the research on designing efficient algorithms for general large-scale
\textsf{WDRO}s is still quite limited, to the best of our knowledge.
\textit{Coreset} is an important tool for compressing large dataset, and thus
it has been widely applied to reduce the computational complexities for many
optimization problems. In this paper, we introduce a unified framework to
construct the -coreset for the general \textsf{WDRO} problems. Though
it is challenging to obtain a conventional coreset for \textsf{WDRO} due to the
uncertainty issue of ambiguous data, we show that we can compute a ``dual
coreset'' by using the strong duality property of \textsf{WDRO}. Also, the
error introduced by the dual coreset can be theoretically guaranteed for the
original \textsf{WDRO} objective. To construct the dual coreset, we propose a
novel grid sampling approach that is particularly suitable for the dual
formulation of \textsf{WDRO}. Finally, we implement our coreset approach and
illustrate its effectiveness for several \textsf{WDRO} problems in the
experiments
Classification without labels: Learning from mixed samples in high energy physics
Modern machine learning techniques can be used to construct powerful models
for difficult collider physics problems. In many applications, however, these
models are trained on imperfect simulations due to a lack of truth-level
information in the data, which risks the model learning artifacts of the
simulation. In this paper, we introduce the paradigm of classification without
labels (CWoLa) in which a classifier is trained to distinguish statistical
mixtures of classes, which are common in collider physics. Crucially, neither
individual labels nor class proportions are required, yet we prove that the
optimal classifier in the CWoLa paradigm is also the optimal classifier in the
traditional fully-supervised case where all label information is available.
After demonstrating the power of this method in an analytical toy example, we
consider a realistic benchmark for collider physics: distinguishing quark-
versus gluon-initiated jets using mixed quark/gluon training samples. More
generally, CWoLa can be applied to any classification problem where labels or
class proportions are unknown or simulations are unreliable, but statistical
mixtures of the classes are available.Comment: 18 pages, 5 figures; v2: intro extended and references added; v3:
additional discussion to match JHEP versio
Object Discovery via Cohesion Measurement
Color and intensity are two important components in an image. Usually, groups
of image pixels, which are similar in color or intensity, are an informative
representation for an object. They are therefore particularly suitable for
computer vision tasks, such as saliency detection and object proposal
generation. However, image pixels, which share a similar real-world color, may
be quite different since colors are often distorted by intensity. In this
paper, we reinvestigate the affinity matrices originally used in image
segmentation methods based on spectral clustering. A new affinity matrix, which
is robust to color distortions, is formulated for object discovery. Moreover, a
Cohesion Measurement (CM) for object regions is also derived based on the
formulated affinity matrix. Based on the new Cohesion Measurement, a novel
object discovery method is proposed to discover objects latent in an image by
utilizing the eigenvectors of the affinity matrix. Then we apply the proposed
method to both saliency detection and object proposal generation. Experimental
results on several evaluation benchmarks demonstrate that the proposed CM based
method has achieved promising performance for these two tasks.Comment: 14 pages, 14 figure
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