41,225 research outputs found
Application of the Ring Theory in the Segmentation of Digital Images
Ring theory is one of the branches of the abstract algebra that has been
broadly used in images. However, ring theory has not been very related with
image segmentation. In this paper, we propose a new index of similarity among
images using Zn rings and the entropy function. This new index was applied as a
new stopping criterion to the Mean Shift Iterative Algorithm with the goal to
reach a better segmentation. An analysis on the performance of the algorithm
with this new stopping criterion is carried out. The obtained results proved
that the new index is a suitable tool to compare images.Comment: Very interesting new index to compute the similarity among images.
arXiv admin note: substantial text overlap with arXiv:1306.262
Learning Discriminative Stein Kernel for SPD Matrices and Its Applications
Stein kernel has recently shown promising performance on classifying images
represented by symmetric positive definite (SPD) matrices. It evaluates the
similarity between two SPD matrices through their eigenvalues. In this paper,
we argue that directly using the original eigenvalues may be problematic
because: i) Eigenvalue estimation becomes biased when the number of samples is
inadequate, which may lead to unreliable kernel evaluation; ii) More
importantly, eigenvalues only reflect the property of an individual SPD matrix.
They are not necessarily optimal for computing Stein kernel when the goal is to
discriminate different sets of SPD matrices. To address the two issues in one
shot, we propose a discriminative Stein kernel, in which an extra parameter
vector is defined to adjust the eigenvalues of the input SPD matrices. The
optimal parameter values are sought by optimizing a proxy of classification
performance. To show the generality of the proposed method, three different
kernel learning criteria that are commonly used in the literature are employed
respectively as a proxy. A comprehensive experimental study is conducted on a
variety of image classification tasks to compare our proposed discriminative
Stein kernel with the original Stein kernel and other commonly used methods for
evaluating the similarity between SPD matrices. The experimental results
demonstrate that, the discriminative Stein kernel can attain greater
discrimination and better align with classification tasks by altering the
eigenvalues. This makes it produce higher classification performance than the
original Stein kernel and other commonly used methods.Comment: 13 page
Weakly supervised segment annotation via expectation kernel density estimation
Since the labelling for the positive images/videos is ambiguous in weakly
supervised segment annotation, negative mining based methods that only use the
intra-class information emerge. In these methods, negative instances are
utilized to penalize unknown instances to rank their likelihood of being an
object, which can be considered as a voting in terms of similarity. However,
these methods 1) ignore the information contained in positive bags, 2) only
rank the likelihood but cannot generate an explicit decision function. In this
paper, we propose a voting scheme involving not only the definite negative
instances but also the ambiguous positive instances to make use of the extra
useful information in the weakly labelled positive bags. In the scheme, each
instance votes for its label with a magnitude arising from the similarity, and
the ambiguous positive instances are assigned soft labels that are iteratively
updated during the voting. It overcomes the limitations of voting using only
the negative bags. We also propose an expectation kernel density estimation
(eKDE) algorithm to gain further insight into the voting mechanism.
Experimental results demonstrate the superiority of our scheme beyond the
baselines.Comment: 9 pages, 2 figure
Positive Definite Kernels in Machine Learning
This survey is an introduction to positive definite kernels and the set of
methods they have inspired in the machine learning literature, namely kernel
methods. We first discuss some properties of positive definite kernels as well
as reproducing kernel Hibert spaces, the natural extension of the set of
functions associated with a kernel defined
on a space . We discuss at length the construction of kernel
functions that take advantage of well-known statistical models. We provide an
overview of numerous data-analysis methods which take advantage of reproducing
kernel Hilbert spaces and discuss the idea of combining several kernels to
improve the performance on certain tasks. We also provide a short cookbook of
different kernels which are particularly useful for certain data-types such as
images, graphs or speech segments.Comment: draft. corrected a typo in figure
Kernel Spectral Clustering and applications
In this chapter we review the main literature related to kernel spectral
clustering (KSC), an approach to clustering cast within a kernel-based
optimization setting. KSC represents a least-squares support vector machine
based formulation of spectral clustering described by a weighted kernel PCA
objective. Just as in the classifier case, the binary clustering model is
expressed by a hyperplane in a high dimensional space induced by a kernel. In
addition, the multi-way clustering can be obtained by combining a set of binary
decision functions via an Error Correcting Output Codes (ECOC) encoding scheme.
Because of its model-based nature, the KSC method encompasses three main steps:
training, validation, testing. In the validation stage model selection is
performed to obtain tuning parameters, like the number of clusters present in
the data. This is a major advantage compared to classical spectral clustering
where the determination of the clustering parameters is unclear and relies on
heuristics. Once a KSC model is trained on a small subset of the entire data,
it is able to generalize well to unseen test points. Beyond the basic
formulation, sparse KSC algorithms based on the Incomplete Cholesky
Decomposition (ICD) and , , Group Lasso regularization are
reviewed. In that respect, we show how it is possible to handle large scale
data. Also, two possible ways to perform hierarchical clustering and a soft
clustering method are presented. Finally, real-world applications such as image
segmentation, power load time-series clustering, document clustering and big
data learning are considered.Comment: chapter contribution to the book "Unsupervised Learning Algorithms
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