Quantization of Random Distributions under KL Divergence

2021 ◽  
Author(s):  
Aviv Adler ◽  
Jennifer Tang ◽  
Yury Polyanskiy
Keyword(s):  
Kl Divergence ◽  
Random Distributions

A Hard C-Means Clustering Algorithm Incorporating Membership KL Divergence and Local Data Information for Noisy Image Segmentation

2017 ◽  
Vol 32 (04) ◽  
pp. 1850012 ◽  
Author(s):  
R. R. Gharieb ◽  
G. Gendy ◽  
H. Selim
Keyword(s):  
Image Segmentation ◽  
Membership Function ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Cluster Center ◽  
Local Data ◽  
Cluster Membership ◽  
Kl Divergence ◽  
Clustering Approach ◽  
Center Distance

In this paper, the standard hard C-means (HCM) clustering approach to image segmentation is modified by incorporating weighted membership Kullback–Leibler (KL) divergence and local data information into the HCM objective function. The membership KL divergence, used for fuzzification, measures the proximity between each cluster membership function of a pixel and the locally-smoothed value of the membership in the pixel vicinity. The fuzzification weight is a function of the pixel to cluster-centers distances. The used pixel to a cluster-center distance is composed of the original pixel data distance plus a fraction of the distance generated from the locally-smoothed pixel data. It is shown that the obtained membership function of a pixel is proportional to the locally-smoothed membership function of this pixel multiplied by an exponentially distributed function of the minus pixel distance relative to the minimum distance provided by the nearest cluster-center to the pixel. Therefore, since incorporating the locally-smoothed membership and data information in addition to the relative distance, which is more tolerant to additive noise than the absolute distance, the proposed algorithm has a threefold noise-handling process. The presented algorithm, named local data and membership KL divergence based fuzzy C-means (LDMKLFCM), is tested by synthetic and real-world noisy images and its results are compared with those of several FCM-based clustering algorithms.

Probability and Random Distributions

2013 ◽  
Vol 58 (2) ◽  
pp. 67-70
Author(s):  
T. C. Nelsen
Keyword(s):  
Random Distributions

scholarly journals Weakly approaching sequences of random distributions

2000 ◽  
Vol 37 (3) ◽  
pp. 807-822 ◽  
Author(s):  
Yuri Belyaev ◽  
Sara Sjöstedt-de Luna
Keyword(s):  
Weak Convergence ◽  
Limit Distribution ◽  
Continuity Theorem ◽  
Statistics And Probability ◽  
Random Distributions

We introduce the notion of weakly approaching sequences of distributions, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.

scholarly journals PLACENTAL STEREOLOGY: SPANNING THE LEVELS FROM MOLECULE TO WHOLE ORGAN

2011 ◽  
Vol 28 (3) ◽  
pp. 121
Author(s):  
Terry M Mayhew
Keyword(s):  
Intrauterine Growth Restriction ◽  
Urban Air Pollution ◽  
Quantitative Information ◽  
Experimental Manipulation ◽  
Organ Function ◽  
Villous Trophoblast ◽  
Quantitative Immunoelectron Microscopy ◽  
Random Distributions ◽  
Cellular Compartments ◽  
Different Levels

Stereology can provide hard (functionally-relevant) quantitative information at different levels of 3D structural organization. My researches have applied established methods to study organ function and developed novel methods to study subcellular localization of marker probes. We have studied whole-organ function (passive diffusion) in the human placenta and quantified various processes at tissue and subcellular levels and in normal and complicated pregnancies. Fetoplacental angiogenesis and villous growth and maturation involve phased changes particularly around mid-gestation. Growth is associated with increased numbers of cells or nuclei and counts have shown that villous trophoblast continuously renews itself via cytotrophoblast (CT) proliferation and recruitment and syncytiotrophoblast (ST) differentiation and extrusion. Integration of these processes results in changes in total oxygen (O2) diffusive conductance which match the growing fetal mass. Similar processes occur during development of the mouse placenta and at least some are compromised in human pregnancies. For example: [a] in pure pre-eclampsia (PE), villous and fetoplacental vascular volumes and surfaces are similar to those seen in uncomplicated pregnancies but reduced in pure intrauterine growth restriction (IUGR) and in PE+IUGR; [b] trophoblast extrusion is accelerated in PE and IUGR but the latter exhibits reduced CT proliferation and this perturbed steady state leads to smaller trophoblast volumes and surfaces; [c] O2 diffusive conductances alter in various pregnancy complications, including IUGR and PE+IUGR; [d] fetal weight is diminished, but diffusive transport increases, in placentas from mice exposed to urban air pollution. Finally, innovations in quantitative immunoelectron microscopy (immunoEM) have produced a portfolio of methods for revealing non-random distributions of marker gold particles in different cellular compartments and for testing whether patterns shift following experimental manipulation. Recently, the methods have been extended to study tissue and cellular distributions of nanoparticles.

scholarly journals Research on the Application of User Recommendation Based on the Fusion Method of Spatially Complex Location Similarity

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lili Wang ◽  
Ting Shi ◽  
Shijin Li
Keyword(s):  
Collaborative Filtering ◽  
Similarity Measure ◽  
Recall Rate ◽  
Cosine Similarity ◽  
Fusion Method ◽  
Complex Matrix ◽  
Recommendation Algorithm ◽  
Kl Divergence ◽  
Experimental Effect ◽  
User Recommendation

Since the user recommendation complex matrix is characterized by strong sparsity, it is difficult to correctly recommend relevant services for users by using the recommendation method based on location and collaborative filtering. The similarity measure between users is low. This paper proposes a fusion method based on KL divergence and cosine similarity. KL divergence and cosine similarity have advantages by comparing three similar metrics at different K values. Using the fusion method of the two, the user’s similarity with the preference is reused. By comparing the location-based collaborative filtering (LCF) algorithm, user-based collaborative filtering (UCF) algorithm, and user recommendation algorithm (F2F), the proposed method has the preparation rate, recall rate, and experimental effect advantage. In different median values, the proposed method also has an advantage in experimental results.

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