Subset Ranking Research Articles

MRI brain image classification using Linear Vector Quantization Classifier

The metastases cancer other than the lifestyle-related or environmental related no known facts for the brain tumors. Only factors that may cause brain tumors might be the exposure to high ionizing radiation and a family history of any brain disease also increase brain cancer risk. The cancerous brain is a brain disorder that shapes masses in cells called tumors. The early diagnosis of brain cancer using the Magnetic Resonance Imaging (MRI) scan image for cancer disease is required to reduce the mortality rate. Dual-Tree Mband Wavelet Transform (DTMBWT) based feature extraction, and Linear Vector Quantization Classifier (LVQC) based MRI brain image classification. DTMBWT decomposes the MRI brain images in the frequency domain as the sub-bands for fuzzy-based low and high components to evaluate the features selected. The Sub-band Energy Features (SEF) for individual and sub-set ranking helps classify normal and abnormal images that LVQC for output prediction characterizes. The results show the classification accuracy of 95% using DTMBWT based SEF and LVQC classifiers.

Huffman-Coded Sphere Shaping and Distribution Matching Algorithms via Lookup Tables

In this paper, we study amplitude shaping schemes for the probabilistic amplitude shaping (PAS) framework as well as algorithms for constant-composition distribution matching (CCDM). Huffman-coded sphere shaping (HCSS) is discussed in detail, which internally uses Huffman coding to determine the composition to be used and relies on conventional CCDM algorithms for mapping and demapping. Numerical simulations show that HCSS closes the performance gap between distribution matching schemes and sphere shaping techniques such as enumerative sphere shaping (ESS). HCSS is based on an architecture that is different from the trellis-based setup of ESS. It allows to tailor the used HCSS compositions to the transmission channel and to take into account complexity constraints. We further discuss in detail multiset ranking (MR) and subset ranking (SR) as alternatives to arithmetic-coding (AC) CCDM. The advantage of MR over AC is that it requires less sequential operations for mapping. SR operates on binary alphabets only, which can introduce some additional rate loss when a nonbinary-to-binary transformation is required. However, the binomial coefficients required for SR can be precomputed and stored in a lookup table (LUT). We perform an analysis of rate loss and decoding performance for the proposed techniques and compare them to other prominent amplitude shaping schemes. For medium to long block lengths, MR-HCSS and SR-HCSS are shown to have similar performance to ESS. SR-HCSS and uniform 64QAM are compared in additive white Gaussian noise simulations and shaping gains of 0.5 dB and 1 dB are demonstrated with 1 kbit and 100 kbit LUT size, respectively.

Parallel-Amplitude Architecture and Subset Ranking for Fast Distribution Matching

A distribution matcher (DM) maps a binary input sequence into a block of nonuniformly distributed symbols. To facilitate the implementation of shaped signaling, fast DM solutions with high throughput and low serialism are required. We propose a novel DM architecture with parallel amplitudes (PA-DM) for which $m-1$ component DMs, each with a different binary output alphabet, are operated in parallel in order to generate a shaped sequence with $m$ amplitudes. With negligible rate loss compared to a single nonbinary DM, PA-DM has a parallelization factor that grows linearly with $m$ , and the component DMs have reduced output lengths. For such binary-output DMs, a novel constant-composition DM (CCDM) algorithm based on subset ranking (SR) is proposed. We present SR-CCDM algorithms that are serial in the minimum number of occurrences of either binary symbol for mapping, and fully parallel for demapping. For distributions that are optimized for the additive white Gaussian noise (AWGN) channel, we numerically show that PA-DM combined with SR-CCDM can reduce the number of sequential processing steps by more than an order of magnitude, while having a rate loss that is comparable to conventional nonbinary CCDM with arithmetic coding.

Operating characteristics of a subset selection procedure applied to a randomized response model for continuous data

The operating characteristics (OCs) of a subset ranking and selection procedure are derived for a randomized response model for continuous data. In this article the operating characteristics for the subset selection procedure are considered for two parameter configurations, the slippage configuration and the equi-spaced configuration, and tables are provided for each case for some specific choices of problems parameters.

On Possible Dimensions of Subspace Intersections for Five Direct Summands

The paper considers the problem on the dimensions of intersections of a subspace in the direct sum of a finite series of finite-dimensional vector spaces with sums of pairs of direct summands, provided that the subspace intersection with each of these direct summands is trivial. The problem naturally splits into finding conditions for the existence and representability of the corresponding matroid. The following theorem is proved: If the ranks of all the unions of a series of blocks satisfying the condition on the ranks of subsets in the matroid are given and the blocks have full rank, then this partial rank function may be extended to a full rank function for all the subsets of the base set (the union of all the blocks). Necessary and sufficient conditions on the dimensions of the direct summands and intersections mentioned above for the corresponding matroid to exist are obtained in the case of five direct summands. Bibliography: 5 titles.

Approximate Simulation Budget Allocation for Subset Ranking

Accurate performance evaluation of discrete event systems needs a huge number of simulation replications and is thus time-consuming and costly. Hence, efficiency is always a big concern when simulations are conducted. To drastically reduce its cost when conducting them, ordinal optimization emerges. To further enhance the efficiency of ordinal optimization, optimal computing budget allocation (OCBA) is proposed to decide the best design accurately and quickly. Its variants have been introduced to achieve goals with distinct assumptions, such as to identify the optimal subset of designs. They are restricted in selecting the best design or optimal subset of designs. However, a highly challenging issue, i.e., subset ranking, remains unaddressed. It goes beyond best design and optimal subset problems. This work develops a new OCBA-based approach to address the issue and establishes its theoretical foundation. The numerical testing results show that, with proper parameters, it can indeed enhance the simulation efficiency and outperform other existing methods in terms of the probability of correct subset ranking and computational efficiency.

Operating Characteristics of a Subset Selection Procedure Applied to a Hybrid Randomized Response Model

The operating characteristics (OCs) of a subset ranking and selection procedure are derived for the hybrid randomized response model developed by Jia and McDonald (2009). The OCs include the probability of a correct P(CS), the individual selection probability γi, and the expected subset size E(S), under the slippage configuration or the equi-spaced configuration. An example comparing failure rates of contraceptive methods is used to illustrate the use of these new results.

О рангах подмножеств пространства двоичных векторов, допускающих встраивание системы Штейнера S(2, 4, v)

О рангах подмножеств пространства двоичных векторов, допускающих встраивание системы Штейнера S(2, 4, v)

Уточнённые оценки экспонентов перемешивающих графов биективных регистров сдвига над множеством двоичных векторов

Уточнённые оценки экспонентов перемешивающих графов биективных регистров сдвига над множеством двоичных векторов

Tune and mix: learning to rank using ensembles of calibrated multi-class classifiers

In subset ranking, the goal is to learn a ranking function that approximates a gold standard partial ordering of a set of objects (in our case, a set of documents retrieved for the same query). The partial ordering is given by relevance labels representing the relevance of documents with respect to the query on an absolute scale. Our approach consists of three simple steps. First, we train standard multi-class classifiers (AdaBoost.MH and multi-class SVM) to discriminate between the relevance labels. Second, the posteriors of multi-class classifiers are calibrated using probabilistic and regression losses in order to estimate the Bayes-scoring function which optimizes the Normalized Discounted Cumulative Gain (NDCG). In the third step, instead of selecting the best multi-class hyperparameters and the best calibration, we mix all the learned models in a simple ensemble scheme. Our extensive experimental study is itself a substantial contribution. We compare most of the existing learning-to-rank techniques on all of the available large-scale benchmark data sets using a standardized implementation of the NDCG score. We show that our approach is competitive with conceptually more complex listwise and pairwise methods, and clearly outperforms them as the data size grows. As a technical contribution, we clarify some of the confusing results related to the ambiguities of the evaluation tools, and propose guidelines for future studies.

Generic subset ranking using binary classifiers

A widespread idea to attack the ranking problem is by reducing it into a set of binary preferences and applying well studied classification methods. In particular, we consider this reduction for generic subset ranking, which is based on minimization of position-sensitive loss functions. The basic question addressed in this paper relates to whether an accurate classifier would transfer directly into a good ranker. We propose a consistent reduction framework guaranteeing that the minimal regret of zero for subset ranking is achievable by learning binary preferences assigned with importance weights. This fact allows us to further develop a novel upper bound on the subset ranking regret in terms of binary regrets. We show that their ratio can be at most 2 times the maximal deviation of discounts between adjacent positions. We also present a refined version of this bound when only the quality over the top rank positions is of concern. These bounds provide theoretical support on the use of the resulting binary classifiers for solving the subset ranking problem.

Statistical Analysis of Bayes Optimal Subset Ranking

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The ranking problem has become increasingly important in modern applications of statistical methods in automated decision making systems. In particular, we consider a formulation of the statistical ranking problem which we call subset ranking, and focus on the discounted cumulated gain (DCG) criterion that measures the quality of items near the top of the rank-list. Similar to error minimization for binary classification, direct optimization of natural ranking criteria such as DCG leads to a nonconvex optimization problems that can be NP-hard. Therefore, a computationally more tractable approach is needed. We present bounds that relate the approximate optimization of DCG to the approximate minimization of certain regression errors. These bounds justify the use of convex learning formulations for solving the subset ranking problem. The resulting estimation methods are not conventional, in that we focus on the estimation quality in the top-portion of the rank-list. We further investigate the asymptotic statistical behavior of these formulations. Under appropriate conditions, the consistency of the estimation schemes with respect to the DCG metric can be derived. </para>

Inequalities for Shannon Entropy and Kolmogorov Complexity

It was mentioned by Kolmogorov (1968, IEEE Trans. Inform. Theory14, 662–664) that the properties of algorithmic complexity and Shannon entropy are similar. We investigate one aspect of this similarity. Namely, we are interested in linear inequalities that are valid for Shannon entropy and for Kolmogorov complexity. It turns out that (1) all linear inequalities that are valid for Kolmogorov complexity are also valid for Shannon entropy and vice versa; (2) all linear inequalities that are valid for Shannon entropy are valid for ranks of finite subsets of linear spaces; (3) the opposite statement is not true; Ingleton's inequality (1971, “Combinatorial Mathematics and Its Applications,” pp. 149–167. Academic Press, San Diego) is valid for ranks but not for Shannon entropy; (4) for some special cases all three classes of inequalities coincide and have simple description. We present an inequality for Kolmogorov complexity that implies Ingleton's inequality for ranks; another application of this inequality is a new simple proof of one of Gács–Körner's results on common information (1973, Problems Control Inform. Theory2, 149–162).