To date, many studies have employed clustering for the classification of unlabeled data. Deep separate clustering applies several deep learning models to conventional clustering algorithms to more clearly separate the distribution of the clusters. In this paper, we employ a convolutional autoencoder to learn the features of input images. Following this, k-means clustering is conducted using the encoded layer features learned by the convolutional autoencoder. A center loss function is then added to aggregate the data points into clusters to increase the intra-cluster homogeneity. Finally, we calculate and increase the inter-cluster separability. We combine all loss functions into a single global objective function. Our new deep clustering method surpasses the performance of existing clustering approaches when compared in experiments under the same conditions.

Workflow nets (WF-nets for short) are a standard way to automate business processes. Well-Structured WF-nets (WS WF-nets for short) are an important subclass of WF-nets because they have a well-balanced capability to expression power and analysis power. In this paper, we revealed structural and behavioral properties of WS WF-nets. Our results on structural properties are: (i) There is no EFC but non-FC WF-net in WS WF-nets; (ii) A WS WF-net is sound iff it is a van Hee et al.'s ST-net. Our results on behavioral properties are: (i) Any WS WF-net is safe; (ii) Any WS WF-net is separable; (iii) A necessary and sufficient condition on reachability of sound WS WF-net (N,[pIk]). Finally we illustrated the usefulness of the proposed properties with an application example of analyzing workflow evolution.

Intelligent information systems captivate people's attention. Examples of such systems include driving support vehicles capable of sensing driver state and communication robots capable of interacting with humans. Modeling how people search visual information is indispensable for designing these kinds of systems. In this paper, we focus on human visual attention, which is closely related to visual search behavior. We propose a computational model to estimate human visual attention while carrying out a visual target search task. Existing models estimate visual attention using the ratio between a representative value of visual feature of a target stimulus and that of distractors or background. The models, however, can not often achieve a better performance for difficult search tasks that require a sequentially spotlighting process. For such tasks, the linear separability effect of a visual feature distribution should be considered. Hence, we introduce this effect to spatially localized activation. Concretely, our top-down model estimates target-specific visual attention using Fisher's variance ratio between a visual feature distribution of a local region in the field of view and that of a target stimulus. We confirm the effectiveness of our computational model through a visual search experiment.

In this paper, we propose a new feature selection algorithm for multi-class classification. The proposed algorithm is based on Gaussian mixture models (GMMs) of the features, and it uses the distance between the two least separable classes as a metric for feature selection. The proposed system was tested with a support vector machine (SVM) for multi-class classification of music. Results show that the proposed feature selection scheme is superior to conventional schemes.

With a Gaussian kernel function, we find that the distance between two classes (DBTC) can be used as a class separability criterion in feature space since the between-class separation and the within-class data distribution are taken into account impliedly. To test the validity of DBTC, we develop a method of tuning the kernel parameters in support vector machine (SVM) algorithm by maximizing the DBTC in feature space. Experimental results on the real-world data show that the proposed method consistently outperforms corresponding hyperparameters tuning methods.

Intelligent scissors is an interactive image segmentation algorithm which allows a user to select piece-wise globally optimal contour segment corresponding to a desired object boundary. However, the intelligent scissors is too sensitive to a noise and texture patterns in an image since it utilizes the gradient information concerning the pixel intensities. This paper describes a new intelligent scissors based on the concept of the separability in order to improve the object boundary extraction performance. The effectiveness of the proposed method has been confirmed by some experiments for actual images acquired by an ordinary digital camera.

This paper surveys how geometric information can be effectively used for efficient algorithms with focus on clustering problems. Given a complete weighted graph G of n vertices, is there a partition of the vertex set into k disjoint subsets so that the maximum weight of an innercluster edge (whose two endpoints both belong to the same subset) is minimized? This problem is known to be NP-complete even for k = 3. The case of k=2, that is, bipartition problem is solvable in polynomial time. On the other hand, in geometric setting where vertices are points in the plane and weights of edges equal the distances between corresponding points, the same problem is solvable in polynomial time even for k 3 as far as k is a fixed constant. For the case k=2, effective use of geometric property of an optimal solution leads to considerable improvement on the computational complexity. Other related topics are also discussed.

A simple algorithm is proposed for representing nonseparable functions by equivalent separable functions. In this algorithm, functions are first represented by computational graphs, which are directed graphs representing the computational process of the functions. Then, the vertices of the computational graphs are searched in preorder or postorder, and the transformation to separable forms is performed at the places where it is necessary. By this repetition of the transformation, nonseparable functions are represented by separable functions automatically. The proposed algorithm will be useful in various fields of science and engineering because funcutions of one variable are easy to deal with.

This paper proposes a robust method for detecting step and ramp edges. In this method, an edge is defined not as a point where there is a large change in intensity, but as a region boundary based on the separability of image features which can be calculated by linear discriminant analysis. Based on this definition of an edge, its intensity can be obtained from the separability, which depends only on the shape of an edge. This characteristic enables easy selection of the optimum threshold value for the extraction of an edge, and this method can be applied to color and texture edge extraction. Experimental results have demonstrated that this proposed method is robust to noise and dulled edges, and, in addition, allows easy selection of the optimum threshold value.

An efficient algorithm is given for finding all solutions of piecewise-linear resistive circuits containing nonseparable transistor models such as the Gummel-Poon model or the Shichman-Hodges model. The proposed algorithm is simple and can be easily programmed using recursive functions.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits containing sophisticated transistor models such as the Gummel-Poon model or the Shichman-Hodges model. When a circuit contains these nonseparable models, the hybrid equation describing the circuit takes a special structure termed pairwise-separability (or tuplewise-separability). This structure is effectively exploited in the new algorithm. A numerical example is given, and it is shown that all solutions are computed very rapidly.

A globally and quadratically convergent algorithm is presented for solving nonlinear resistive networks containing transistors modeled by the Gummel-Poon model or the Shichman-Hodges model. This algorithm is based on the Katzenelson algorithm that is globally convergent for a broad class of piecewise-linear resistive networks. An effective restart technique is introduced, by which the algorithm converges to the solutions of the nonlinear resistive networks quadratically. The quadratic convergence is proved and also verified by numerical examples.

Recently, efficient algorithms that exploit the separability of nonlinear mappings have been proposed for finding all solutions of piecewise-linear resistive circuits. In this letter, it is shown that these algorithms can be extended to circuits containing piecewise-linear resistors that are neither voltage nor current controlled. Using the parametric representation for these resistors, the circuits can be described by systems of nonlinear equations with separable mappings. This separability is effectively exploited in finding all solutions. A numerical example is given, and it is demonstrated that all solutions are computed very rapidly by the new algorithm.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. This makes the number of simultaneous linear equations to be solved much smaller. This test, in its original form, is applied to each linear region; but this is time-consuming because the number of linear regions is generally very large. In this paper, it is shown that the sign test can be applied to super-regions consisting of adjacent linear regions. Therefore, many linear regions are discarded at the same time, and the computational efficiency of the algorithm is substantially improved. The branch-and-bound method is used in applying the sign test to super-regions. Some numerical examples are given, and it is shown that all solutions are computed very rapidly. The proposed algorithm is simple, efficient, and can be easily programmed.

Finding DC solutions of nonlinear networks is one of the most difficult tasks in circuit simulation, and many circuit designers experience difficulties in finding DC solutions using Newton's method. Piecewise-linear analysis has been studied to overcome this difficulty. However, efficient piecewiselinear algorithms have not been proposed for nonlinear resistive networks containing the Gummel-Poon models or the Shichman-Hodges models. In this paper, a new piecewise-linear algorithm is presented for solving nonlinear resistive networks containing these sophisticated transistor models. The basic idea of the algorithm is to exploit the special structure of the nonlinear network equations, namely, the pairwise-separability. The proposed algorithm is globally convergent and much more efficient than the conventional simplical-type piecewise-linear algorithms.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. Therefore, the number of simultaneous linear equations to be solved is substantially decreased. This test, in its original form, requires O(Ln2) additions and comparisons in the worst case, where n is the number of variables and L is the number of linear regions. In this paper, an effective technique is proposed that reduces the computational complexity of the sign test to O(Ln). Some numerical examples are given, and it is shown that all solutions can be computed very efficiently. The proposed algorithm is simple and can be easily programmed by using recursive functions.

Separability is a valuable property of nonlinear mappings. By exploiting this property, computational complexity of many numerical algorithms can be substantially reduced. In this letter, a new algorithm is presented that detects the separability of nonlinear mappings using the concept of "computational graph". A hybrid algorithm using both the top-down search and the bottom-up search is proposed. It is shown that this hybrid algorithm is advantageous in detecting the separability of nonlinear simultaneous functions.

The aim of this article is to show the effectiveness of exploiting separability in numerical analysis of nonlinear systems. Separability is a valuable property of nonlinear mappings which appears with surprising frequency in science and engineering. By exploiting this property, computational complexity of many numerical algorithms can be substantially improved. However, this idea has not been received much attention in the fields of electronics, information and communication engineerings. In recent years, efficient algorithms that exploit the separability have been proposed in the areas of circuit analysis, homotopy methods, integer labeling methods, nonlinear programming, information theory, numerical differentiation, and neural networks. In this article, these algorithms are surveyed, and it is shown that considerable improvement of computational efficiency can be achieved by exploiting the separability.