Sunil Bharitkar

The hysteretic Hopfield neural network

A new neuron activation function based on a property found in physical systems--hysteresis--is proposed. We incorporate this neuron activation in a fully connected dynamical system to form the hysteretic Hopfield neural network (HHNN). We then present an analog implementation of this architecture and its associated dynamical equation and energy function.We proceed to prove Lyapunov stability for this new model, and then solve a combinatorial optimization problem (i.e., the N-queen problem) using this network. We demonstrate the advantages of hysteresis by showing increased frequency of convergence to a solution, when the parameters associated with the activation function are varied.

A NEURAL NETWORK APPROACH TO FACILITY LAYOUT PROBLEMS

Abstract A near-optimum parallel algorithm for solving facility layout problems is presented in this paper where the problem is NP-complete. The facility layout problem is one of the most fundamental quadratic assignment problems in Operations Research. The goal of the problem is to locate N facilities on an N-square (location) array so as to minimize the total cost. The proposed system is composed of N × N neurons based on an artificial two-dimensional maximum neural network for an N-facility layout problem. Our algorithm has given improved solutions for several benchmark problems over the best existing algorithms.

A cluster centroid method for room response equalization at multiple locations

We address the problem of simultaneous room response equalization for multiple listeners. Traditional approaches to this problem have used a single microphone at the listening position to measure impulse responses from a loudspeaker and then use an inverse filter to correct the frequency response. The problem with that approach is that it only works well for that one point and in most cases is not practical even for one listener with a typical ear spacing of 18 cm. It does not work at all for other listeners in the room, or if the listener changes positions even slightly. We propose a new approach that is based on the fuzzy c-means clustering technique. We use this method to design equalization filters and demonstrate that we can achieve better equalization performance for several locations in the room simultaneously as compared to single point or simple averaging methods.

Robustness of spatial average equalization: A statistical reverberation model approach

Traditionally, multiple listener room equalization is performed to improve sound quality at all listeners, during audio playback, in a multiple listener environment (e.g., movie theaters, automobiles, etc.). A typical way of doing multiple listener equalization is through spatial averaging, where the room responses are averaged spatially between positions and an inverse equalization filter is found from the spatially averaged result. However, the equalization performance, will be affected if there is a mismatch between the position of the microphones (which are used for measuring the room responses for designing the equalization filter) and the actual center of listener head position (during playback). In this paper, we will present results on the effects of microphone-listener mismatch on spatial average equalization performance. The results indicate that, for the analyzed rectangular configuration, the region of effective equalization depends on (i) the distance of a listener from the source, (ii) the amount of mismatch between the responses, and (iii) the frequency of the audio signal. We also present some convergence analysis to interpret the results.

Perceptual multiple location equalization with clustering

Typically, room equalization techniques do not focus on designing filters that equalize the room transfer functions on perceptually relevant spectral features. In this paper, we address the problem of room equalization for multiple listeners, simultaneously, using perceptually designed equalization filter based on pattern recognition techniques. Some features of the proposed filter are, its ability to perform simultaneous equalization of multiple locations, a reduced order, and a psychoacoustically motivated design. In summary, the simultaneous multiple location equalization, using a pattern recognition method, is performed over perceptually relevant spectral components derived from the auditory filtering mechanism.

Microcode optimization with neural networks

Microcode optimization is an NP-complete combinatorial optimization problem. This paper proposes a new method based on the Hopfield neural network for optimizing the wordwidth in the control memory of a microprogrammed digital computer. We present two methodologies, viz., the maximum clique approach, and a cost function based method to minimize an objective function. The maximum clique approach albeit being near O(1) in complexity, is limited in its use for small problem sizes, since it only partitions the data based on the compatibility between the microoperations, and does not minimize the cost function. We thereby use this approach to condition the data initially (to form compatibility classes), and then use the proposed second method to optimize on the cost function. The latter method is then able to discover better solutions than other schemes for the benchmark data set.

An online learning vector quantization algorithm

We propose an online learning algorithm for the learning vector quantization (LVQ) approach in nonlinear supervised classification. The advantage of this approach is the ability of the LVQ to adjust its codebook vectors as new patterns become available, so as to accurately model the class representation of the patterns. Moreover this algorithm does not significantly increase the computational complexity over the original LVQ algorithm.

Visualization of Multiple Listener Room Acoustic Equalization With the Sammon Map

In this paper, a new method, using the Sammon map, is proposed for visualizing room responses and room response equalization. Specifically, the map provides an important perspective on the formation of clusters of acoustic room responses when cluster validity measures are unable to clearly identify the number of clusters. Additionally, the Sammon map can also be used for displaying the uniformity of the equalized responses at multiple positions. Furthermore, the map does not impose significant computational requirements, when the number of measured responses is reasonably small, and hence can be readily implemented for analyzing multiple position (viz., multiple listener) room equalization performance

A comparison between multi-channel audio equalization filters using warping

Typically, room equalization techniques do not focus on designing filters that equalize the room responses at perceptually relevant frequencies. Thus, by performing Bark warping of the room responses and using lower order spectral models, it is possible to design low order psycho-acoustically motivated equalization filters. We compare the performance, through experiments, between the traditional RMS averaging filter (with and without warping to the Bark scale) and our pattern recognition based multiple listener equalization filter with warping (Bharitkar, S. and Kyriakakis, C., Proc. 36th Asilomar Conf. on Signals, Systems and Computers, 2002). It is shown that our pattern recognition filter, using warping, outperforms the RMS averaging filter (with and without warping to the Bark scale).

A classification scheme for acoustical room responses

Room acoustical modes, particularly in small rooms, cause a significant variation in the room responses measured at different locations. Responses measured only a few cm apart can vary by up to 15-20 dB at certain frequencies. This makes it difficult to equalize an audio system for multiple simultaneous listeners. Previous methods have utilized multiple microphones and spatial averaging with equal weighting. We determine representative prototypical room responses derived from several room responses that share similar characteristics. We present a fuzzy unsupervised technique for finding similarities between room responses by clustering the room responses, and determining their prototypical responses. These prototypical responses can then be combined to form a general point response. When we use the inverse of the general point response as an equalizing filter, our results show a significant improvement in equalization performance over single point equalization and spatial averaging methods. Our method also allows a unique determination of the optimal number of representatives that are required for a given set of room responses. Applications of this method thus include equalization and multiple point sound control at home and in automobiles.