Probabilistic principal component analysis based on JoyStick Probability Selector

Abstract

Principal component analysis (PCA) is a commonly applied technique for data analysis and processing, e.g, compression or clustering. In this paper we propose a probabilistic PCA model based on the Born rule. In off-line realization it can be seen as a successive optimization problem. In the on-line realization it will be solved by introduction of two different time scales. It will be shown that recently proposed time oriented hierarchical method, used for realization of biologically plausible peA neural networks, represents a special case of the proposed model. The proposed model gives a general framework for creating different PCA realizations/algorithms. A particular realization can optimize locality of calculation, convergence speed, preciseness or some other parameter of interest. We will present some experimental results to illustrate effectiveness of the proposed model.

Feature Extraction Techniques for Speech Processing: A Review

“…The difference is that in WPD it applies the transform step to the low pass and high pass results whereas in DWT it only apply to low pass results [18].…”

Applications of probabilistic model based on joystick probability selector

“…In this section we will give the recently proposed, simple interpretation of the probability that is related to the Born rule [3]. Here we will assume that we are dealing with finite dimensional discrete variable.…”

“…It has been shown that proposed probabilistic interpretation is suitable for modeling of on-line learning algorithms for Principal/Minor/Independent Component Analysis, which could be realized on parallel hardware based on very simple computational units [2][3][4]. In such applications, the proposed concept (model) can be used in the context of improving algorithm convergence speed, learning factor choice, input signal scale robustness, and can be easily deployed on parallel hardware.…”

“…This rule states that the probability of an outcome (a) given a state (Ψ) is the square of their inner product (a T Ψ) 2 . This section is based on a similar section in [5,3].…”

Quantum Low Entropy based Associative Reasoning–QLEAR Learning

“…Recently, it has been shown that a probabilistic model based on two of the main concepts in quantum physics -a density matrix and the Born rule, can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework. It has been shown that the proposed probabilistic interpretation is suitable for modeling on-line learning algorithms for Independent /Principal/Minor Component Analysis [2][3][4][5], which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point or anomalies detection [6,7] as well as simple classification problems [7].…”