Parzen windows in pattern recognition

Parzen Windows works on the basis of considering all sample points of given sample data based on scheme of voting and assigning weights w. It does not consider the neighbors and labelled weights. Also, it does not requires any training data as it can affect the speed of operation. Parzen windows decision function can be represented by: Parzen Window where, P X is the Gaussian function which is also known as Parzen probability density estimation in 2-D.

In K-Nearest Neighbor algorithm, class of an object is determined on the basis of class of its neighbor.

How It Works? Consider a training sample of Squares and circles and circles. Squares and Circles. High Space Complexity. High Time Complexity. Since we would like to think of this density estimation practically, imagine that we have a finite number of samples n and take V to zero. If we allow the number of samples n to go to infinity, however, we are able to establish convergence of the previous equation to equality. Let us rewrite the previous equation with equality instead of approximation as a sequence that changes with n :.

We have already established that we need condition 1 to be true if we would like to establish true equality in our most recent equation. Now that we have established that we can design a function that converges to the true p. This parameterization has the form. Now comes the distinctive feature of the Parzen window technique. The above formula is the one most commonly associated with the Parzen windowing method.

It essentially says that the estimated p. Please refer to Duda, Hart, and Stork, Chapter 4, p. Some popular choices are a uniform p. Note in the figures above how much influence the h parameter has on the fidelity of the estimated p. In practice, this is a major drawback of the Parzen windowing method, as there are not truly robust ways to determine the h parameter if one does not have some prior information about what the underlying p. Note the similarities between Figures [3] and [4].

How is one supposed to determine which of these two is more likely to represent the underlying p. No looking at Figure [2] - that's cheating! Clearly Figure [5] uses an h parameter that is too sensitive to the data, and looks very noisy as a result. Density estimation in Pattern Recognition can be achieved by using the approach of the Parzen Windows. Parzen window density estimation technique is a kind of generalization of the histogram technique.

It is used to derive a density function,. When we have a new sample feature and when there is a need to compute the value of the class conditional densities, is used. An n-dimensional hypercube is considered which is assumed to possess k-data samples. The length of the edge of the hypercube is assumed to be h n. Skip to content. Change Language. Related Articles.