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The paper “ Locality Preserving Projection by He and Niyogi” is a cogent example of an article on information technology. In the 21st century, as technological advances continue to emerge, a few proposals have been proposed regarding manifold learning algorithms like the Laplacian Eigenmap (LE), Locally Linear Embedding (LLE), ISOMAP and Locality Preserving Projection (LPP). These algorithms' main aim is to discover the meaningful data space low dimensional structure. The aim of this report is to explore and analyze the Locality Preserving Projection proposed by He, X. and Niyogi, P (2004) from the University of Chicago in their article namely; Locality preserving projections.

The analysis of the article will be based on the content of the article, novelty (Innovation), technical quality rating, x-factor, quality of the presentation, and research work application. ContentTitleIn terms of the content and the title, the title of the article provides a full overview of what the research article is all about. However, the topic is broad in the sense that it does not specify what the title objective is. Upon reading the article, a reader realizes that the title Locality Preserving Projections is a solution to an existing problem in dimensionality reduction.

A more appropriate title would have been more straightforward in providing a detailed summary of the article in one sentence such as Locality Preserving Projections in dimensionality reduction. Such a title is appropriate for this article because of its high-quality work. ContextThe authors introduce a regression method of Locality Preserving Projections (LPP) and define it as linear projective maps arising from solving variational problems that preserve the data sets neighborhood structure optimally as an algorithm for linear dimensionality reduction method in information processing.

This algorithm is introduced as a solution to a problem statement of dimensionality reduction where the authors provide an example of a situation where there is a collection of dimensional real vectors data points taken from a probability distribution that is unknown. The problem statementAccording to the authors, the LPP, in this case, creates a graph that incorporates the data sets neighborhood information after which employing the graphs Laplacian notion, an individual then computes a transformational matrix that maps to a subspace, the data points.

The transformation which is linear maintains the local neighborhood information optimally in a positive sense. The generated representation map by the algorithm can be seen as a linear discrete approximation that arises naturally from the manifold geometry to a map that is continuous. The authors present a problem statement of linear dimensionality reduction was provided a set of one is needed to find a transformational matrix A that will map them points to points so that “ represents” where = The authors use a practical applicability method where the case is special in that and in this case is a nonlinear manifold that is embedded in. Locality Preserving Projections ImplementationAccording to the authors, there are three steps followed when solving the problem statement using the LPP algorithm where they provide the steps which start with the construction of the adjacency graph.

In this step, indicates a graph with nodes. An edge is then put between the nodes and in the case and is close. However, there are two variations of -neighborhoods where [parameter]. and nodes are linked if ║by an edge where the common Euclidean norm is the norm and nearest neighbors where [parameter]. and nodes are linked if is one of nearest neighbors of.

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