Engineering topics

Jaeckel, Louis A.

Publications and source records attributed to Jaeckel, Louis A..

8 records

NASA NTRS1992

User's manual for the Gaussian windows program

'Gaussian Windows' is a method for exploring a set of multivariate data, in order to estimate the shape of the underlying density function. The method can be used to find and describe structural features in the data. The method is described in two earlier papers. I assume that the reader has access to both of these papers, so I will not repeat material from them. The program described herein is written in BASIC and it runs on an IBM PC or PS/2 with the DOS 3.3 operating system. Although the program is slow and has limited memory space, it is adequate for experimenting with the method. Since it is written in BASIC, it is relatively easy to modify. The program and some related files are available on a 3-inch diskette. A listing of the program is also available. This user's manual explains the use of the program. First, it gives a brief tutorial, illustrating some of the program's features with a set of artificial data. Then, it describes the results displayed after the program does a Gaussian window, and it explains each of the items on the various menus.

Jaeckel, Louis A.↗

NASA NTRS1991

Using Gaussian windows to explore a multivariate data set

In an earlier paper, I recounted an exploratory analysis, using Gaussian windows, of a data set derived from the Infrared Astronomical Satellite. Here, my goals are to develop strategies for finding structural features in a data set in a many-dimensional space, and to find ways to describe the shape of such a data set. After a brief review of Gaussian windows, I describe the current implementation of the method. I give some ways of describing features that we might find in the data, such as clusters and saddle points, and also extended structures such as a 'bar', which is an essentially one-dimensional concentration of data points. I then define a distance function, which I use to determine which data points are 'associated' with a feature. Data points not associated with any feature are called 'outliers'. I then explore the data set, giving the strategies that I used and quantitative descriptions of the features that I found, including clusters, bars, and a saddle point. I tried to use strategies and procedures that could, in principle, be used in any number of dimensions.

Jaeckel, Louis A.↗

NASA NTRS1990

Gaussian windows: A tool for exploring multivariate data

Presented here is a method for interactively exploring a large set of quantitative multivariate data, in order to estimate the shape of the underlying density function. It is assumed that the density function is more or less smooth, but no other specific assumptions are made concerning its structure. The local structure of the data in a given region may be examined by viewing the data through a Gaussian window, whose location and shape are chosen by the user. A Gaussian window is defined by giving each data point a weight based on a multivariate Gaussian function. The weighted sample mean and sample covariance matrix are then computed, using the weights attached to the data points. These quantities are used to compute an estimate of the shape of the density function in the window region. The local structure of the data is described by a method similar to the method of principal components. By taking many such local views of the data, we can form an idea of the structure of the data set. The method is applicable in any number of dimensions. The method can be used to find and describe simple structural features such as peaks, valleys, and saddle points in the density function, and also extended structures in higher dimensions. With some practice, we can apply our geometrical intuition to these structural features in any number of dimensions, so that we can think about and describe the structure of the data. Since the computations involved are relatively simple, the method can easily be implemented on a small computer.

Jaeckel, Louis A.↗

NASA NTRS1990

Recognition of simple visual images using a sparse distributed memory: Some implementations and experiments

Previously, a method was described of representing a class of simple visual images so that they could be used with a Sparse Distributed Memory (SDM). Herein, two possible implementations are described of a SDM, for which these images, suitably encoded, will serve both as addresses to the memory and as data to be stored in the memory. A key feature of both implementations is that a pattern that is represented as an unordered set with a variable number of members can be used as an address to the memory. In the 1st model, an image is encoded as a 9072 bit string to be used as a read or write address; the bit string may also be used as data to be stored in the memory. Another representation, in which an image is encoded as a 256 bit string, may be used with either model as data to be stored in the memory, but not as an address. In the 2nd model, an image is not represented as a vector of fixed length to be used as an address. Instead, a rule is given for determining which memory locations are to be activated in response to an encoded image. This activation rule treats the pieces of an image as an unordered set. With this model, the memory can be simulated, based on a method of computing the approximate result of a read operation.

Jaeckel, Louis A.↗

NASA NTRS1989

An alternative design for a sparse distributed memory

A new design for a Sparse Distributed Memory, called the selected-coordinate design, is described. As in the original design, there are a large number of memory locations, each of which may be activated by many different addresses (binary vectors) in a very large address space. Each memory location is defined by specifying ten selected coordinates (bit positions in the address vectors) and a set of corresponding assigned values, consisting of one bit for each selected coordinate. A memory location is activated by an address if, for all ten of the locations's selected coordinates, the corresponding bits in the address vector match the respective assigned value bits, regardless of the other bits in the address vector. Some comparative memory capacity and signal-to-noise ratio estimates for the both the new and original designs are given. A few possible hardware embodiments of the new design are described.

Jaeckel, Louis A.↗

NASA NTRS1989

A class of designs for a sparse distributed memory

A general class of designs for a space distributed memory (SDM) is described. The author shows that Kanerva's original design and the selected-coordinate design are related, and that there is a series of possible intermediate designs between those two designs. In each such design, the set of addresses that activate a memory location is a sphere in the address space. We can also have hybrid designs, in which the memory locations may be a mixture of those found in the other designs. In some applications, the bits of the read and write addresses that will actually be used might be mostly zeros; that is, the addresses might lie on or near z hyperplane in the address space. The author describes a hyperplane design which is adapted to this situation and compares it to an adaptation of Kanerva's design. To study the performance of these designs, he computes the expected number of memory locations activated by both of two addresses.

Jaeckel, Louis A.↗

NASA NTRS1989

Some methods of encoding simple visual images for use with a sparse distributed memory, with applications to character recognition

To study the problems of encoding visual images for use with a Sparse Distributed Memory (SDM), I consider a specific class of images- those that consist of several pieces, each of which is a line segment or an arc of a circle. This class includes line drawings of characters such as letters of the alphabet. I give a method of representing a segment of an arc by five numbers in a continuous way; that is, similar arcs have similar representations. I also give methods for encoding these numbers as bit strings in an approximately continuous way. The set of possible segments and arcs may be viewed as a five-dimensional manifold M, whose structure is like a Mobious strip. An image, considered to be an unordered set of segments and arcs, is therefore represented by a set of points in M - one for each piece. I then discuss the problem of constructing a preprocessor to find the segments and arcs in these images, although a preprocessor has not been developed. I also describe a possible extension of the representation.

Jaeckel, Louis A.↗

NASA NTRS1988

Two alternate proofs of Wang's lune formula for sparse distributed memory and an integral approximation

In Kanerva's Sparse Distributed Memory, writing to and reading from the memory are done in relation to spheres in an n-dimensional binary vector space. Thus it is important to know how many points are in the intersection of two spheres in this space. Two proofs are given of Wang's formula for spheres of unequal radii, and an integral approximation for the intersection in this case.

Jaeckel, Louis A.↗