So what about hyperspace? Data classification problems often involve more than three dimensions or an input vector of length n > 3. This is when our conversation got a little more interesting. We moved onto discussing problems having more dimensions than can be physically interpreted. In my experience, and probably his too, these kinds of problems are often encountered in machine learning applications where data sets can take on hyperspace dimensionality. Problems containing more variables than can be visualized have led (?) to the development of data reduction techniques that work to capture the bulk of information in a mathematical environment in fewer variables. Techniques of this nature are things like principal component analysis (PCA) or self-organizing maps (Kohonen maps). 

After thinking about it some more, I have decided We Live In No Less Than Six Dimensions. We can all agree that the first four dimensions are space and time. The next two dimensions seem more controversial. Is memory really a dimension? I think it is because memory is the dimension that lets you internally travel backwards in space and time while continuing to experience the four dimensions that always surround us. Now what about data? Well, data alone can take on more than six dimensions, so if we consider our original four dimensions along with memory and now data, I say We Live In No Less Than Six Dimensions. The sixth dimension is more complicated than memory I think. In my opinion, data is not only another dimension but can take on many dimensions at once. When data is analyzed correctly it conveys such meaningful information that it is hard for me not to think of it as another dimension. A lot of times speculation can be tested by collecting and analyzing data. Is such and such a thing really behaving how we say? To test such and such a thing we have to set up an experiment, collect some data and analyze it to find out if what we speculated is wrong. We commonly look to data for answers, of which often comeback saying something other than what we originally speculated, so to me data is the sixth dimension.

Now if you’re curious about the venn diagram suspended in space in the image above, you’re going to have to wait for my further explanation of how all six dimensions really tie together. When I think of data, memory, and time, there are overlaps between each idea as well as things common to all three ideas. This part I need to spend additional time thinking about because it is still a little confusing to me and I have not fixed my thoughts on the subject just yet. In the mean time, how many dimensions do you think we live in? I would love to hear your opinion on this matter, so feel free to drop a comment below and subscribe so you can stay engaged in future conversations at julianbaldwin.com

Below are a couple graphs I generated in Mathematica that capture how the synaptic weights between the input neurons and hidden layer neurons change as they learn to classify 80 samples of nine variable input vectors with gold standard. In supervised learning, the gold standard plays a role in both the training and validation of a select technique, here an ANN. Iteration (n) count increases from n=0 to n=1000 along the abscissa and along the ordinate real-valued synaptic weights are measured at each iteration.

The image above shows the training path of the ten synaptic connections coming into the first neuron in the hidden layer.

The image above shows the training path of the ten synaptic connections coming into the second neuron in the hidden layer. 

Now a few observations. The most obvious one being that the training of synaptic weights follows a non-linear path. This is to be expected when observing real biological phenomenon and gives confidence that this ANN simulates to some degree of accuracy what is happening when we learn something new. The variance between the final min and max connection strengths for each hidden layer neuron seems quite large. For the first HL neuron the min = -28.6 and the max = 18.2 and for the second HL neuron the min = -30.7 and the max = 6.9. This is interesting because it might say that in order for artificial neurons to learn they need to read and interpret a diverse range of quality in information. Which could be translated to learned content might be the result of some combination of both discrete high quality and discrete low quality packets of information.

Early in the training cycle, most synaptic edges seem to have a general sense of the training direction they will head. More learning seems to occur during the first 400 iterations and more refining seems to occur during the remaining 600 iterations. All at once, the small oscillatory behavior of each synaptic weight minimizes at around 850 iterations. This might suggest that the ANN has maximally learned its environment within any design constraints and subject to the quality of data provided. It may or may not be coincidence that each HL neuron has 3 real-valued positive synaptic edges and 7 real-valued negative synaptic edges. If this is not coincidence, it may suggest that some form of symmetry exists across synaptic connections to neurons involved in the learning process. It is also interesting that among the connections going into both HL neurons, there exist a small cluster of synapses with similar connection strengths. This hints there might be some inherent redundancy in the way new information is learned. 

The network architecture in place for this small experiment is 10 input layer neurons (9 input variables + bias), 3 hidden layer neurons (2 neurons with 10 synaptic connections each coming from a neuron in the input layer + bias), and 1 output layer neuron. The number of output layer neurons corresponds to the dimension of the gold standard. For this training routine the gold standard is a binary classifier and each input vector corresponds to a 0 or 1. A sigmoid (exponential) activation function was used to mimic electrical activity in the cerebellum.

To know that technology is impacting our behavior and thinking in unsuspecting ways is enough to provoke a conversation about the benefits of technology and how well they offset the consequences. Questions of this type are by no means new and have been asked since technology first began. The origins of technology are far from being an agreeable topic. What you consider to be the earliest form of technology is probably different than what the previous reader thinks and what the next reader will think. And all four of our opinions are most certainly different from those who thought they really were using the first artifacts of technology. Fortunately, we don’t need to know when or how technology started to say that it changes everything about how we communicate, perceive future applications that will improve the quality of life, store/access/distribute information, and habits we silently develop through continued use.

Understanding how such changes take shape in the context of todays world is most important for encouraging a favorable ratio between the benefits and consequences of integrating technology into our daily lives. I think before moving into anything of great detail that it is fair to say technology is not going to stop evolving anytime soon and that we have no choice but to learn how to make the most of the technology available to us today. In many ways technology is responsible for an increase in the average life span. By nature it seems among our greatest concerns to live longer as well as help create a world for future progeny that is better than the one that exists today. These desires are engrained in many of us and contribute to the changing role technology plays in our lives. When new knowledge is discovered or a technology is perfected, it comes at the cost of not knowing how people will link this new information with existing information.    

Not only do potential risks for people to abuse knowledge and technology emerge, but social phenomenon tend to emerge in powerful strides. Technology is becoming more personal while at the same time it becomes more social. I think about when the telephone was first introduced and how it belonged to all members of the household. What is interesting is how our behavior started to change when this link to the outside world shifted from a shared commodity to a personal commodity. Introducing freedom has a remarkable effect on how people behave when they become the sole controller of a piece of technology. There are so many things, most of them we don’t even know about, that people do on cell phones now that they never would do if they continued to share their phone with another person or group of persons. And more importantly, lifting the confined radius of in home use and extending telecommunications to include national coverage from almost anywhere within the country, influences behavior that is not isolated from other aspects of life. 

Technology has an interesting ability to spread and influence everything. Just as technology has become more popular in conversation with other people, it also spreads in more explicit ways to change who we are and how we perceive the world that we are becoming more connected to everyday. Now would be a great time to list some examples and elaborate on each, so I will save these for my next post on How Technology Changes Everything and leave you with the decision to subscribe and return to read more of my ramblings or to never come back again. Whatever you decide, I hope you have started to think about how much technology is changing you and the rest of us very quickly. Although how do we capture and measure the velocity at which technology is changing us today as compared to how technology changed people of the past?

Saturday August 29th, 2009

R

E

S

Ults

_________________________________________________________________________

Sunday August 2nd, 2009

3rd Place Sprint Team Relay

Total Time – 1:22:05

Travis Bortz – 0:16:46 (750-meter swim)

Julian Baldwin – 0:44:34 (14-mile bike)

Jim Warner – 0:19:35 (5K run)

Weather – Cloudy, Rain

The idea is to label a network over a geographic area to convey meaningful information to viewers. The kind of information plotted and conveyed is context dependent. Coordinates of latitude and longitude will be our input data and used to plot markers or create paths over the geographic area of interest. Markers indicate which points in the map space hold greater meaning than the other points surrounding them and paths show a relationship exists between points found in the map space.

To plot markers and paths we write a long URL that begins with http://maps.google.com/staticmap? Following the ? we specify the use of various parameters. There are 12 parameters to learn about: center, zoom, size, format, maptype, markers, path, span, frame, h1, key, and sensor. I recommend reading the tutorial developed by Google. This tutorial is easy to follow and covers what each parameter means along with examples of how each parameter can be used.

In the mean time I plan to put together a few examples of how you can use Google static maps API in interesting ways. I also plan to share a small trick that will let you use Google static maps API outside the browser without needing to embed the long URL inside an <img> tag. This is really useful for when you want to plot geo data without making your final map public. If you know any interesting tips about Google static maps API feel free to post them in a comment below.