Image representation

• Grayscale image = matrix, each entry = a pixel.
• entry values $\epsilon [0,255]$

Image classification

Using FFNNs

Problems:

1. Many weight inputs
   • The first layer will require at least as many neurons as there are pixels in the image, leading to an impractical number of parameters
2. Variability in position
   • Small translations in the input image will cause the network to produce incorrect predictions
   • due to a lack of spatial invariance
   • may struggle to detect feature in inputs that deviate from the specific positions covered in the training dataset.
   • Solution Suggestion: Collecting numerous recordings with various positions of the feature may help
     • but it might be impractical to cover all possible permutations.
   • Proposal for a More Flexible Network:
     • recognize the target irrespective of its specific location within the recording (input).
     • develop models that generalize well to different permutations of the target pattern within the data.

Scanning for a pattern in a timeseries

Algorithm:

• sliding window approach to making predictions using a neural network on a time series.

1 given a neural network $M$ and a timeseries $X$ with length of $T$ 2 choose a scanning width $w$ 3 for $t=1$ to $T-W+1$ 4 select a segment $X_{\text {segment }}=X(t: t+w-1)$ of timeseries $X$ 5 generate a prediction $y(t)=M\left(X_{\text {segment }}\right)$ 6 predict the maximum $y(\mathrm{t})$ value

• Neural Network and Time Series: You have a neural network$M$ that is trained to make predictions based on input data. In this case, the input data is a time series $X$ with $T$ data points.

• Scanning Width: You choose a scanning width $w$. This is essentially the size of the window that will slide over your time series.

• Loop Over Time Series: You iterate over the time series from$t = 1$ to $T - w + 1$. This loop is responsible for moving the window over the time series.

• Select Segment: At each step of the loop, you select a segment $X_{\text {segment }}$ of the time series. This segment has a length of$w$and starts from the current position $t$ and goes up to$t + w - 1$

• Generate Prediction: You feed this segment $X_{\text {segment }}$ into your neural network $M$ to generate a prediction $y(t)$. Essentially, you're asking the neural network to predict what comes next based on the current segment of the time series.

• Predict the Maximum: Finally, you record the maximum predicted value $y(t)$ for each iteration of the loop. This means you're interested in the highest prediction value across all the windows as you slide through the time series.

• this algorithm is a way of applying a trained neural network

• to make predictions

• on different segments of a time series

• by sliding a window over it

• and recording the maximum prediction at each step.

• This could be useful for identifying peaks or significant changes in the time series data.

Weight-sharing

• same set of weights is used of the same layer.

• weights shared across multiple instances of the time series

• can learn and recognize patterns in a more generalized manner

  • as it is not learning separate sets of weights for each segment.

• alternative approach: using fully-connected layer instead of simply selecting the max value

  • takes into account information from the entire segment, not just the maximum value
  • provides a more comprehensive analysis of the segment
  • might capture more complex patterns.
  • using fully connected neural networks to classify images is not efficient

• enhance ability to recognize patterns during the scanning process of a time series.