To combat this, we wil take the log of ring count.
The age of an Abalone can be found by counting the number of rings in its shell using a microscope, which is a laborious task. The column name Char_Len means characteristic length.
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We could probably afford to drop one of these as well. I doubt keeping more features would significantly improve this. Look for outliers or weird data. We could use a spline again, but looking at the plots above I think a linear model should be fine.
I then partitioned the data into two parts according to the "is infant" variable, and fit separate spline curves to each part. \theta_1 \leftarrow \theta_1 + \frac{\alpha}{m}\sum_{i} \left[ y^{(i)} - e^{f(x^{(i)})} \right]x^{(i)} One could argue that since the original data set is relatively small and there are only a few features it's unnecessary to trim data out. Let's plot them against each other. Let's construct separate splines for the infant and non-infant values. \begin{gather}
To learn more about our use of cookies see our Privacy Statement. Learn more. Ideally we should choose the value of the smoothing factor using a cross validation set. Other measurements, which are easier to obtain, are used to predict the age.
Height is strongly correlated with the remaining features, but not as strongly as, say, length with diameter. The objective of this project is to predicting the age of abalone from physical measurements using the 1994 abalone data "The Population Biology of Abalone (Haliotis species) in Tasmania. According to the data set description on the website, all continuous values have been scaled down by a factor of 200. All of the features features associated with weight are pretty much perfectly correlated with each other, with pearson coefficients > 0.95 for whole weight. Predict the age of abalone based on physical characteristics. \end{gather}. The shape suggests the characteristic length, $\ell$, is related to the weight, $w$, by a power law: $\ell \propto w^{\alpha}$, with $\alpha < 1$. Explore the relationship between features and output varaibles. Abalone-Age-Prediction. After all more data gives more predictive power. Let's handle that later. The number of rings dictates the age of the abalone, so the problem is to develop a model to predict the age of an abalone. What conclusions can we make? }, #data_trunc["Log_Rings"] = np.log(data_trunc["Rings"]), #data_trunc.plot(kind='scatter', x='Whole_Weight', y='Char_Len' ). Abalone is a shellfish considered a delicacy in many parts of the world.
\theta_0 \leftarrow \theta_0 + \frac{\alpha}{m}\sum_{i} \left[ y^{(i)} - e^{f(x^{(i)})} \right] \ Scrubbing or cleaning the data. We use cookies and similar technologies ("cookies") to provide and secure our websites, as well as to analyze the usage of our websites, in order to offer you a great user experience. The data is highly correlated, and I think a single feature captures the data well. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. \ell = \sum_{i} y^{(i)}f(x^{(i)}) - e^{f(x^{(i)})} - \log (y^{(i)}!) they're used to log you in. Second, the smallest weight is (after rescaling) significantly less than a gram. In this notebook we will use regression. We use essential cookies to perform essential website functions, e.g. We model the data using a spline as well as with Poisson regression. Each data point contains multiple physical characteristics of a single abalone, and the goal is to develop a model to predict the number of rings. Abalone Age Prediction ¶ Description- Predicting the age of abalone from physical measurements. \end{equation}, It's easy to check that the log-likelihood $\ell$ is given by, \begin{equation} Contribute to ChiaoSun/Abalone_Age_Prediction development by creating an account on GitHub.
We could try fiddling around with the power but this is working well enough that I don't think it's necessary. p(y|x) = \frac{\lambda^{y}e^{-\lambda}}{y !} It's just two entries with height 0, so I think it's safe to drop them. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. Let's see how well $\alpha = 1/3$ works. Since rings come in integer values, both classification and regression are viable options. Alright, let's get to modelling the data. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. Almost everything is strongly correlated with everything else, except ring count! Explore and run machine learning code with Kaggle Notebooks | Using data from Abalone Dataset
This includes data imputation (filling in missing values) and adjusting column names. However when I set the smoothing factor and plot the resulting splines certain values of $x$ don't show up.
See the plots below. Let's construct a correlation matrix and a heatmap for our data. The Abalone is a type of marine snail animal. Looking at this table I suspect that the low weight entry is real, since it only has one ring and has small length, diameter, and height. When I created a scatter plot for ring count versus $x$, I found that there was a flaring effect present, where the values became increasingly spread out as $x$ increased.
Select Accept all to consent to this use, Reject all to decline this use, or More info to control your cookie preferences. I already added column names (hence the typo in one of the columns!) To learn more about our use of cookies see our Privacy Statement. Use Git or checkout with SVN using the web URL. I argued that because the whole weight, $w$, was nearly perfectly correlated with the remaining three weights, and because $w$ is the most natural weight scale, we can remove the other three values. \end{equation}, For simplicty, let's take $f(x) = \theta_0 + \theta_1 x$. Let's combine the M and F categories and repllace the sex column with a binary Is_Infant column. I replaced the three length scales with their geometric mean, which I called $\ell$.
If nothing happens, download Xcode and try again. What are the most important factors (features)?
The 7 continuous predictors were found to be highly correlated, so I thought it would be a useful simplification to reduce the number of predictors. \partial_{\theta}\ell = \sum_{i} \left[ y^{(i)} - e^{f(x^{(i)})} \right] \frac{\partial f}{\partial \theta}(x^{(i)}) If nothing happens, download GitHub Desktop and try again. Since weight scales with volume, or in this case $w \sim \ell^{3}$, we can keep a single predictor $x \equiv w^{1/3}$ (and sex).
GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. Construct a correlation matrix. The age of abalone is determined by cutting the shell through the cone, staining it, and counting the number of rings through a microscope -- a boring and time-consuming task. To deal with this I took the logarithm of the ring count as the dependent variable. You can always update your selection by clicking Cookie Preferences at the bottom of the page.
Use Git or checkout with SVN using the web URL. We can also adjust the smoothing factor, $\lambda$. Still, we can at least get a qualitative understanding of the relationship between age and weight. We use cookies and similar technologies ("cookies") to provide and secure our websites, as well as to analyze the usage of our websites, in order to offer you a great user experience. Rather than keep weight, define $x \equiv w^{1/3}$ and just use that. Just for fun, let's see how it does on the infant case (which looks the most linear). Predicting Algae's age using different attributes and Machine Learning Algorithms for Regression Analysis. Let's sort the first few values sorted by height.
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