DREAM-High: Finding Patterns with Heatmaps (Python)

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Big idea: data can hide patterns

Large biological datasets are often too big to understand by reading numbers in a table.

In DREAM-High, we will eventually use heatmaps to look for patterns in breast cancer gene expression data from The Cancer Genome Atlas. A heatmap can help us ask:

• Which samples look similar to each other?
• Which genes behave similarly across patients?
• Can visual patterns help us discover tumor subtypes?

Today we practice the same idea using a small, familiar dataset.

Main idea: A heatmap turns numbers into colors so that hidden structure becomes easier to see.

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The practice dataset: mtcars

R has built-in datasets; Python does not, but mtcars is freely available online. The chunk below loads it and prints its dimensions.

import pandas as pd

# Load mtcars and keep only numeric columns
mtcars = pd.read_csv(
    "https://vincentarelbundock.github.io/Rdatasets/csv/datasets/mtcars.csv",
    index_col=0
)
mtcars = mtcars.select_dtypes(include="number")

# dim(mtcars) in R  →  .shape in Python
print(mtcars.shape)   # (32, 11): 32 cars, 11 features

## (32, 11)

Each row is a car; each column is a feature:

• mpg = miles per gallon
• wt = weight
• hp = horsepower
• cyl = number of cylinders

# head(mtcars) in R  →  mtcars.head() in Python
print(mtcars.head())

##                     mpg  cyl   disp   hp  drat  ...   qsec  vs  am  gear  carb
## rownames                                        ...                           
## Mazda RX4          21.0    6  160.0  110  3.90  ...  16.46   0   1     4     4
## Mazda RX4 Wag      21.0    6  160.0  110  3.90  ...  17.02   0   1     4     4
## Datsun 710         22.8    4  108.0   93  3.85  ...  18.61   1   1     4     1
## Hornet 4 Drive     21.4    6  258.0  110  3.08  ...  19.44   1   0     3     1
## Hornet Sportabout  18.7    8  360.0  175  3.15  ...  17.02   0   0     3     2
## 
## [5 rows x 11 columns]

Quick reflection

What do you notice first when you look at this table?

Write your answer here:

When I look at this table, the first thing that hits me is how uneven the engine specs are across the cars, for the jumps in cylinders, displacement and horsepower immediately catch my eye and make the differences feel pretty stark.

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Learning to Inspect Data

Before making a plot, scientists usually inspect the data.

# dim(mtcars) in R  →  .shape in Python
print(mtcars.shape)

## (32, 11)

print()

# colnames(mtcars) in R  →  .columns in Python
print(mtcars.columns.tolist())

## ['mpg', 'cyl', 'disp', 'hp', 'drat', 'wt', 'qsec', 'vs', 'am', 'gear', 'carb']

print()

# class(mtcars) in R  →  type() in Python
print(type(mtcars))

## <class 'pandas.core.frame.DataFrame'>

Check yourself

View the entire dataset:

View(mtcars)

• How many cars are in the dataset?
• How many features are measured for each car?

Write your answer here:

There are 32 cars in the dataset, with 11 features measured for each car.

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Getting help in Python

The easiest way to get help on python functions is to move back to R and use the function browseURL.

browseURL("https://seaborn.pydata.org/generated/seaborn.clustermap.html")

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From data frame to matrix

The heatmap() function in R works with a numeric matrix. In Python, seaborn.clustermap works directly with a DataFrame, but we convert to a NumPy array here to mirror the R workflow.

import numpy as np

# as.matrix(mtcars) in R  →  .to_numpy() in Python
data = mtcars.to_numpy()

# class(data) in R  →  type() in Python
print(type(data))

## <class 'numpy.ndarray'>

# typeof(data) in R  →  .dtype in Python
print(data.dtype)   # float64 = R's "double"

## float64

The assignment operator in Python is = (R uses <-):

x = 5   # x <- 5 in R
print(x)

## 5

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First heatmap: raw data

import seaborn as sns
import matplotlib.pyplot as plt

g = sns.clustermap(
    mtcars,
    figsize=(10, 12),
    xticklabels=True,
    yticklabels=True,
    cbar=False
)

g.cax.remove()

# Remove the automatic axis titles
g.ax_heatmap.set_xlabel("")
g.ax_heatmap.set_ylabel("")

# Adjust tick label sizes
g.ax_heatmap.tick_params(axis="x", labelsize=9)
g.ax_heatmap.tick_params(axis="y", labelsize=8)

# Give the x-axis labels room
g.fig.subplots_adjust(bottom=0.15)

plt.show()

The heatmap turns numbers into colors and clusters:

• rows — cars that look similar across features
• columns — features that vary in similar ways

The tree diagrams on the sides are called dendrograms.

Interpretation question

Is it easy to see meaningful patterns? Why or why not?

It’s not very easy to see meaningful patterns because the colors feel crowded and a lot of the variables sit close in value, so nothing really jumps out at me. The overall shading blends together, which makes it harder to quickly spot clear relationships.

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Second heatmap: scaled data

Let’s create a heatmap that allows us to find the true underlying patterns.

Why scaling matters

Some columns are measured on very different scales. Compare cyl and disp:

# min(mtcars$cyl) in R  →  mtcars["cyl"].min() in Python
print("cyl: ", mtcars["cyl"].min(), "to", mtcars["cyl"].max())

## cyl:  4 to 8

print("disp:", mtcars["disp"].min(), "to", mtcars["disp"].max())

## disp: 71.1 to 472.0

A value of 8 is high for cyl but tiny for disp. Without scaling, large-number columns dominate the heatmap colors. The same problem appears in gene expression data.

Prediction

What do you think will change after we scale the data?

After we scale the data, I think the heatmap will feel a lot clearer because the features will all be on the same scale, so the colors will actually reflect meaningful differences instead of being dominated by the variables with the biggest numerical ranges. It should be much easier to spot patterns since the shading will highlight relative relationships rather than raw magnitudes.

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Scaling the data

scale() in R standardizes each column to a mean of 0 and standard deviation of 1. We use the same function from the sklearn library in Python.

from sklearn.preprocessing import scale

# scale(data) in R  →  scale(mtcars) from sklearn in Python
data_scaled = pd.DataFrame(
    scale(mtcars),
    index=mtcars.index,
    columns=mtcars.columns
)

Let’s compare a few values before and after scaling.

# data[1:5, 1:5] in R  →  .iloc[0:5, 0:5] in Python (Python counts from 0)
print("Before scaling:")

## Before scaling:

print(mtcars.iloc[0:5, 0:5])

##                     mpg  cyl   disp   hp  drat
## rownames                                      
## Mazda RX4          21.0    6  160.0  110  3.90
## Mazda RX4 Wag      21.0    6  160.0  110  3.90
## Datsun 710         22.8    4  108.0   93  3.85
## Hornet 4 Drive     21.4    6  258.0  110  3.08
## Hornet Sportabout  18.7    8  360.0  175  3.15

print()

print("After scaling:")

## After scaling:

print(data_scaled.iloc[0:5, 0:5])

##                         mpg       cyl      disp        hp      drat
## rownames                                                           
## Mazda RX4          0.153299 -0.106668 -0.579750 -0.543655  0.576594
## Mazda RX4 Wag      0.153299 -0.106668 -0.579750 -0.543655  0.576594
## Datsun 710         0.456737 -1.244457 -1.006026 -0.795570  0.481584
## Hornet 4 Drive     0.220730 -0.106668  0.223615 -0.543655 -0.981576
## Hornet Sportabout -0.234427  1.031121  1.059772  0.419550 -0.848562

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Now let’s try the heatmap with data_scaled.

g = sns.clustermap(
    data_scaled,
    figsize=(10, 12),
    xticklabels=True,
    yticklabels=True,
    cbar=False
)

g.cax.remove()

# Remove the automatic axis titles
g.ax_heatmap.set_xlabel("")
g.ax_heatmap.set_ylabel("")

# Adjust tick label sizes
g.ax_heatmap.tick_params(axis="x", labelsize=9)
g.ax_heatmap.tick_params(axis="y", labelsize=8)

# Give the x-axis labels room
g.fig.subplots_adjust(bottom=0.15)

plt.show()

Interpretation questions

1. Does this heatmap look more informative than the raw-data heatmap?
2. Which features seem to group together?
3. Do mpg and wt show similar or opposite patterns?
4. Do the car groupings make sense based on what you know about cars?

The scaled heatmap feels more informative because the colors actually reflect meaningful differences once everything is on the same scale. Features like cyl, disp, hp and wt tend to move together, while mpg, drat, qsec, vs and am sit on the opposite side. mpg and wt show opposite patterns, which makes sense since heavier cars usually get lower fuel efficiency. The car groupings also line up with what I’d expect: the big high‑power models fall together, the lighter small‑engine cars sit near each other, and the mid‑range ones land in between.

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Color choices

We can change the color palette to make patterns easier to see. The chunk below shows a selection of available palettes.

# display.brewer.all() in R  →  color swatches in Python
palette_names = [
    "Blues", "Greens", "Oranges", "Purples", "Reds",
    "coolwarm", "rocket", "mako", "YlOrRd", "RdBu"
]

fig, axes = plt.subplots(len(palette_names), 1, figsize=(6, len(palette_names) * 0.6))
for ax, name in zip(axes, palette_names):
    colors = sns.color_palette(name, 10)
    ax.imshow([colors], aspect="auto")
    ax.set_yticks([])
    ax.set_xticks([])
    ax.set_ylabel(name, rotation=0, labelpad=60, va="center", fontsize=9)
plt.tight_layout()
plt.show()

Now use a palette in a heatmap:

# col = brewer.pal(8, "Greens") in R  →  cmap="Greens" in Python
# Try changing "Greens" to another name from the list above

# col = brewer.pal(8, "Greens") in R  →  cmap="Greens" in Python
# Try changing "Greens" to another name from the list above

# Assign clustermap to a variable 'g' to access its axes
g = sns.clustermap(
    data_scaled,
    cmap="Greens",
    figsize=(10, 12),
    xticklabels=True,
    yticklabels=True,
    cbar=False
)

g.cax.remove()

# Remove the automatic axis titles
g.ax_heatmap.set_xlabel("")
g.ax_heatmap.set_ylabel("")

# Adjust tick label sizes
g.ax_heatmap.tick_params(axis="x", labelsize=9)
g.ax_heatmap.tick_params(axis="y", labelsize=8)

# Give the x-axis labels room
g.fig.subplots_adjust(bottom=0.15)

plt.show()

Challenge Question 1:

Customization challenge

Replace "Greens" below with a palette of your choice and run the chunk.

# Change "Greens" in the cmap line to your color scheme
g = sns.clustermap(
    data_scaled,
    cmap="mako",
    figsize=(10, 12),
    xticklabels=True,
    yticklabels=True,
    cbar=False
)

g.cax.remove()

# Remove the automatic axis titles
g.ax_heatmap.set_xlabel("")
g.ax_heatmap.set_ylabel("")

# Adjust tick label sizes
g.ax_heatmap.tick_params(axis="x", labelsize=9)
g.ax_heatmap.tick_params(axis="y", labelsize=8)

# Give the x-axis labels room
g.fig.subplots_adjust(bottom=0.15)

plt.show()

Which palette did you choose, and why?

I chose mako because the color set had an extensive range of hues from dark to light, which makes meaningful patterns stand out more in the dataset.

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Challenge Question 2

A more focused question: relationships among features

Sometimes we care less about individual rows and more about how variables relate to one another.

Correlation refers to the statistical relationship between two variables (feature), describing how they change together. For example:

import pandas as pd

# Calculate a single correlation coefficient
correlation = mtcars["mpg"].corr(mtcars["wt"])
print("Correlation:", correlation)

## Correlation: -0.8676593765172279

This means that across cars, mpg decreases as weight increases. This matches our intuition. Consider the scatterplot where each point corresponds to a car:

import matplotlib.pyplot as plt

plt.figure(figsize=(6, 4))

plt.scatter(mtcars["wt"], mtcars["mpg"])
plt.xlabel("Weight")
plt.ylabel("Miles per Gallon")

plt.show()

A correlation matrix shows how strongly pairs of features move together.

• Positive correlation: both features increase together
• Negative correlation: one increases as the other decreases
• Near zero: little relationship

# cor(mtcars) in R  →  .corr() in Python
cor_mtcars = mtcars.corr()

# round(cor_mtcars, 2) in R  →  .round(2) in Python
print(cor_mtcars.round(2))

##        mpg   cyl  disp    hp  drat    wt  qsec    vs    am  gear  carb
## mpg   1.00 -0.85 -0.85 -0.78  0.68 -0.87  0.42  0.66  0.60  0.48 -0.55
## cyl  -0.85  1.00  0.90  0.83 -0.70  0.78 -0.59 -0.81 -0.52 -0.49  0.53
## disp -0.85  0.90  1.00  0.79 -0.71  0.89 -0.43 -0.71 -0.59 -0.56  0.39
## hp   -0.78  0.83  0.79  1.00 -0.45  0.66 -0.71 -0.72 -0.24 -0.13  0.75
## drat  0.68 -0.70 -0.71 -0.45  1.00 -0.71  0.09  0.44  0.71  0.70 -0.09
## wt   -0.87  0.78  0.89  0.66 -0.71  1.00 -0.17 -0.55 -0.69 -0.58  0.43
## qsec  0.42 -0.59 -0.43 -0.71  0.09 -0.17  1.00  0.74 -0.23 -0.21 -0.66
## vs    0.66 -0.81 -0.71 -0.72  0.44 -0.55  0.74  1.00  0.17  0.21 -0.57
## am    0.60 -0.52 -0.59 -0.24  0.71 -0.69 -0.23  0.17  1.00  0.79  0.06
## gear  0.48 -0.49 -0.56 -0.13  0.70 -0.58 -0.21  0.21  0.79  1.00  0.27
## carb -0.55  0.53  0.39  0.75 -0.09  0.43 -0.66 -0.57  0.06  0.27  1.00

# heatmap(cor_mtcars, symm=TRUE) in R  →  sns.clustermap() in Python
# A diverging palette (blue = positive, red = negative) works well here
import seaborn as sns
import matplotlib.pyplot as plt

g = sns.clustermap(
    cor_mtcars,
    cmap="RdBu_r",
    vmin=-1, vmax=1,
    figsize=(5.5, 5.5),      # smaller figure
    dendrogram_ratio=0.12,   # smaller dendrograms
    cbar_pos=(0.02, 0.82, 0.04, 0.15)  # smaller color bar
)

# Make the labels smaller
g.ax_heatmap.tick_params(axis='x', labelsize=9)
g.ax_heatmap.tick_params(axis='y', labelsize=9)

plt.show()

Interpretation question

Find one pair of features with a strong positive relationship and one with a strong negative relationship.

The heatmap highlights a strong positive correlation between cyl/cylinders and disp/displacement, reflecting how larger engines consistently pair with higher cylinder counts. In contrast, miles per gallon and weight show a pronounced negative relationship, underscoring how increased vehicle mass reliably diminishes fuel efficiency.

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Why this matters for cancer biology

Today we used cars because the dataset is small and easy to practice with. The same workflow applies to biological data:

patients or samples  → rows
genes or features    → columns
expression values    → numbers in the matrix
heatmap              → visual pattern discovery
clustering           → grouping similar samples or genes

In breast cancer data, heatmaps can reveal groups of patients with similar molecular patterns — patterns that sometimes correspond to tumor subtypes with different clinical outcomes.

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Final reflection

1. What did scaling change about the heatmap?
2. Why might heatmaps be useful for studying cancer data?
3. What is one Python concept you feel more comfortable with now?
4. What is one Python concept you still find confusing?

Scaling made the heatmap more balanced by putting every variable on the same range, which lets the color patterns reflect true correlations instead of being skewed by features with larger numeric values. Heatmaps are especially useful in cancer research because they help reveal structure in high‑dimensional data, such as gene expression patterns or tumor subtypes, in a way that is visually intuitive. I feel more comfortable now with data visualization, especially using Python commands like print(mtcars.head()) to inspect data, mtcars.corr() to compute correlation matrices, and sns.clustermap(data) to generate clustered heatmaps. However, I find clustering algorithms confusing, particularly how tools such as scale(mtcars) from sklearn, data.iloc[0:5, 0:5] for subsetting, and mtcars.to_numpy() for matrix conversion interact with functions like hierarchical clustering to define similarity and determine which samples should be grouped together, since these choices can subtly influence the patterns that appear in the final heatmap.

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Knit your report

Click Knit → Knit to HTML. Your report should include your name, your code, your heatmaps, and your answers to all the reflection questions.

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Summary

In this activity you practiced:

• running Python chunks in RStudio
• loading and inspecting a dataset with pandas
• converting a DataFrame to a NumPy array
• using = for assignment and .iloc[] for indexing
• making heatmaps with seaborn
• scaling data so features are comparable
• changing color palettes
• computing and visualizing a correlation matrix

Computational tools can help us discover patterns hidden inside large biological datasets.

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R vs Python quick reference

Task	R	Python
Load data	built-in mtcars	pd.read_csv("url", index_col=0)
First few rows	head(mtcars)	print(mtcars.head())
Dimensions	dim(mtcars)	print(mtcars.shape)
Column names	colnames(mtcars)	print(mtcars.columns.tolist())
Object class	class(x)	print(type(x))
Data type	typeof(x)	print(x.dtype)
Convert to matrix	as.matrix(mtcars)	mtcars.to_numpy()
Assignment	x <- 5	x = 5
Index rows & cols	data[1:5, 1:5]	data.iloc[0:5, 0:5]
Column min / max	min(mtcars$cyl)	mtcars["cyl"].min()
Scale columns	scale(data)	scale(mtcars) from sklearn
Correlation matrix	cor(mtcars)	mtcars.corr()
Round values	round(x, 2)	x.round(2)
Heatmap	heatmap(data)	sns.clustermap(data)
Color palette	col = brewer.pal(8, "Greens")	cmap="Greens"
Comment	# text	# text
Get help	help(heatmap)	help(sns.clustermap)